# kb

id: hierarchy-problem-20260505-1
file: data/en.wikipedia.org/wiki/Hierarchy_problem-1.md
category: reference
title: Hierarchy problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hierarchy_problem
date_saved: 2026-05-05T11:05:31.442462+00:00
instance: kb-cron
parent: hierarchy-problem-20260505-0
summary:
Δ m H 2 = − | λ f | 2 8 π 2 [ Λ UV 2 + … ] . {\displaystyle \Delta m_{\text{H}}^{2}=-{\frac {|\lambda _{f}|^{2}}{8\pi ^{2}}}[\Lambda _{\text{UV}}^{2}+\dots ].} The Λ UV {\displaystyle \Lambda _{\text{UV}}} is called the ultraviolet cutoff and is the scale up to which the Standard Model is valid. If we take this scale to be the Planck scale, then we have the quadratically diverging Lagrangian. However, suppose there existed two complex scalars (taken to be spin-0) such that λ S = | λ f | 2 {\displaystyle \lambda _{S}=|\lambda _{f}|^{2}} (the couplings to the Higgs are exactly the same). Then by the Feynman rules, the correction (from both scalars) is Δ m H 2 = 2 × λ S 16 π 2 [ Λ UV 2 + … ] . {\displaystyle \Delta m_{\text{H}}^{2}=2\times {\frac {\lambda _{S}}{16\pi ^{2}}}[\Lambda _{\text{UV}}^{2}+\dots ].} (Note that the contribution here is positive. This is because of the spin–statistics theorem, which means that fermions have a negative contribution, and bosons a positive contribution. This fact is exploited.) This gives a total contribution to the Higgs mass to be zero if we include both the fermionic and bosonic particles. Supersymmetry is an extension


id: hierarchy-problem-20260505-2
file: data/en.wikipedia.org/wiki/Hierarchy_problem-2.md
category: reference
title: Hierarchy problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hierarchy_problem
date_saved: 2026-05-05T11:05:31.442462+00:00
instance: kb-cron
parent: hierarchy-problem-20260505-0
summary:
In 1998 Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali proposed the ADD model, also known as the model with large extra dimensions, an alternative scenario to explain the weakness of gravity relative to the other forces. This theory requires that the fields of the Standard Model are confined to a four-dimensional membrane, while gravity propagates in several additional spatial dimensions that are large compared to the Planck scale. In 1998–99 Merab Gogberashvili published on arXiv (and subsequently in peer-reviewed journals) a number of articles where he showed that if the Universe is considered as a thin shell (a mathematical synonym for "brane") expanding in 5-dimensional space then it is possible to obtain one scale for particle theory corresponding to the 5-dimensional cosmological constant and Universe thickness, and thus to solve the hierarchy problem. It was also shown that four-dimensionality of the Universe is the result of a stability requirement since the extra component of the Einstein field equations giving the localized solution for matter fields coincides with one of the conditions of stability. Subsequently, there were proposed the closely related Randall–Sundrum scenarios which offered their solution to the hierarchy problem. ==== UV/IR mixing ==== In 2019, a pair of researchers


id: high-temperature-superconductivity-20260505-0
file: data/en.wikipedia.org/wiki/High-temperature_superconductivity-0.md
category: reference
title: High-temperature superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/High-temperature_superconductivity
date_saved: 2026-05-05T11:05:32.684766+00:00
instance: kb-cron
parent: high-temperature-superconductivity-20260505-0
summary:
High-temperature superconductivity (high-Tc or HTS) is superconductivity in materials with a critical temperature (the temperature below which the material behaves as a superconductor) above 77 K (−196.2 °C; −321.1 °F), the boiling point of liquid nitrogen. They are "high-temperature" only relative to previously known superconductors, which function only closer to absolute zero. The first high-temperature superconductor was discovered in 1986 by IBM researchers Georg Bednorz and K. Alex Müller. Although the critical temperature is around 35.1 K (−238.1 °C; −396.5 °F), this material was modified by Ching-Wu Chu to make the first high-temperature superconductor with critical temperature 93 K (−180.2 °C; −292.3 °F). Bednorz and Müller were awarded the Nobel Prize in Physics in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials". Most high-Tc materials are type-II superconductors. The major advantage of high-temperature superconductors is that they can be cooled using liquid nitrogen, in contrast to previously known superconductors, which require expensive and hard-to-handle coolants, primarily liquid helium. A second advantage of high-Tc materials is they retain their superconductivity in higher magnetic fields than previous materials. This is important when constructing superconducting magnets, a primary application of high-Tc materials. The majority of high-temperature superconductors are


id: high-temperature-superconductivity-20260505-1
file: data/en.wikipedia.org/wiki/High-temperature_superconductivity-1.md
category: reference
title: High-temperature superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/High-temperature_superconductivity
date_saved: 2026-05-05T11:05:32.684766+00:00
instance: kb-cron
parent: high-temperature-superconductivity-20260505-0
summary:
Superconductivity was discovered by Kamerlingh Onnes in 1911, in a metal solid. Ever since, researchers have attempted to create superconductivity at higher temperatures with the goal of finding a room-temperature superconductor. By the late 1970s, superconductivity was observed in several metallic compounds (in particular Nb-based, such as NbTi, Nb3Sn, and Nb3Ge) at temperatures that were much higher than those for elemental metals and which could even exceed 20 K (−253.2 °C). In 1986, at the IBM research lab near Zürich in Switzerland, Bednorz and Müller were looking for superconductivity in a new class of ceramics: the copper oxides, or cuprates. In that year, Bednorz and Müller discovered superconductivity in lanthanum barium copper oxide (LBCO), a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was soon found that replacing the lanthanum with yttrium (i.e., making YBCO) raised the critical temperature above 90 K. Their results were soon confirmed by many groups. In 1987, Philip W. Anderson gave the first theoretical description of these materials, based on the resonating valence bond (RVB) theory, but a full understanding of these materials is still developing today. These superconductors are now known to possess a


id: high-temperature-superconductivity-20260505-2
file: data/en.wikipedia.org/wiki/High-temperature_superconductivity-2.md
category: reference
title: High-temperature superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/High-temperature_superconductivity
date_saved: 2026-05-05T11:05:32.684766+00:00
instance: kb-cron
parent: high-temperature-superconductivity-20260505-0
summary:
== Properties == The "high-temperature" superconductor class has had many definitions. The label high-Tc should be reserved for materials with critical temperatures greater than the boiling point of liquid nitrogen. However, a number of materials – including the original discovery and recently discovered pnictide superconductors – have critical temperatures below 77 K (−196.2 °C) but nonetheless are commonly referred to in publications as high-Tc class. A substance with a critical temperature above the boiling point of liquid nitrogen, together with a high critical magnetic field and critical current density (above which superconductivity is destroyed), would greatly benefit technological applications. In magnet applications, the high critical magnetic field may prove more valuable than the high Tc itself. Some cuprates have an upper critical field of about 100 tesla. However, cuprate materials are brittle ceramics that are expensive to manufacture and not easily turned into wires or other useful shapes. Furthermore, high-temperature superconductors do not form large, continuous superconducting domains, rather clusters of microdomains within which superconductivity occurs. They are therefore unsuitable for applications requiring actual superconductive currents, such as magnets for magnetic resonance spectrometers. For a solution to this (powders), see HTS wire. There has been considerable debate regarding high-temperature superconductivity


id: high-temperature-superconductivity-20260505-3
file: data/en.wikipedia.org/wiki/High-temperature_superconductivity-3.md
category: reference
title: High-temperature superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/High-temperature_superconductivity
date_saved: 2026-05-05T11:05:32.684766+00:00
instance: kb-cron
parent: high-temperature-superconductivity-20260505-0
summary:
== Production == Liquid nitrogen can be produced relatively cheaply, even on-site. The higher temperatures additionally help to avoid some of the problems that arise at liquid helium temperatures, such as the formation of plugs of frozen air that can block cryogenic lines and cause unanticipated and potentially hazardous pressure buildup. == Ongoing research == The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical condensed matter physics. The mechanism that causes the electrons in these crystals to form pairs is not known. Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modelling difficult. Improving the quality and variety of samples also gives rise to considerable research, both with the aim of improved characterisation of the physical properties of existing compounds, and synthesizing new materials, often with the hope of increasing Tc. Technological research focuses on making HTS materials in sufficient quantities to make their use economically viable as well as in optimizing their properties in relation to applications. LK-99, copper-doped lead-apatite, has also been proposed


id: high-temperature-superconductivity-20260505-4
file: data/en.wikipedia.org/wiki/High-temperature_superconductivity-4.md
category: reference
title: High-temperature superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/High-temperature_superconductivity
date_saved: 2026-05-05T11:05:32.684766+00:00
instance: kb-cron
parent: high-temperature-superconductivity-20260505-0
summary:
==== Qualitative explanation ==== In a superconductor, the flow of electrons cannot be resolved into individual electrons, but instead consists of pairs of bound electrons, called Cooper pairs. In conventional superconductors, these pairs are formed when an electron moving through the material distorts the surrounding crystal lattice, which attracts another electron and forms a bound pair. This is sometimes called the "water bed" effect. Each Cooper pair requires a certain minimum energy to be displaced, and if the thermal fluctuations in the crystal lattice are smaller than this energy the pair can flow without dissipating energy. Electron flow without resistance is superconductivity. In a high-Tc superconductor, the mechanism is extremely similar to a conventional superconductor, except that phonons play virtually no role, replaced by spin-density waves. Just as all known conventional superconductors are strong phonon systems, all known high-Tc superconductors are strong spin-density wave systems, within close vicinity of a magnetic transition to, for example, an antiferromagnet. When an electron moves in a high-Tc superconductor, its spin creates a spin-density wave around it. This spin-density wave in turn causes a nearby electron to fall into the spin depression created by the first electron (water-bed). When the system temperature is lowered,


id: hilbert-s-sixth-problem-20260505-0
file: data/en.wikipedia.org/wiki/Hilbert's_sixth_problem-0.md
category: reference
title: Hilbert's sixth problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hilbert's_sixth_problem
date_saved: 2026-05-05T11:05:33.864738+00:00
instance: kb-cron
parent: hilbert-s-sixth-problem-20260505-0
summary:
Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's problems in mathematics that he presented in the year 1900. Quoted in its common English translation, the explicit statement reads: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics. Hilbert gave a further explanation of this problem and its possible specific forms: As to the axioms of the theory of probabilities, it seems to me desirable that their logical investigation should be accompanied by a rigorous and satisfactory development of the method of mean values in mathematical physics, and in particular in the kinetic theory of gases. ... Boltzmann's work on the principles of mechanics suggests the problem of developing mathematically the limiting processes, there merely indicated, which lead from the atomistic view to the laws of motion of continua. == History == David Hilbert himself devoted much of his research to the sixth problem; in particular, he worked in those fields of physics that arose after he stated the problem. In


id: koide-formula-20260505-0
file: data/en.wikipedia.org/wiki/Koide_formula-0.md
category: reference
title: Koide formula
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Koide_formula
date_saved: 2026-05-05T11:05:35.059661+00:00
instance: kb-cron
parent: koide-formula-20260505-0
summary:
The Koide formula is an unexplained empirical equation proposed by Yoshio Koide ([ko.i.de], koe-ee-day) in 1981. It relates the masses of the charged leptons, the electron, muon and tau in the following way: Q = m e + m μ + m τ ( m e + m μ + m τ ) 2 = 2 3 , {\displaystyle Q={\frac {m_{\text{e}}+m_{\mu }+m_{\tau }}{\left({\sqrt {m_{\text{e}}}}+{\sqrt {m_{\mu }}}+{\sqrt {m_{\tau }}}\right)^{2}}}={\frac {2}{3}},} This exact value of 2 3 {\displaystyle {\frac {2}{3}}} is still within experimental bounds as of 2014. Koide's formula was first derived based on a preon model that also predicted values for quarks and CKM angles. However, these other predictions are now ruled out experimentally. Later authors have extended similar relations to neutrinos, quarks, and other families of particles. == Overview == The Koide formula is given as: Q = m e + m μ + m τ ( m e + m μ + m τ ) 2 = 2 3 , {\displaystyle Q={\frac {m_{\text{e}}+m_{\mu }+m_{\tau }}{\left({\sqrt {m_{\text{e}}}}+{\sqrt {m_{\mu }}}+{\sqrt {m_{\tau }}}\right)^{2}}}={\frac {2}{3}},} The masses of the electron, muon, and tau are measured respectively as me = 0.51099895000(15) MeV/c2, mμ = 105.6583755(23) MeV/c2, and mτ = 1776.93(09) MeV/c2; the digits


id: koide-formula-20260505-1
file: data/en.wikipedia.org/wiki/Koide_formula-1.md
category: reference
title: Koide formula
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Koide_formula
date_saved: 2026-05-05T11:05:35.059661+00:00
instance: kb-cron
parent: koide-formula-20260505-0
summary:
== Origins == The original derivation postulates m e i ∝ ( z 0 + z i ) 2 {\displaystyle m_{e_{i}}\propto (z_{0}+z_{i})^{2}} with the conditions z 1 + z 2 + z 3 = 0 {\displaystyle z_{1}+z_{2}+z_{3}=0} 1 3 ( z 1 2 + z 2 2 + z 3 2 ) = z 0 2 {\displaystyle {\tfrac {1}{3}}(z_{1}^{2}+z_{2}^{2}+z_{3}^{2})=z_{0}^{2}} from which the formula follows. Besides, masses for neutrinos and down quarks were postulated to be proportional to z i 2 {\displaystyle z_{i}^{2}} while masses for up quarks were postulated to be ∝ ( z 0 + 2 z i ) 2 . {\displaystyle \propto (z_{0}+2z_{i})^{2}~.} The published model justifies the first condition as part of a symmetry breaking scheme, and the second one as a "flavor charge" for preons in the interaction that causes this symmetry breaking. Note that in matrix form with M = A A † {\displaystyle M=A\ A^{\dagger }} and A = Z 0 + Z {\displaystyle A=Z_{0}+Z} the equations are simply tr ⁡ Z = 0 {\displaystyle \operatorname {tr} Z=0} and tr ⁡ Z 0 2 = tr ⁡ Z 2 . {\displaystyle \operatorname {tr} Z_{0}^{2}=\operatorname {tr} Z^{2}.} == Phase formulation == The formula reduces to


id: koide-formula-20260505-2
file: data/en.wikipedia.org/wiki/Koide_formula-2.md
category: reference
title: Koide formula
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Koide_formula
date_saved: 2026-05-05T11:05:35.059661+00:00
instance: kb-cron
parent: koide-formula-20260505-0
summary:
( 2 x 3 − 6 n x 2 + 3 n 2 x − 3 ) ( 2 x 3 + 6 n x 2 + 3 n 2 x + 3 ) {\displaystyle (2x^{3}-6nx^{2}+3n^{2}x-3)(2x^{3}+6nx^{2}+3n^{2}x+3)} or 4 ( x 3 − 3 n x 2 + 3 2 n 2 x − 3 2 ) ( x 3 + 3 n x 2 + 3 2 n 2 x + 3 2 ) {\displaystyle 4(x^{3}-3nx^{2}+{\tfrac {3}{2}}n^{2}x-{\tfrac {3}{2}})(x^{3}+3nx^{2}+{\tfrac {3}{2}}n^{2}x+{\tfrac {3}{2}})} The elementary symmetric polynomials of the roots must reproduce the corresponding coefficients from the polynomial that they solve, so x 1 + x 2 + x 3 = ± 3 n {\displaystyle x_{1}+x_{2}+x_{3}=\pm 3n} and x 1 x 2 + x 2 x 3 + x 3 x 1 = + 3 2 n 2 . {\displaystyle x_{1}x_{2}+x_{2}x_{3}+x_{3}x_{1}=+{\tfrac {3}{2}}n^{2}.} Taking the ratio of these symmetric polynomials, but squaring the first so we divide out the unknown parameter n , {\displaystyle n,} we get a Koide-type formula: Regardless of the value of n , {\displaystyle n,} the solutions to the cubic equation for x {\displaystyle x} must satisfy 2 ( x 1 x 2 + x 2 x 3 + x


id: list-of-hypothetical-particles-20260505-0
file: data/en.wikipedia.org/wiki/List_of_hypothetical_particles-0.md
category: reference
title: List of hypothetical particles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_hypothetical_particles
date_saved: 2026-05-05T11:05:36.279943+00:00
instance: kb-cron
parent: list-of-hypothetical-particles-20260505-0
summary:
This is a list of hypothetical particles. Hypothetical particles are proposed subatomic or composite entities arising in theoretical particle physics and cosmology that have not been experimentally confirmed. They are typically introduced to address limitations of the Standard Model, unify fundamental interactions, or explain unresolved observations such as dark matter, neutrino masses, baryon asymmetry, or cosmic inflation. Many are mathematically well defined within quantum field theory or its extensions and serve as mediators or constituents in speculative but testable frameworks beyond the Standard Model. Prominent classes include gauge or symmetry-related particles such as the graviton or graviphoton in quantum gravity and extra-dimensional theories, and supersymmetric partners (e.g., neutralinos or charginos) predicted by supersymmetry. Others address specific phenomena, including hidden-sector bosons such as dark photons or light force carriers proposed to explain nuclear anomalies. Hypothetical particles also encompass predicted bound states (e.g., glueballs), topological objects such as magnetic monopoles, and unconventional statistical entities such as anyons or tachyons. Collectively, they form a central component of theoretical model building, guiding experimental searches for physics beyond currently known particles. == Elementary particles == Some theories predict the existence of additional elementary bosons and fermions that are not found in the Standard Model. ===


id: list-of-particles-20260505-0
file: data/en.wikipedia.org/wiki/List_of_particles-0.md
category: reference
title: List of particles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_particles
date_saved: 2026-05-05T11:05:37.534299+00:00
instance: kb-cron
parent: list-of-particles-20260505-0
summary:
This is a list of known and hypothesized molecular, atomic, and subatomic particles in particle physics, condensed matter physics and cosmology. == Standard Model elementary particles == Elementary particles are particles with no measurable internal structure; that is, it is unknown whether they are composed of other particles. They are the fundamental objects of quantum field theory. Many families and sub-families of elementary particles exist. Elementary particles are classified according to their spin. Fermions have half-integer spin while bosons have integer spin. All the elementary particles of the Standard Model have been experimentally observed, including the Higgs boson in 2012. Many other hypothetical elementary particles, such as the graviton, have been proposed, but not observed experimentally. Notes: [†] An anti-electron (e+) is conventionally called a "positron". === Fermions === Fermions are one of the two fundamental classes of particles, the other being bosons. Fermion particles are described by Fermi–Dirac statistics and have quantum numbers described by the Pauli exclusion principle. They include the quarks and leptons, as well as any composite particles consisting of an odd number of these, such as all baryons and many atoms and nuclei. Fermions have half-integer spin; for all known elementary fermions this is ⁠1/2⁠ħ.


id: list-of-particles-20260505-1
file: data/en.wikipedia.org/wiki/List_of_particles-1.md
category: reference
title: List of particles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_particles
date_saved: 2026-05-05T11:05:37.534299+00:00
instance: kb-cron
parent: list-of-particles-20260505-0
summary:
Ordinary mesons are made up of a valence quark and a valence antiquark. Because mesons have integer spin (0 or 1) and are not themselves elementary particles, they are classified as "composite" bosons, although being made of elementary fermions. Examples of mesons include the pion, kaon, and the J/ψ. In quantum hadrodynamics, mesons mediate the residual strong force between nucleons. At one time or another, positive signatures have been reported for all of the following exotic mesons but their existences have yet to be confirmed. A tetraquark consists of two valence quarks and two valence antiquarks; A glueball is a bound state of gluons with no valence quarks; Hybrid mesons consist of one or more valence quark–antiquark pairs and one or more real gluons. === Atomic nuclei === Atomic nuclei typically consist of protons and neutrons, although exotic nuclei may consist of other baryons, such as hypertriton which contains a hyperon. These baryons (protons, neutrons, hyperons, etc.) which comprise the nucleus are called nucleons. Each type of nucleus is called a "nuclide", and each nuclide is defined by the specific number of each type of nucleon. "Isotopes" are nuclides which have the same number of protons but differing numbers of


id: list-of-particles-20260505-2
file: data/en.wikipedia.org/wiki/List_of_particles-2.md
category: reference
title: List of particles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_particles
date_saved: 2026-05-05T11:05:37.534299+00:00
instance: kb-cron
parent: list-of-particles-20260505-0
summary:
== Auxiliary particles == Virtual particles are mathematical tools used in calculations that exhibits some of the characteristics of an ordinary particle but do not obey the mass-shell relation. These particles are unphysical and unobservable. These include: Ghost particles, like Faddeev–Popov ghosts and Pauli–Villars ghosts Spurions, auxiliary field in a quantum field theory that can be used to parameterize any symmetry Soft photons, photons with energies below detectable in experiment. There are also instantons, field configurations which are a local minimum of the Yang–Mills field equation. Instantons are used in nonperturbative calculations of tunneling rates. Instantons have properties similar to particles, specific examples include: Calorons, finite temperature generalization of instantons. Merons, a field configuration which is a non-self-dual solution of the Yang–Mills field equation. The instanton is believed to be composed of two merons. Sphalerons are a field configuration which is a saddle point of the Yang–Mills field equations. Sphalerons are used in nonperturbative calculations of non-tunneling rates. Renormalons, a possible type of singularity arising when using Borel summation. It is a counterpart of an instanton singularity. == Classification by speed == A bradyon (or tardyon) travels slower than the speed of light in vacuum and has a non-zero, real


id: long-delayed-echo-20260505-0
file: data/en.wikipedia.org/wiki/Long_delayed_echo-0.md
category: reference
title: Long delayed echo
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Long_delayed_echo
date_saved: 2026-05-05T11:05:38.710429+00:00
instance: kb-cron
parent: long-delayed-echo-20260505-0
summary:
Long delayed echoes (LDEs) are radio echoes which return to the sender several seconds after a radio transmission has occurred. Delays of longer than 2.7 seconds are considered LDEs. LDEs are considered anomalous and have a number of proposed scientific origins. == History == These echoes were first observed in 1927 by civil engineer and amateur radio operator Jørgen Hals from his home near Oslo, Norway. Hals had repeatedly observed an unexpected second radio echo with a significant time delay after the primary radio echo ended. Unable to account for this strange phenomenon, he wrote a letter to Norwegian physicist Carl Størmer, explaining the event: At the end of the summer of 1927 I repeatedly heard signals from the Dutch short-wave transmitting station PCJJ at Eindhoven. At the same time as I heard these I also heard echoes. I heard the usual echo which goes round the Earth with an interval of about 1/7 of a second as well as a weaker echo about three seconds after the principal echo had gone. When the principal signal was especially strong, I suppose the amplitude for the last echo three seconds later, lay between 1/10 and 1/20 of the principal signal in


id: m82-x-2-20260505-0
file: data/en.wikipedia.org/wiki/M82_X-2-0.md
category: reference
title: M82 X-2
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/M82_X-2
date_saved: 2026-05-05T11:05:39.882670+00:00
instance: kb-cron
parent: m82-x-2-20260505-0
summary:
M82 X-2 is an X-ray pulsar located in the galaxy Messier 82, approximately 12 million light-years from Earth. It is exceptionally luminous, radiating energy equivalent to approximately ten million Suns. This object is part of a binary system: If the pulsar is of an average size, 1.4 M☉, then its companion is at least 5.2 M☉. On average, the pulsar rotates every 1.37 seconds, and revolves around its more massive companion every 2.5 days. M82 X-2 is an ultraluminous X-ray source (ULX), shining about 100 times brighter than theory suggests something of its mass should be able to. Its brightness is many times higher than the Eddington limit, a basic physics guideline that sets an upper limit on the brightness that an object of a given mass should be able to achieve. Possible explanations for violations of the Eddington limit include geometrical effects arising from the funneling of in-falling material along magnetic field lines. While M82 X-2 was previously known as an X-ray source, it was not until an observation campaign to study the newly discovered supernova SN 2014J in January 2014 that X-2's true nature was uncovered. Scientists looking at data from the NuSTAR spacecraft noticed a pulsing in


id: magnetic-monopole-20260505-0
file: data/en.wikipedia.org/wiki/Magnetic_monopole-0.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
In particle physics, a magnetic monopole is a hypothetical particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from particle theories, notably grand unified and superstring theories, which predict their existence. The known elementary particles that have electric charge are electric monopoles. Magnetism in bar magnets and electromagnets is not caused by magnetic monopoles, and indeed, there is no known experimental or observational evidence that magnetic monopoles exist. A magnetic monopole is not necessarily an elementary particle, and models for magnetic monopole production can include (but are not limited to) spin-0 monopoles or spin-1 massive vector mesons. The term "magnetic monopole" only refers to the nature of the particle, rather than a designation for a single particle. Some condensed matter systems contain effective (non-isolated) magnetic monopole quasi-particles, or contain phenomena that are mathematically analogous to magnetic monopoles. == Historical background == === Early science and classical physics === Many early scientists attributed the magnetism of lodestones to two different "magnetic fluids" ("effluvia"), a north-pole fluid at one end and a


id: magnetic-monopole-20260505-1
file: data/en.wikipedia.org/wiki/Magnetic_monopole-1.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
== Maxwell's equations == Maxwell's equations of electromagnetism relate the electric and magnetic fields to each other and to the distribution of electric charge and current. The standard equations provide for electric charge, but they posit zero magnetic charge and current. Except for this constraint, the equations are symmetric under the interchange of the electric and magnetic fields. Maxwell's equations are symmetric when the charge and electric current density are zero everywhere, as in vacuum. Maxwell's equations can also be written in a fully symmetric form if one allows for "magnetic charge" analogous to electric charge. With the inclusion of a variable for the density of magnetic charge, say ρm, there is also a "magnetic current density" variable in the equations, jm. If magnetic charge does not exist – or if it exists but is absent in a region of space – then the new terms in Maxwell's equations are all zero, and the extended equations reduce to the conventional equations of electromagnetism such as ∇ ⋅ B = 0 (where ∇⋅ is the divergence operator and B is the magnetic flux density). === In SI units === In the International System of Quantities used with the SI, there are


id: magnetic-monopole-20260505-2
file: data/en.wikipedia.org/wiki/Magnetic_monopole-2.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
== Dirac's quantization == One of the defining advances in quantum theory was Paul Dirac's work on developing a relativistic quantum electromagnetism. Before his formulation, the presence of electric charge was simply inserted into the equations of quantum mechanics (QM), but in 1931 Dirac showed that a discrete charge is implied by QM. That is to say, we can maintain the form of Maxwell's equations and still have magnetic charges. Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole, which would not exert any forces on each other. Classically, the electromagnetic field surrounding them has a momentum density given by the Poynting vector, and it also has a total angular momentum, which is proportional to the product qeqm, and is independent of the distance between them. Quantum mechanics dictates, however, that angular momentum is quantized as a multiple of ħ, so therefore the product qeqm must also be quantized. This means that if even a single magnetic monopole existed in the universe, and the form of Maxwell's equations is valid, all electric charges would then be quantized. Although it would be possible simply to integrate over all space to find


id: magnetic-monopole-20260505-3
file: data/en.wikipedia.org/wiki/Magnetic_monopole-3.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
So that the phase a charged particle gets when going in a loop is the magnetic flux through the loop. When a small solenoid has a magnetic flux, there are interference fringes for charged particles which go around the solenoid, or around different sides of the solenoid, which reveal its presence. But if all particle charges are integer multiples of e, solenoids with a flux of 2π/e have no interference fringes, because the phase factor for any charged particle is exp(2πi) = 1. Such a solenoid, if thin enough, is quantum-mechanically invisible. If such a solenoid were to carry a flux of 2π/e, when the flux leaked out from one of its ends it would be indistinguishable from a monopole. Dirac's monopole solution in fact describes an infinitesimal line solenoid ending at a point, and the location of the solenoid is the singular part of the solution, the Dirac string. Dirac strings link monopoles and antimonopoles of opposite magnetic charge, although in Dirac's version, the string just goes off to infinity. The string is unobservable, so you can put it anywhere, and by using two coordinate patches, the field in each patch can be made nonsingular by sliding the string


id: magnetic-monopole-20260505-4
file: data/en.wikipedia.org/wiki/Magnetic_monopole-4.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
The holonomy of a gauge field maps loops to elements of the gauge group. Infinitesimal loops are mapped to group elements infinitesimally close to the identity. If you imagine a big sphere in space, you can deform an infinitesimal loop that starts and ends at the north pole as follows: stretch out the loop over the western hemisphere until it becomes a great circle (which still starts and ends at the north pole) then let it shrink back to a little loop while going over the eastern hemisphere. This is called lassoing the sphere. Lassoing is a sequence of loops, so the holonomy maps it to a sequence of group elements, a continuous path in the gauge group. Since the loop at the beginning of the lassoing is the same as the loop at the end, the path in the group is closed. If the group path associated to the lassoing procedure winds around the U(1), the sphere contains magnetic charge. During the lassoing, the holonomy changes by the amount of magnetic flux through the sphere. Since the holonomy at the beginning and at the end is the identity, the total magnetic flux is quantized. The magnetic charge is proportional


id: magnetic-monopole-20260505-5
file: data/en.wikipedia.org/wiki/Magnetic_monopole-5.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
In mathematics, a (classical) gauge field is defined as a connection over a principal G-bundle over spacetime. G is the gauge group, and it acts on each fiber of the bundle separately. A connection on a G-bundle tells you how to glue fibers together at nearby points of M. It starts with a continuous symmetry group G that acts on the fiber F, and then it associates a group element with each infinitesimal path. Group multiplication along any path tells you how to move from one point on the bundle to another, by having the G element associated to a path act on the fiber F. In mathematics, the definition of bundle is designed to emphasize topology, so the notion of connection is added on as an afterthought. In physics, the connection is the fundamental physical object. One of the fundamental observations in the theory of characteristic classes in algebraic topology is that many homotopical structures of nontrivial principal bundles may be expressed as an integral of some polynomial over any connection over it. Note that a connection over a trivial bundle can never give us a nontrivial principal bundle. If spacetime is R 4 {\displaystyle \mathbb {R} ^{4}} the


id: magnetic-monopole-20260505-6
file: data/en.wikipedia.org/wiki/Magnetic_monopole-6.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
== Grand unified theories == In more recent years, a new class of theories has also suggested the existence of magnetic monopoles. During the early 1970s, the successes of quantum field theory and gauge theory in the development of electroweak theory and the mathematics of the strong nuclear force led many theorists to move on to attempt to combine them in a single theory known as a Grand Unified Theory (GUT). Several GUTs were proposed, most of which implied the presence of a real magnetic monopole particle. More accurately, GUTs predicted a range of particles known as dyons, of which the most basic state was a monopole. The charge on magnetic monopoles predicted by GUTs is either 1 or 2 gD, depending on the theory. The majority of particles appearing in any quantum field theory are unstable, and they decay into other particles in a variety of reactions that must satisfy various conservation laws. Stable particles are stable because there are no lighter particles into which they can decay and still satisfy the conservation laws. For instance, the electron has a lepton number of one and an electric charge of one, and there are no lighter particles that conserve these


id: magnetic-monopole-20260505-7
file: data/en.wikipedia.org/wiki/Magnetic_monopole-7.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
== Searches for magnetic monopoles == Experimental searches for magnetic monopoles can be placed in one of two categories: those that try to detect preexisting magnetic monopoles and those that try to create and detect new magnetic monopoles. Passing a magnetic monopole through a coil of wire induces a net current in the coil. This is not the case for a magnetic dipole or higher order magnetic pole, for which the net induced current is zero, and hence the effect can be used as an unambiguous test for the presence of magnetic monopoles. In a wire with finite resistance, the induced current quickly dissipates its energy as heat, but in a superconducting loop the induced current is long-lived. By using a highly sensitive "superconducting quantum interference device" (SQUID) one can, in principle, detect even a single magnetic monopole. According to standard inflationary cosmology, magnetic monopoles produced before inflation would have been diluted to an extremely low density today. Magnetic monopoles may also have been produced thermally after inflation, during the period of reheating. However, the current bounds on the reheating temperature span 18 orders of magnitude and as a consequence the density of magnetic monopoles today is not well constrained


id: magnetic-monopole-20260505-8
file: data/en.wikipedia.org/wiki/Magnetic_monopole-8.md
category: reference
title: Magnetic monopole
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_monopole
date_saved: 2026-05-05T11:05:41.099153+00:00
instance: kb-cron
parent: magnetic-monopole-20260505-0
summary:
== "Monopoles" in condensed-matter systems == Since around 2003, various condensed-matter physics groups have used the term "magnetic monopole" to describe a different and largely unrelated phenomenon. A true magnetic monopole would be a new elementary particle, and would violate Gauss's law for magnetism ∇⋅B = 0. A monopole of this kind, which would help to explain the law of charge quantization as formulated by Paul Dirac in 1931, has never been observed in experiments. The monopoles studied by condensed-matter groups have none of these properties. They are not a new elementary particle, but rather are an emergent phenomenon in systems of everyday particles (protons, neutrons, electrons, photons); in other words, they are quasi-particles. They are not sources for the B-field (i.e., they do not violate ∇⋅B = 0); instead, they are sources for other fields, for example the H-field, the "B*-field" (related to superfluid vorticity), or various other quantum fields. They are not directly relevant to grand unified theories or other aspects of particle physics, and do not help explain charge quantization—except insofar as studies of analogous situations can help confirm that the mathematical analyses involved are sound. There are a number of examples in condensed-matter physics where collective


id: mass-in-general-relativity-20260505-0
file: data/en.wikipedia.org/wiki/Mass_in_general_relativity-0.md
category: reference
title: Mass in general relativity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mass_in_general_relativity
date_saved: 2026-05-05T11:05:42.338004+00:00
instance: kb-cron
parent: mass-in-general-relativity-20260505-0
summary:
In general relativity, the notion of mass is more subtle than in classical mechanics or special relativity. The theory itself does not single out a preferred local definition of mass, and several distinct notions of mass have been introduced that are applicable under different geometric or physical circumstances. This subtlety stems from the fact that the energy and momentum of the gravitational field cannot be unambiguously localized. As a consequence, mass in general relativity cannot be defined as a local quantity in the same sense as in Newtonian physics, since there is no invariant local energy density for the gravitational field. Instead, notions of mass are recovered indirectly from global or boundary data, which typically requires additional geometric structure, such as symmetries or assumptions about the asymptotic behavior of spacetime. Well-defined notions of total mass exist in important classes of spacetimes, such as asymptotically flat spacetimes and asymptotically anti-de Sitter spacetimes, where suitable boundary conditions allow for a meaningful definition. Other settings require different or more refined constructions. == Conceptual obstacles == In special relativity, the rest mass of a particle can be defined unambiguously in terms of its energy and momentum (see Mass in special relativity). In general relativity,


id: mass-in-general-relativity-20260505-1
file: data/en.wikipedia.org/wiki/Mass_in_general_relativity-1.md
category: reference
title: Mass in general relativity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mass_in_general_relativity
date_saved: 2026-05-05T11:05:42.338004+00:00
instance: kb-cron
parent: mass-in-general-relativity-20260505-0
summary:
g μ ν = η μ ν + h μ ν , {\displaystyle g_{\mu \nu }=\eta _{\mu \nu }+h_{\mu \nu },} where η μ ν {\displaystyle \eta _{\mu \nu }} is the flat Minkowski metric and h μ ν {\displaystyle h_{\mu \nu }} represents deviations that decay suitably at infinity. These expressions provide a coordinate realization of the Hamiltonian definitions given above. In this formulation, the ADM energy E A D M = P 0 {\displaystyle E_{\mathrm {ADM} }=P^{0}} is given by the flux integral P 0 = 1 16 π G ∫ ( ∂ k h j k − ∂ j h k k ) d 2 S j , {\displaystyle P^{0}={\frac {1}{16\pi G}}\int \left(\partial ^{k}h_{jk}-\partial ^{j}h_{kk}\right)d^{2}S_{j},} where S {\displaystyle S} is a large sphere at spatial infinity, S j {\displaystyle S_{j}} denotes its outward-pointing unit normal, and the Einstein summation convention is assumed over spatial indices. Ordinary derivatives appear in this expression because the metric is assumed to approach the flat metric asymptotically. Some intuition for this formula can be obtained by considering spherical surfaces of large radius r {\displaystyle r} . At large distances from the sources, the components of h i j {\displaystyle h_{ij}} typically decay


id: mass-in-general-relativity-20260505-2
file: data/en.wikipedia.org/wiki/Mass_in_general_relativity-2.md
category: reference
title: Mass in general relativity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mass_in_general_relativity
date_saved: 2026-05-05T11:05:42.338004+00:00
instance: kb-cron
parent: mass-in-general-relativity-20260505-0
summary:
== Quasi-local quantities == A limitation of the mass definitions discussed above is that they are defined only at null or spatial infinity and therefore require information about the spacetime geometry arbitrarily far from the gravitating system. In realistic physical situations, such global information is generally unavailable, making such notions of mass difficult to interpret or measure without access to the entire system or a large portion of it. This has motivated the search for notions of mass that can be associated with a finite region of spacetime. Since the 1970s, physicists and mathematicians have therefore pursued the more ambitious goal of defining suitable quasi-local quantities. A quasi-local mass is intended to measure the mass or energy contained within a region enclosed by a closed surface, using only geometric and physical data defined on or inside that surface. The term “quasi-local” reflects the fact that, while such quantities depend on a finite region rather than asymptotic infinity, they cannot be strictly local, since general relativity does not admit a well-defined local energy density for the gravitational field. A wide variety of quasi-local mass and energy definitions have been proposed, including the Hawking energy, the Geroch energy, the Bartnik mass, the


id: mass-in-general-relativity-20260505-3
file: data/en.wikipedia.org/wiki/Mass_in_general_relativity-3.md
category: reference
title: Mass in general relativity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mass_in_general_relativity
date_saved: 2026-05-05T11:05:42.338004+00:00
instance: kb-cron
parent: mass-in-general-relativity-20260505-0
summary:
== References == Ashtekar, Abhay; Magnon-Ashtekar, Anne (1979). "On conserved quantities in general relativity". Journal of Mathematical Physics. 20 (5). AIP Publishing: 793–800. Bibcode:1979JMP....20..793A. doi:10.1063/1.524151. ISSN 0022-2488. Komar, Arthur (1959). "Covariant Conservation Laws in General Relativity". Phys. Rev. 113 (3): 934–936. Bibcode:1959PhRv..113..934K. doi:10.1103/PhysRev.113.934. Arnowitt, R.; Deser, S.; Misner, C. W. (1960-03-15). "Canonical Variables for General Relativity" (PDF). Physical Review. 117 (6). American Physical Society (APS): 1595–1602. Bibcode:1960PhRv..117.1595A. doi:10.1103/physrev.117.1595. ISSN 0031-899X. S2CID 120715041. Arnowitt, Richard; Deser, Stanley; Misner, Charles W. (1962). "The dynamics of general relativity". In Witten, L. (ed.). Gravitation: An Introduction to Current Research. Wiley. pp. 227–265. Bondi, H.; Van Der Burg, M. G. J.; Metzner, A. W. K. (1962-08-21). "Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 269 (1336). The Royal Society: 21–52. Bibcode:1962RSPSA.269...21B. doi:10.1098/rspa.1962.0161. ISSN 2053-9169. S2CID 120125096. Held (1980). General Relativity and Gravitation, One Hundred Years After the Birth of Einstein, Vol 2. Plenum Press. ISBN 978-0-306-40266-1. Szabados, László B. (2004). "Quasi-Local Energy-Momentum and Angular Momentum in GR". Living Rev. Relativ. 7 (1): 4. Bibcode:2004LRR.....7....4S. doi:10.12942/lrr-2004-4. PMC 5255888. PMID 28179865. Townsend, P. K. (1997). "Black Holes (Lecture notes)". arXiv:gr-qc/9707012. Wald,


id: measure-problem-cosmology-20260505-0
file: data/en.wikipedia.org/wiki/Measure_problem_(cosmology)-0.md
category: reference
title: Measure problem (cosmology)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Measure_problem_(cosmology)
date_saved: 2026-05-05T11:05:43.583664+00:00
instance: kb-cron
parent: measure-problem-cosmology-20260505-0
summary:
The measure problem in cosmology concerns how to compute the ratios of universes of different types within a multiverse. It typically arises in the context of eternal inflation. The problem arises because different approaches to calculating these ratios yield different results, and it is not clear which approach (if any) is correct. Measures can be evaluated by whether they predict observed physical constants, as well as whether they avoid counterintuitive implications, such as the youngness paradox or Boltzmann brains. While dozens of measures have been proposed, few physicists consider the problem to be solved. == The problem == Infinite multiverse theories are becoming increasingly popular, but because they involve infinitely many instances of different types of universes, it is unclear how to compute the fractions of each type of universe. Alan Guth put it this way: In a single universe, cows born with two heads are rarer than cows born with one head. [But in an infinitely branching multiverse] there are an infinite number of one-headed cows and an infinite number of two-headed cows. What happens to the ratio? Sean M. Carroll offered another informal example: Say there are an infinite number of universes in which George W. Bush became


id: measure-problem-cosmology-20260505-1
file: data/en.wikipedia.org/wiki/Measure_problem_(cosmology)-1.md
category: reference
title: Measure problem (cosmology)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Measure_problem_(cosmology)
date_saved: 2026-05-05T11:05:43.583664+00:00
instance: kb-cron
parent: measure-problem-cosmology-20260505-0
summary:
=== Scale-factor cutoff === Time can be parameterized in different ways than proper time. One choice is to parameterize by the scale factor of space a {\displaystyle a} , or more commonly by η ∼ log ⁡ a {\displaystyle \eta \sim \log a} . Then a given region of space expands as e 3 Δ η {\displaystyle e^{3\Delta \eta }} , independent of H {\displaystyle H} . This approach can be generalized to a family of measures in which a small region grows as e 3 H β Δ t β {\displaystyle e^{3H^{\beta }\Delta t_{\beta }}} for some β {\displaystyle \beta } and time-slicing approach t β {\displaystyle t_{\beta }} . Any choice for β {\displaystyle \beta } remains stationary for large times. The scale-factor cutoff measure takes β = 0 {\displaystyle \beta =0} , which avoids the youngness paradox by not giving greater weight to regions that retain high energy density for long periods. This measure is very sensitive to the choice of β {\displaystyle \beta } because any β > 0 {\displaystyle \beta >0} yields the youngness paradox, while any β < 0 {\displaystyle \beta <0} yields an "oldness paradox" in which most life is predicted to exist


id: michigan-spin-physics-center-20260505-0
file: data/en.wikipedia.org/wiki/Michigan_Spin_Physics_Center-0.md
category: reference
title: Michigan Spin Physics Center
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Michigan_Spin_Physics_Center
date_saved: 2026-05-05T11:05:44.773056+00:00
instance: kb-cron
parent: michigan-spin-physics-center-20260505-0
summary:
The University of Michigan Spin Physics Center focuses on studies of spin effects in high polarized proton-proton elastic and inelastic scattering. These polarized scattering experiments use the world-class solid and jet polarized proton targets, which are developed, upgraded and tested at the center. The Center obtained a record density of about 1012 spin-polarized hydrogen atoms per cm3. The center also led the development of the world's first accelerated polarized beams at the 12 GeV Argonne ZGS (in 1973) and then at the 28 GeV Brookhaven AGS. The Center led pioneering experiments at the IUCF Cooler Ring from 1988 until its 2003 shutdown, which developed and tested Siberian snakes and Spin-flippers, which are now used to accelerate, store and use high energy polarized proton beams. The center also leads the International SPIN Collaboration and its proton polarization know-how is used in many experiments worldwide. == Main discoveries == In 1978 the Center found that protons with parallel spins interact much stronger than protons with anti-parallel spin. According to Quantum Chromodynamics the interaction between parallel and anti-parallel spinning proton beams should be the same. Sheldon Glashow called this effect "the thorn in the side of QCD". This effect remained unexplained until today.


id: modified-newtonian-dynamics-20260505-0
file: data/en.wikipedia.org/wiki/Modified_Newtonian_dynamics-0.md
category: reference
title: Modified Newtonian dynamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
date_saved: 2026-05-05T11:05:46.022752+00:00
instance: kb-cron
parent: modified-newtonian-dynamics-20260505-0
summary:
Modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's laws to account for observed properties of galaxies. Modifying Newton's law of gravity results in modified gravity, while modifying Newton's second law results in modified inertia. The latter has received little attention compared to the modified gravity version. Its primary motivation is to explain galaxy rotation curves without invoking dark matter, and is one of the most well-known theories of this class. MOND was developed in 1982 and presented in 1983 by Israeli physicist Mordehai Milgrom. Milgrom noted that galaxy rotation curve data, which seemed to show that galaxies contain more matter than is observed, could also be explained if the gravitational force experienced by a star in the outer regions of a galaxy decays more slowly than predicted by Newton's law of gravity. MOND modifies Newton's laws for extremely small accelerations, which are common in galaxies and galaxy clusters. This provides a good fit to galaxy rotation curve data while leaving the dynamics of the Solar System with its strong gravitational field intact. However, the theory predicts that the gravitational field of the galaxy could influence the orbits of Kuiper Belt objects through the external field


id: modified-newtonian-dynamics-20260505-1
file: data/en.wikipedia.org/wiki/Modified_Newtonian_dynamics-1.md
category: reference
title: Modified Newtonian dynamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
date_saved: 2026-05-05T11:05:46.022752+00:00
instance: kb-cron
parent: modified-newtonian-dynamics-20260505-0
summary:
Modified inertia: One possibility is to treat it as a modification to Newton's second law, so that the force on an object is not proportional to the particle's acceleration a but rather to μ ( a a 0 ) a . {\textstyle \mu \left({\frac {a}{a_{0}}}\right)a.} In this case, the modified dynamics would apply not only to gravitational phenomena, but also those generated by other forces, for example electromagnetism. This interpretation is experimentally disfavoured by laboratory experiments. Modified gravity: Alternatively, Milgrom's law can be viewed as modifying Newton's universal law of gravity instead, so that the true gravitational force on an object of mass m due to another of mass M is roughly of the form G M m ν ( a 0 a ) r 2 . {\textstyle {\frac {GMm}{\nu \left({\frac {a_{0}}{a}}\right)r^{2}}}.} In this interpretation, Milgrom's modification would apply exclusively to gravitational phenomena. This interpretation has received more attention between the two. Milgrom's law states that for accelerations smaller than a0 accelerations increasingly depart from the standard M · G / r 2 Newtonian relationship of mass and distance, wherein gravitational strength is linearly proportional to mass and the inverse square of distance. Instead, the theory holds that the gravitational


id: modified-newtonian-dynamics-20260505-2
file: data/en.wikipedia.org/wiki/Modified_Newtonian_dynamics-2.md
category: reference
title: Modified Newtonian dynamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
date_saved: 2026-05-05T11:05:46.022752+00:00
instance: kb-cron
parent: modified-newtonian-dynamics-20260505-0
summary:
a e x < a i n < a 0 {\displaystyle a_{\mathrm {ex} }<a_{\mathrm {in} }<a_{0}} : Deep-MOND regime a i n < a 0 < a e x {\displaystyle a_{\mathrm {in} }<a_{0}<a_{\mathrm {ex} }} : The external field is dominant and the behavior of the system is Newtonian. a i n < a e x < a 0 {\displaystyle a_{\mathrm {in} }<a_{\mathrm {ex} }<a_{0}} : The external field is larger than the internal acceleration of the system, but both are smaller than the critical value. In this case, dynamics is Newtonian but the effective value of G is enhanced by a factor of a0/aex. The external field effect implies a fundamental break with the strong equivalence principle (but not the weak equivalence principle which is required by the Lagrangian). The effect was postulated by Milgrom in the first of his 1983 papers to explain why some open clusters were observed to have no mass discrepancy even though their internal accelerations were below a0. It has since come to be recognized as a crucial element of the MOND paradigm. The dependence in MOND of the internal dynamics of a system on its external environment (in principle, the rest of the


id: modified-newtonian-dynamics-20260505-3
file: data/en.wikipedia.org/wiki/Modified_Newtonian_dynamics-3.md
category: reference
title: Modified Newtonian dynamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
date_saved: 2026-05-05T11:05:46.022752+00:00
instance: kb-cron
parent: modified-newtonian-dynamics-20260505-0
summary:
Since this Lagrangian does not explicitly depend on time and is invariant under spatial translations this means energy and momentum are conserved according to Noether's theorem. Varying over r yields m a = m g {\displaystyle ma=mg} showing that the weak equivalence principle always applies in QUMOND. However, since ϕ {\displaystyle \phi } and ϕ N {\displaystyle \phi _{N}} are not identical and are non-linearly related this means that the strong equivalence principle must be violated. This can be observed by measuring the external field effect. Furthermore, by varying over ϕ {\displaystyle \phi } we get the following Newton-Poisson equation familiar from Newtonian gravity but now with a subscript to denote that in QUMOND this equation determines the auxiliary gravitational field ϕ N {\displaystyle \phi _{N}} : ∇ 2 ϕ N = 4 π G ρ . {\displaystyle \nabla ^{2}\phi _{N}=4\pi G\rho .} Finally by varying the QUMOND Lagrangian with respect to ϕ N {\displaystyle \phi _{N}} we get the QUMOND field equation: ∇ 2 ϕ = ∇ ⋅ [ ν ( a 0 ‖ ∇ ϕ N ‖ ) ∇ ϕ N ] {\displaystyle \nabla ^{2}\phi =\nabla \cdot \left[\nu \left({\frac {a_{0}}{\left\|\nabla \phi _{N}\right\|}}\right)\nabla \phi _{N}\right]} These two field equations


id: modified-newtonian-dynamics-20260505-4
file: data/en.wikipedia.org/wiki/Modified_Newtonian_dynamics-4.md
category: reference
title: Modified Newtonian dynamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
date_saved: 2026-05-05T11:05:46.022752+00:00
instance: kb-cron
parent: modified-newtonian-dynamics-20260505-0
summary:
=== Dwarf galaxies === Recent work has shown that many of the dwarf galaxies around the Milky Way and Andromeda are located preferentially in a single plane and have correlated motions. This suggests that they may have formed during a close encounter with another galaxy and hence are tidal dwarf galaxies. If so, the presence of mass discrepancies in these systems constitutes evidence for MOND. In addition, it has been claimed that a gravitational force stronger than Newton's (such as Milgrom's) is required for these galaxies to retain their orbits over time. Centaurus A has a similar plane of dwarf galaxies around it which is challenging for LCDM which expects uniform halos of dwarf galaxies. In MOND, all isolated gravitationally bound objects with a < a0 that are in equilibrium – regardless of their origin – should exhibit a mass discrepancy when analyzed using Newtonian mechanics, and should lie on the BTFR. Under the dark matter hypothesis, objects formed from baryonic material ejected during the merger or tidal interaction of two galaxies ("tidal dwarf galaxies") are expected to be devoid of dark matter and hence show no mass discrepancy. Three objects unambiguously identified as tidal dwarf galaxies appear to have


id: modified-newtonian-dynamics-20260505-5
file: data/en.wikipedia.org/wiki/Modified_Newtonian_dynamics-5.md
category: reference
title: Modified Newtonian dynamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
date_saved: 2026-05-05T11:05:46.022752+00:00
instance: kb-cron
parent: modified-newtonian-dynamics-20260505-0
summary:
==== Solar System ==== Almost the entire Solar System has gravitational field strengths many orders of magnitude higher than a0 so the increase in gravity due to MOND is negligible. However solar system tests are extremely precise and most observations have proven difficult for MOND to explain. Notably data from lunar laser ranging rules out the simple interpolation function. Radio tracking data of the Cassini spacecraft towards Saturn rules out both the simple and standard interpolation functions by testing an anomalous quadrupole effect predicted by MOND. It is also possible that a full fit of solar system ephemerides where the masses of planets and asteroids are allowed to vary can accommodate this anomalous quadrupole effect since these are currently determined using general relativity only. Observations of long period comets also seem to conflict with higher order predictions of MOND. Furthermore, laboratory experiments of Newton's second law seem to have ruled out modified inertia versions of MOND with experimental accelerations reaching as low as 0.1% of a0 without deviation from the Newtonian expectation. Some solar system observations could support MOND as it has been suggested that the orbits of Kuiper Belt objects are best explained through MOND's external field effect, rather


id: modified-newtonian-dynamics-20260505-6
file: data/en.wikipedia.org/wiki/Modified_Newtonian_dynamics-6.md
category: reference
title: Modified Newtonian dynamics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
date_saved: 2026-05-05T11:05:46.022752+00:00
instance: kb-cron
parent: modified-newtonian-dynamics-20260505-0
summary:
==== Cosmology ==== It has been claimed that MOND is generally unsuited to forming the basis of cosmology. A significant piece of evidence in favor of standard dark matter is the observed anisotropies in the cosmic microwave background. While ΛCDM is able to explain the observed angular power spectrum, MOND has a much harder time. It is possible to construct relativistic generalizations of MOND that can fit CMB observations, but it requires terms that do not look natural, and several observations (such as the amount of gravitational lensing) are still difficult to explain. MOND also encounters difficulties explaining structure formation, with density perturbations in MOND perhaps growing so rapidly that too much structure is formed by the present epoch. However, galaxy surveys appear to show massive galaxy formation occurring at much greater rapidity early in time than is possible according to ΛCDM. There is a potential link between MOND and cosmology. It has been noted that the value of a0 is within an order of magnitude of cH0, where c is the speed of light and H0 is the Hubble constant (a measure of the present-day expansion rate of the universe). It is also close to the acceleration rate of


id: mpemba-effect-20260505-0
file: data/en.wikipedia.org/wiki/Mpemba_effect-0.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T11:05:47.274258+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
The Mpemba effect is the observation that very hot liquids or colloids (such as ice cream) can freeze more quickly than colder ones, for similar volumes and surrounding conditions. Physicists remain divided on the effect's reproducibility, precise definition, and underlying mechanisms. It is named after Erasto Mpemba, a Tanzanian teenager who studied it scientifically in the 1960s for the first time, along with Denis Osborne. The Mpemba effect was initially observed in only ice cream and water, and later in other colloids. It has been studied extensively in water, with mixed results, and some experiments finding no reproducible effect. It has also been studied in magnetic alloys, nanomechanical systems, and quantum systems. == Definition == The definition of the Mpemba effect used in theoretical studies varies, making it difficult to compare experiments. Monwhea Jeng proposed this definition for the effect in water: "There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will freeze sooner." Even this definition does not specify whether "freezing" refers to the point at which a visible surface layer of ice has formed,


id: mpemba-effect-20260505-1
file: data/en.wikipedia.org/wiki/Mpemba_effect-1.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T11:05:47.274258+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
=== Studies of the effect in water === Modern studies using freezers with well-understood properties have observed the Mpemba effect where water supercools before freezing. Water that starts out cooler tends to reach a lower supercooled temperature before freezing. Some studies measure the time it takes for a sample to begin to freeze (the start of recalescence, the moment where the heat of freezing first starts to be released) the time it takes to completely freeze, or the difference: the time from the onset of recalescence to the completion of freezing. Some also measure the time it takes for a sample to reach the freezing point of the fluid, before any freezing has begun. In 1995, David Auerbach studied glass beakers placed into a liquid cooling bath, where the water supercooled to −6 to −18 °C (21 to 0 °F; 267 to 255 K) before freezing. In some cases water which started off hotter began freezing first. Considerable random variation was observed in the time required for spontaneous freezing to start, and Auerbach observed the Mpemba effect more frequently when the ambient temperature was between −6 and −12 °C (21 and 10 °F). James Brownridge later studied a variety of


id: mpemba-effect-20260505-2
file: data/en.wikipedia.org/wiki/Mpemba_effect-2.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T11:05:47.274258+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
== Theoretical explanations == While the definition of the Mpemba effect used in theoretical studies varies, several explanations have been offered for its occurrence. In 2017, two research groups independently and simultaneously found a theoretical Mpemba effect and also predicted a new "inverse" Mpemba effect in which heating a cooled, far-from-equilibrium system takes less time than another system that is initially closer to equilibrium. Zhiyue Lu and Oren Raz yielded a general criterion based on Markovian statistical mechanics, predicting the appearance of the inverse Mpemba effect in the Ising model and diffusion dynamics. Antonio Lasanta and co-authors also predicted the direct and inverse Mpemba effects for a granular gas in a far-from-equilibrium initial state. Lasanta's paper also suggested that a very generic mechanism leading to both Mpemba effects is due to a particle velocity distribution function that significantly deviates from the Maxwell–Boltzmann distribution. In 2024, building on Kumar's work, Isha Malhotra simulated single colloids placed in a different, double-well potential, and predicted conditions under which two specific ranges of hotter starting temperatures lead to faster freezing, but not temperatures in between those ranges. Supercooling is a component of many theoretical explanations, particularly the tendency of hot liquids that are cooled


id: mpemba-effect-20260505-3
file: data/en.wikipedia.org/wiki/Mpemba_effect-3.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T11:05:47.274258+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
"Heat questions". HyperPhysics. Georgia State University. "Mpemba effect: Why hot water can freeze faster than cold". A possible explanation of the Mpemba Effect Tyrovolas, Ilias J. (2019). "New Explanation for the Mpemba Effect". The 5th International Electronic Conference on Entropy and Its Applications. p. 2. doi:10.3390/ecea-5-06658. "The Mpemba effect: Hot Water may Freeze Faster than Cold Water". An analysis of the Mpemba effect London South Bank University "The Mpemba Effect". Archived from the original on 9 October 2011. – History and analysis of the Mpemba effect "The story of the Mpemba effect told by the protagonists". YouTube. 10 January 2013. Archived from the original on 12 December 2021. An historical interview with Erasto B. Mpemba, Dr Denis G. Osborne and Ray deSouza "Which freezes quicker, hot or cold water?". Retrieved 25 August 2021. High school experiment description, with link to experimental results Adams, Cecil; M. Q. C., Mary (1996). "Which freezes faster, hot water or cold water?". The Straight Dope. Chicago Reader, Inc. Brownridge, James (2010). "A search for the Mpemba effect: When hot water freezes faster than cold water". arXiv:1003.3185 [physics.pop-ph]. Jeng, Monwhea (November 1998). "Can hot water freeze faster than cold water?". in the University of California Usenet


id: mutually-unbiased-bases-20260505-0
file: data/en.wikipedia.org/wiki/Mutually_unbiased_bases-0.md
category: reference
title: Mutually unbiased bases
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mutually_unbiased_bases
date_saved: 2026-05-05T11:05:48.549584+00:00
instance: kb-cron
parent: mutually-unbiased-bases-20260505-0
summary:
In quantum information theory, a set of bases in Hilbert space Cd are said to be mutually unbiased if when a system is prepared in an eigenstate of one of the bases, then all outcomes of the measurement with respect to the other basis are predicted to occur with an equal probability of 1/d. == Overview == The notion of mutually unbiased bases was first introduced by Julian Schwinger in 1960, and the first person to consider applications of mutually unbiased bases was I. D. Ivanovic in the problem of quantum state determination. Mutually unbiased bases (MUBs) and their existence problem is now known to have several closely related problems and equivalent avatars in several other branches of mathematics and quantum sciences, such as SIC-POVMs, finite projective/affine planes, complex Hadamard matrices and more [see section: Related problems]. MUBs are important for quantum key distribution, more specifically in secure quantum key exchange. MUBs are used in many protocols since the outcome is random when a measurement is made in a basis unbiased to that in which the state was prepared. When two remote parties share two non-orthogonal quantum states, attempts by an eavesdropper to distinguish between these by measurements will affect


id: mutually-unbiased-bases-20260505-1
file: data/en.wikipedia.org/wiki/Mutually_unbiased_bases-1.md
category: reference
title: Mutually unbiased bases
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mutually_unbiased_bases
date_saved: 2026-05-05T11:05:48.549584+00:00
instance: kb-cron
parent: mutually-unbiased-bases-20260505-0
summary:
p 1 n 1 < p 2 n 2 < ⋯ < p k n k {\displaystyle p_{1}^{n_{1}}<p_{2}^{n_{2}}<\cdots <p_{k}^{n_{k}}} then the maximum number of mutually unbiased bases which can be constructed satisfies p 1 n 1 + 1 ≤ M ( d ) ≤ d + 1. {\displaystyle p_{1}^{n_{1}}+1\leq {\mathfrak {M}}(d)\leq d+1.} It follows that if the dimension of a Hilbert space d is an integer power of a prime number, then it is possible to find d + 1 mutually unbiased bases. This can be seen in the previous equation, as the prime number decomposition of d simply is d = p n {\displaystyle d=p^{n}} . Therefore, M ( p n ) = p n + 1. {\displaystyle {\mathfrak {M}}(p^{n})=p^{n}+1.} Thus, the maximum number of mutually unbiased bases is known when d is an integer power of a prime number, but it is not known for arbitrary d. The smallest dimension that is not an integer power of a prime is d = 6. This is also the smallest dimension for which the number of mutually unbiased bases is not known. The methods used to determine the number of mutually unbiased bases when d is an integer power of


id: mutually-unbiased-bases-20260505-2
file: data/en.wikipedia.org/wiki/Mutually_unbiased_bases-2.md
category: reference
title: Mutually unbiased bases
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mutually_unbiased_bases
date_saved: 2026-05-05T11:05:48.549584+00:00
instance: kb-cron
parent: mutually-unbiased-bases-20260505-0
summary:
{ | a ⟩ | a ∈ F d } {\displaystyle \{|a\rangle |a\in \mathbb {F} _{d}\}} . We define the operators X a ^ {\displaystyle {\hat {X_{a}}}} and Z b ^ {\displaystyle {\hat {Z_{b}}}} in the following way X a ^ = ∑ c ∈ F d | c + a ⟩ ⟨ c | {\displaystyle {\hat {X_{a}}}=\sum _{c\in \mathbb {F} _{d}}|c+a\rangle \langle c|} Z b ^ = ∑ c ∈ F d χ ( b c ) | c ⟩ ⟨ c | {\displaystyle {\hat {Z_{b}}}=\sum _{c\in \mathbb {F} _{d}}\chi (bc)|c\rangle \langle c|} where χ ( θ ) = exp ⁡ [ 2 π i p ( θ + θ p + θ p 2 + ⋯ + θ p r − 1 ) ] , {\displaystyle \chi (\theta )=\exp \left[{\frac {2\pi i}{p}}\left(\theta +\theta ^{p}+\theta ^{p^{2}}+\cdots +\theta ^{p^{r-1}}\right)\right],} is an additive character over the field and the addition and multiplication in the kets and χ ( ⋅ ) {\displaystyle \chi (\cdot )} is that of F d {\displaystyle \mathbb {F} _{d}} . Then we form d + 1 sets of commuting unitary operators: { Z s ^ | s ∈ F d } {\displaystyle \{{\hat {Z_{s}}}|s\in \mathbb {F} _{d}\}}


id: mutually-unbiased-bases-20260505-3
file: data/en.wikipedia.org/wiki/Mutually_unbiased_bases-3.md
category: reference
title: Mutually unbiased bases
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mutually_unbiased_bases
date_saved: 2026-05-05T11:05:48.549584+00:00
instance: kb-cron
parent: mutually-unbiased-bases-20260505-0
summary:
== Infinite dimension Hilbert spaces == While there has been investigation into mutually unbiased bases in infinite dimension Hilbert space, their existence remains an open question. It is conjectured that in a continuous Hilbert space, two orthonormal bases | ψ s b ⟩ {\displaystyle |\psi _{s}^{b}\rangle } and | ψ s ′ b ′ ⟩ {\displaystyle |\psi _{s'}^{b'}\rangle } are said to be mutually unbiased if | ⟨ ψ s b | ψ s ′ b ′ ⟩ | 2 = k > 0 , s , s ′ ∈ R {\displaystyle |\langle \psi _{s}^{b}|\psi _{s'}^{b'}\rangle |^{2}=k>0,s,s'\in \mathbb {R} } For the generalized position and momentum eigenstates | q ⟩ , q ∈ R {\displaystyle |q\rangle ,q\in \mathbb {R} } and | p ⟩ , p ∈ R {\displaystyle |p\rangle ,p\in \mathbb {R} } , the value of k is | ⟨ q | p ⟩ | 2 = 1 2 π ℏ {\displaystyle |\langle q|p\rangle |^{2}={\frac {1}{2\pi \hbar }}} The existence of mutually unbiased bases in a continuous Hilbert space remains open for debate, as further research in their existence is required before any conclusions can be reached. Position states | q ⟩ {\displaystyle |q\rangle } and momentum states


id: naga-fireball-20260505-0
file: data/en.wikipedia.org/wiki/Naga_fireball-0.md
category: reference
title: Naga fireball
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Naga_fireball
date_saved: 2026-05-05T11:05:49.767037+00:00
instance: kb-cron
parent: naga-fireball-20260505-0
summary:
Naga fireballs (Thai: บั้งไฟพญานาค; RTGS: bang fai phaya nak), also known as bung fai phaya nak or "Mekong lights" and formerly "ghost lights", are a phenomenon said to be seen annually on the Mekong River. Glowing balls are alleged to naturally rise from the water high into the air. The balls are said to be reddish and to range in size from smaller sparkles up to the size of basketballs. They quickly rise up to a couple of hundred metres before disappearing. The number of fireballs reported varies between tens and thousands per night. The phenomenon is locally attributed to phaya nak, a giant serpent (Nāga) said to live in the Mekong. == Description == The fireballs are most often reported around the night of Wan Ok Phansa at the end of Vassa in late-October. Naga fireballs have been reported over an approximately 250 km (160 mi) long section of the Mekong River centered approximately on Phon Phisai in the Phon Phisai District. Fireballs have also been reported rising from smaller rivers, lakes and ponds in the region. The fireballs were called "ghost lights" by locals until the mid-1980s, when the local council officially named them "phaya nak lights". In


id: navier-stokes-existence-and-smoothness-20260505-0
file: data/en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness-0.md
category: reference
title: Navier–Stokes existence and smoothness
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
date_saved: 2026-05-05T11:05:51.019518+00:00
instance: kb-cron
parent: navier-stokes-existence-and-smoothness-20260505-0
summary:
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier–Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. Even more basic (and seemingly intuitive) properties of the solutions to Navier–Stokes have never been proven. For the three-dimensional system of equations, and given some initial conditions, mathematicians have neither proved that smooth solutions always exist, nor found any counter-examples. This is called the Navier–Stokes existence and smoothness problem. Since understanding the Navier–Stokes equations is considered to be the first step to understanding the elusive phenomenon of turbulence, the Clay Mathematics Institute in May 2000 made this problem one of its seven Millennium Prize problems in mathematics. It offered a US$1,000,000 prize to the first person providing a solution for a specific statement of the problem: Prove or give a counter-example of the following statement: In three space dimensions


id: navier-stokes-existence-and-smoothness-20260505-1
file: data/en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness-1.md
category: reference
title: Navier–Stokes existence and smoothness
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
date_saved: 2026-05-05T11:05:51.019518+00:00
instance: kb-cron
parent: navier-stokes-existence-and-smoothness-20260505-0
summary:
Due to this last property, the solutions for the Navier–Stokes equations are searched in the set of solenoidal ("divergence-free") functions. For this flow of a homogeneous medium, density and viscosity are constants. Since only its gradient appears, the pressure p can be eliminated by taking the curl of both sides of the Navier–Stokes equations. In this case the Navier–Stokes equations reduce to the vorticity-transport equations. The Navier–Stokes equations are nonlinear, meaning that the terms in the equations do not have a simple linear relationship with each other. This means that the equations cannot be solved using traditional linear techniques, and more advanced methods must be used instead. This nonlinearity allows the equations to describe a wide range of fluid dynamics phenomena, including the formation of shock waves and other complex flow patterns. One way to understand the nonlinearity of the Navier–Stokes equations is to consider the term ( v ⋅ ∇ ) v {\displaystyle (\mathbf {v} \cdot \nabla )\mathbf {v} } in the equations. This term represents the acceleration of the fluid, and it is a product of the velocity vector v and the gradient operator ∇. Because the gradient operator is a linear operator, the term (v · ∇)v


id: navier-stokes-existence-and-smoothness-20260505-2
file: data/en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness-2.md
category: reference
title: Navier–Stokes existence and smoothness
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
date_saved: 2026-05-05T11:05:51.019518+00:00
instance: kb-cron
parent: navier-stokes-existence-and-smoothness-20260505-0
summary:
d U i d t = − 1 ρ ∑ j = 1 N ( ∂ p ∂ x ) j ∫ Ω ϕ j ∂ ϕ i ∂ x d Ω + ν ∑ j = 1 N ∫ Ω ( ∂ 2 u ∂ x 2 ) ϕ j ∂ 2 ϕ i ∂ x 2 d Ω + ∫ Ω f x ϕ i d Ω {\displaystyle {\frac {dU_{i}}{dt}}=-{\frac {1}{\rho }}\sum _{j=1}^{N}\left({\frac {\partial p}{\partial x}}\right)j\int {\Omega }\phi _{j}{\frac {\partial \phi _{i}}{\partial x}}d\Omega +\nu \sum _{j=1}^{N}\int _{\Omega }\left({\frac {\partial ^{2}u}{\partial x^{2}}}\right)\phi _{j}{\frac {\partial ^{2}\phi _{i}}{\partial x^{2}}}d\Omega +\int {\Omega }f_{x}\phi _{i}d\Omega } where Ω {\displaystyle \Omega } is the domain, and the integrals are over the domain. This system of ordinary differential equations can be solved using techniques such as the finite element method or spectral methods. Here, we will use the finite difference method. To do this, we can divide the time interval [ t 0 , t f ] {\displaystyle [t_{0},t_{f}]} into a series of smaller time steps, and approximate the derivative at each time step using a finite difference formula: U i + 1 − U i Δ t ≈ − 1 ρ ∑ j =


id: navier-stokes-existence-and-smoothness-20260505-3
file: data/en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness-3.md
category: reference
title: Navier–Stokes existence and smoothness
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
date_saved: 2026-05-05T11:05:51.019518+00:00
instance: kb-cron
parent: navier-stokes-existence-and-smoothness-20260505-0
summary:
There exists a constant E ∈ ( 0 , ∞ ) {\displaystyle E\in (0,\infty )} such that ∫ R 3 | v ( x , t ) | 2 d x < E {\displaystyle \int _{\mathbb {R} ^{3}}\vert \mathbf {v} (x,t)\vert ^{2}\,dx<E} for all t ≥ 0 . {\displaystyle t\geq 0\,.} Condition 1 implies that the functions are smooth and globally defined and condition 2 means that the kinetic energy of the solution is globally bounded. === The Millennium Prize conjectures in the whole space === (A) Existence and smoothness of the Navier–Stokes solutions in R 3 {\displaystyle \mathbb {R} ^{3}} Let f ( x , t ) ≡ 0 {\displaystyle \mathbf {f} (x,t)\equiv 0} . For any initial condition v 0 ( x ) {\displaystyle \mathbf {v} _{0}(x)} satisfying the above hypotheses there exist smooth and globally defined solutions to the Navier–Stokes equations, i.e. there is a velocity vector v ( x , t ) {\displaystyle \mathbf {v} (x,t)} and a pressure p ( x , t ) {\displaystyle p(x,t)} satisfying conditions 1 and 2 above. (B) Breakdown of the Navier–Stokes solutions in R 3 {\displaystyle \mathbb {R} ^{3}} There exists an initial condition v 0 ( x )


id: navier-stokes-existence-and-smoothness-20260505-4
file: data/en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness-4.md
category: reference
title: Navier–Stokes existence and smoothness
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
date_saved: 2026-05-05T11:05:51.019518+00:00
instance: kb-cron
parent: navier-stokes-existence-and-smoothness-20260505-0
summary:
where ρ {\displaystyle \rho } is the density, ν {\displaystyle \nu } is the kinematic viscosity, and f ( x , y , t ) = ( f x ( x , y , t ) , f y ( x , y , t ) ) {\displaystyle \mathbf {f} (x,y,t)=(f_{x}(x,y,t),f_{y}(x,y,t))} is an external force. The boundary conditions might specify that the velocity is fixed at the walls of the domain, or that the pressure is fixed at certain points. To solve these equations numerically, we can divide the domain into a series of smaller elements, and solve the equations locally within each element. For example, using a finite element method, we might represent the velocity and pressure fields as: u ( x , y , t ) = ∑ i = 1 N U i ( t ) ϕ i ( x , y ) {\displaystyle u(x,y,t)=\sum _{i=1}^{N}U_{i}(t)\phi _{i}(x,y)} v ( x , y , t ) = ∑ i = 1 N V i ( t ) ϕ i ( x , y ) {\displaystyle v(x,y,t)=\sum _{i=1}^{N}V_{i}(t)\phi _{i}(x,y)} p ( x , y , t ) = ∑ i = 1 N P i ( t ) ϕ


id: navier-stokes-existence-and-smoothness-20260505-5
file: data/en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness-5.md
category: reference
title: Navier–Stokes existence and smoothness
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
date_saved: 2026-05-05T11:05:51.019518+00:00
instance: kb-cron
parent: navier-stokes-existence-and-smoothness-20260505-0
summary:
== Partial results == In 1934, Jean Leray proved that there are smooth and globally defined solutions to the Navier–Stokes equations under the assumption that the initial velocity v 0 ( x ) {\displaystyle \mathbf {v} _{0}(x)} is sufficiently small. He also proved the existence of so-called weak solutions to the Navier–Stokes equations, which may not satisfy the equations pointwise but do satisfy them in mean value. In the 1960s, the finite difference method was proven to be convergent for the Navier–Stokes equations and the equations were numerically solved. It was also proven that there are smooth and globally defined solutions to the Navier–Stokes equations in 2 dimensions. It is known that given an initial velocity v 0 ( x ) {\displaystyle \mathbf {v} _{0}(x)} there exists a finite "blowup time" T, depending on v 0 ( x ) {\displaystyle \mathbf {v} _{0}(x)} , such that the Navier–Stokes equations on R 3 × ( 0 , T ) {\displaystyle \mathbb {R} ^{3}\times (0,T)} have smooth solutions v ( x , t ) {\displaystyle \mathbf {v} (x,t)} and p ( x , t ) {\displaystyle p(x,t)} . These solutions may, however, not hold for values of t {\displaystyle t} beyond the


id: numerical-sign-problem-20260505-0
file: data/en.wikipedia.org/wiki/Numerical_sign_problem-0.md
category: reference
title: Numerical sign problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Numerical_sign_problem
date_saved: 2026-05-05T11:06:08.014515+00:00
instance: kb-cron
parent: numerical-sign-problem-20260505-0
summary:
In applied mathematics, the numerical sign problem is the problem of numerically evaluating the integral of a highly oscillatory function of a large number of variables. Numerical methods fail because of the near-cancellation of the positive and negative contributions to the integral. Each has to be integrated to very high precision in order for their difference to be obtained with useful accuracy. The sign problem is one of the major unsolved problems in the physics of many-particle systems. It often arises in calculations of the properties of a quantum mechanical system with large number of strongly interacting fermions, or in field theories involving a non-zero density of strongly interacting fermions. == Overview == In physics the sign problem is typically (but not exclusively) encountered in calculations of the properties of a quantum mechanical system with large number of strongly interacting fermions, or in field theories involving a non-zero density of strongly interacting fermions. Because the particles are strongly interacting, perturbation theory is inapplicable, and one is forced to use brute-force numerical methods. Because the particles are fermions, their wavefunction changes sign when any two fermions are interchanged (due to the anti-symmetry of the wave function, see Pauli principle). So unless


id: numerical-sign-problem-20260505-1
file: data/en.wikipedia.org/wiki/Numerical_sign_problem-1.md
category: reference
title: Numerical sign problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Numerical_sign_problem
date_saved: 2026-05-05T11:06:08.014515+00:00
instance: kb-cron
parent: numerical-sign-problem-20260505-0
summary:
⟨ A ⟩ ρ = ∫ D σ A [ σ ] exp ⁡ ( i θ [ σ ] ) p [ σ ] ∫ D σ exp ⁡ ( i θ [ σ ] ) p [ σ ] = ⟨ A [ σ ] exp ⁡ ( i θ [ σ ] ) ⟩ p ⟨ exp ⁡ ( i θ [ σ ] ) ⟩ p . {\displaystyle \langle A\rangle _{\rho }={\frac {\int D\sigma A[\sigma ]\exp(i\theta [\sigma ])\,p[\sigma ]}{\int D\sigma \exp(i\theta [\sigma ])\,p[\sigma ]}}={\frac {\langle A[\sigma ]\exp(i\theta [\sigma ])\rangle _{p}}{\langle \exp(i\theta [\sigma ])\rangle _{p}}}.} Note that the desired expectation value is now a ratio where the numerator and denominator are expectation values that both use a positive weighting function p [ σ ] {\displaystyle p[\sigma ]} . However, the phase exp ⁡ ( i θ [ σ ] ) {\displaystyle \exp(i\theta [\sigma ])} is a highly oscillatory function in the configuration space, so if one uses Monte Carlo methods to evaluate the numerator and denominator, each of them will evaluate to a very small number, whose exact value is swamped by the noise inherent in the Monte Carlo sampling process. The "badness" of the sign problem


id: physics-beyond-the-standard-model-20260505-0
file: data/en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model-0.md
category: reference
title: Physics beyond the Standard Model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model
date_saved: 2026-05-05T11:06:09.206638+00:00
instance: kb-cron
parent: physics-beyond-the-standard-model-20260505-0
summary:
Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the Standard Model, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itself: the Standard Model is inconsistent with that of general relativity, and one or both theories break down under certain conditions, such as spacetime singularities like the Big Bang and black hole event horizons. Theories that lie beyond the Standard Model include various extensions of the standard model through supersymmetry, such as the Minimal Supersymmetric Standard Model (MSSM) and Next-to-Minimal Supersymmetric Standard Model (NMSSM), and entirely novel explanations, such as string theory, M-theory, and extra dimensions. As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the "best step" towards a Theory of Everything, can only be settled via experiments, and is one of the most active areas of research in both theoretical and experimental physics. == Problems with the Standard Model == Despite being the


id: physics-beyond-the-standard-model-20260505-1
file: data/en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model-1.md
category: reference
title: Physics beyond the Standard Model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model
date_saved: 2026-05-05T11:06:09.206638+00:00
instance: kb-cron
parent: physics-beyond-the-standard-model-20260505-0
summary:
B meson decay etc. – results from a BaBar experiment may suggest a surplus over Standard Model predictions of a type of particle decay ( B → D(*) τ− ντ ). In this, an electron and positron collide, resulting in a B meson and an antimatter B meson, which then decays into a D meson and a tau lepton as well as a tau antineutrino. While the level of certainty of the excess (3.4 σ in statistical jargon) is not enough to declare a break from the Standard Model, the results are a potential sign of something amiss and are likely to affect existing theories, including those attempting to deduce the properties of Higgs bosons. In 2015, LHCb reported observing a 2.1 σ excess in the same ratio of branching fractions. The Belle experiment also reported an excess. In 2017 a meta analysis of all available data reported a cumulative 5 σ deviation from SM. Neutron lifetime puzzle – Free neutrons are not stable but decay after some time. Currently there are two methods used to measure this lifetime ("bottle" versus "beam") that give different values not within each other's error margin. Currently the lifetime from the bottle method is


id: physics-beyond-the-standard-model-20260505-2
file: data/en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model-2.md
category: reference
title: Physics beyond the Standard Model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model
date_saved: 2026-05-05T11:06:09.206638+00:00
instance: kb-cron
parent: physics-beyond-the-standard-model-20260505-0
summary:
Hierarchy problem – the Standard Model introduces particle masses through a process known as spontaneous symmetry breaking caused by the Higgs field. Within the Standard Model, the mass of the Higgs particle gets some very large quantum corrections due to the presence of virtual particles (mostly virtual top quarks). These corrections are much larger than the actual mass of the Higgs. This means that the bare mass parameter of the Higgs in the Standard Model must be fine tuned in such a way that almost completely cancels the quantum corrections. This level of fine-tuning is deemed unnatural by many theorists. The problem cannot be formulated in the strict context of the Standard Model, for the Higgs mass cannot be calculated. In a sense, the problem amounts to the worry that a future theory of fundamental particles, in which the Higgs boson mass will be calculable, should not have excessive fine-tunings. Number of parameters – the Standard Model depends on 19 parameter numbers. Their values are known from experiment, but the origin of the values is unknown. Some theorists have tried to find relations between different parameters, for example, between the masses of particles in different generations or calculating particle masses,


id: physics-beyond-the-standard-model-20260505-3
file: data/en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model-3.md
category: reference
title: Physics beyond the Standard Model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model
date_saved: 2026-05-05T11:06:09.206638+00:00
instance: kb-cron
parent: physics-beyond-the-standard-model-20260505-0
summary:
== Neutrinos == In the Standard Model, neutrinos cannot spontaneously change flavor. Measurements however indicated that neutrinos do spontaneously change flavor, in what is called neutrino oscillations. Neutrino oscillations are usually explained using massive neutrinos. In the Standard Model, neutrinos have exactly zero mass, as the Standard Model only contains left-handed neutrinos. With no suitable right-handed partner, it is impossible to add a renormalizable mass term to the Standard Model. These measurements only give the mass differences between the different flavours. The best constraint on the absolute mass of the neutrinos comes from precision measurements of tritium decay, providing an upper limit 2 eV, which makes them at least five orders of magnitude lighter than the other particles in the Standard Model. This necessitates an extension of the Standard Model, which not only needs to explain how neutrinos get their mass, but also why the mass is so small. One approach to add masses to the neutrinos, the so-called seesaw mechanism, is to add right-handed neutrinos and have these couple to left-handed neutrinos with a Dirac mass term. The right-handed neutrinos have to be sterile, meaning that they do not participate in any of the Standard Model interactions. Because they


id: physics-beyond-the-standard-model-20260505-4
file: data/en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model-4.md
category: reference
title: Physics beyond the Standard Model
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model
date_saved: 2026-05-05T11:06:09.206638+00:00
instance: kb-cron
parent: physics-beyond-the-standard-model-20260505-0
summary:
Extensions, revisions, replacements, and reorganizations of the Standard Model exist in attempt to correct for these and other issues. String theory is one such reinvention, and many theoretical physicists think that such theories are the next theoretical step toward a true Theory of Everything. Among the numerous variants of string theory, M-theory, whose mathematical existence was first proposed at a String Conference in 1995 by Edward Witten, is believed by many to be a proper "ToE" candidate, notably by physicists Brian Greene and Stephen Hawking. Though a full mathematical description is not yet known, solutions to the theory exist for specific cases. Recent works have also proposed alternate string models, some of which lack the various harder-to-test features of M-theory (e.g. the existence of Calabi–Yau manifolds, many extra dimensions, etc.) including works by well-published physicists such as Lisa Randall. === Unified Gravity === Unified Gravity treats gravity as a gauge field from a set of compact U(1) symmetries in an extended spinor space. This allows creating a Lagrangian that contains all known fundamental interactions of nature. == See also == == Footnotes == == References == == Further reading == Lisa Randall (2005). Warped Passages: Unraveling the Mysteries of the


id: proton-spin-crisis-20260505-0
file: data/en.wikipedia.org/wiki/Proton_spin_crisis-0.md
category: reference
title: Proton spin crisis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Proton_spin_crisis
date_saved: 2026-05-05T11:06:11.743787+00:00
instance: kb-cron
parent: proton-spin-crisis-20260505-0
summary:
The proton spin crisis (or proton spin puzzle) is a theoretical crisis precipitated by a 1987 experiment by the European Muon Collaboration (EMC), which tried to determine the distribution of spin within the proton. Physicists expected that the quarks carry all of a proton's spin. However, not only was the total proton spin carried by quarks far smaller than 100%, these results were consistent with almost zero (4–24%) proton spin being carried by quarks. This surprising and puzzling result was termed the "proton spin crisis". The problem is considered one of the important unsolved problems in physics. == Background == A key question is how the nucleons' spins are distributed amongst their constituent parts ("partons": quarks and gluons). The components of the proton's spin are the expectation values of the individual sources of angular momentum. These values depend on the renormalization scale, because their operators are not separately conserved. Physicists originally expected that valence quarks would carry all of the nucleon spin. A proton is built from three valence quarks (two up quarks and one down quark), virtual gluons, and virtual (or sea) quarks and antiquarks (virtual particles do not influence the proton's quantum numbers). The ruling hypothesis was that


id: qcd-matter-20260505-0
file: data/en.wikipedia.org/wiki/QCD_matter-0.md
category: reference
title: QCD matter
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/QCD_matter
date_saved: 2026-05-05T11:06:12.997806+00:00
instance: kb-cron
parent: qcd-matter-20260505-0
summary:
Quark matter or QCD matter refers to matter governed by quantum chromodynamics and involving quarks and gluons. At different temperatures and densities quark matter takes different forms, including a hadron gas, nuclear matter, quark-gluon plasma, and regions of color superconductivity. Quarks are liberated into quark matter at extremely high temperatures and/or densities, and some of them are still only theoretical as they require conditions so extreme that they cannot be produced in any laboratory, especially not at equilibrium conditions. Under these extreme conditions, the familiar structure of matter, where the basic constituents are nuclei (consisting of nucleons which are bound states of quarks) and electrons, is disrupted. In quark matter it is more appropriate to treat the quarks themselves as the basic degrees of freedom. In the Standard Model of particle physics, the strong force is described by the theory of QCD. At ordinary temperatures or densities this force just confines the quarks into composite particles (hadrons) of size around 10−15 m = 1 femtometer = 1 fm (corresponding to the QCD energy scale ΛQCD ≈ 200 MeV) and its effects are not noticeable at longer distances. However, when the temperature reaches the QCD energy scale (T of order 1012


id: qcd-matter-20260505-1
file: data/en.wikipedia.org/wiki/QCD_matter-1.md
category: reference
title: QCD matter
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/QCD_matter
date_saved: 2026-05-05T11:06:12.997806+00:00
instance: kb-cron
parent: qcd-matter-20260505-0
summary:
== Thermodynamics == The context for understanding the thermodynamics of quark matter is the Standard Model of particle physics, which contains six different flavors of quarks, as well as leptons like electrons and neutrinos. These interact via the strong interaction, electromagnetism, and also the weak interaction which allows one flavor of quark to turn into another. Electromagnetic interactions occur between particles that carry electrical charge; strong interactions occur between particles that carry color charge. The correct thermodynamic treatment of quark matter depends on the physical context. For large quantities that exist for long periods of time (the "thermodynamic limit"), we must take into account the fact that the only conserved charges in the standard model are quark number (equivalent to baryon number), electric charge, the eight color charges, and lepton number. Each of these can have an associated chemical potential. However, large volumes of matter must be electrically and color-neutral, which determines the electric and color charge chemical potentials. This leaves a three-dimensional phase space, parameterized by quark chemical potential, lepton chemical potential, and temperature. In compact stars quark matter would occupy cubic kilometers and exist for millions of years, so the thermodynamic limit is appropriate. However, the neutrinos escape,


id: qcd-matter-20260505-2
file: data/en.wikipedia.org/wiki/QCD_matter-2.md
category: reference
title: QCD matter
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/QCD_matter
date_saved: 2026-05-05T11:06:12.997806+00:00
instance: kb-cron
parent: qcd-matter-20260505-0
summary:
== Theoretical challenges: calculation techniques == The phase structure of quark matter remains mostly conjectural because it is difficult to perform calculations predicting the properties of quark matter. The reason is that QCD, the theory describing the dominant interaction between quarks, is strongly coupled at the densities and temperatures of greatest physical interest, and hence it is very hard to obtain any predictions from it. Here are brief descriptions of some of the standard approaches. === Lattice gauge theory === The only first-principles calculational tool currently available is lattice QCD, i.e. brute-force computer calculations. Because of a technical obstacle known as the fermion sign problem, this method can only be used at low density and high temperature (μ < T), and it predicts that the crossover to the quark–gluon plasma will occur around T = 150 MeV However, it cannot be used to investigate the interesting color-superconducting phase structure at high density and low temperature. === Weak coupling theory === Because QCD is asymptotically free it becomes weakly coupled at unrealistically high densities, and diagrammatic methods can be used. Such methods show that the CFL phase occurs at very high density. At high temperatures, however, diagrammatic methods are still not


id: quark-star-20260505-0
file: data/en.wikipedia.org/wiki/Quark_star-0.md
category: reference
title: Quark star
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quark_star
date_saved: 2026-05-05T11:06:14.297455+00:00
instance: kb-cron
parent: quark-star-20260505-0
summary:
A quark star is a hypothetical type of compact, exotic star, where extremely high core temperature and pressure have forced nuclear particles to form quark matter, a continuous state of matter consisting of free quarks. == Background == Some massive stars collapse to form neutron stars at the end of their life cycle, as has been both observed and explained theoretically. Under the extreme temperatures and pressures inside neutron stars, the neutrons are normally kept apart by a degeneracy pressure, stabilizing the star and hindering further gravitational collapse. However, it is hypothesized that under even more extreme temperature and pressure, the degeneracy pressure of the neutrons is overcome, and the neutrons are forced to merge and dissolve into their constituent quarks, creating an ultra-dense phase of quark matter based on densely packed quarks. In this state, a new equilibrium is supposed to emerge, as a new degeneracy pressure between the quarks, as well as repulsive electromagnetic forces, will occur and hinder total gravitational collapse that would form a stellar black hole. If these ideas are correct, quark stars might occur, and be observable, somewhere in the universe. Numerical simulations of the physics inside neutron stars predict quark deconfinement is likely.Such


id: quark-star-20260505-1
file: data/en.wikipedia.org/wiki/Quark_star-1.md
category: reference
title: Quark star
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quark_star
date_saved: 2026-05-05T11:06:14.297455+00:00
instance: kb-cron
parent: quark-star-20260505-0
summary:
At least under the assumptions mentioned above, the probability of a given neutron star being a quark star is low, so in the Milky Way there would only be a small population of quark stars. If it is correct, however, that overdense neutron stars can turn into quark stars, that makes the possible number of quark stars higher than was originally thought, as observers would be looking for the wrong type of star. A neutron star without deconfinement to quarks and higher densities cannot have a rotational period shorter than a millisecond; even with the unimaginable gravity of such a condensed object the centrifugal force of faster rotation would eject matter from the surface, so detection of a pulsar of millisecond or less period would be strong evidence of a quark star. Observations released by the Chandra X-ray Observatory on April 10, 2002, detected two possible quark stars, designated RX J1856.5−3754 and 3C 58, which had previously been thought to be neutron stars. Based on the known laws of physics, the former appeared much smaller and the latter much colder than it should be, suggesting that they are composed of material denser than neutron-degenerate matter. However, these observations are met


id: shower-curtain-effect-20260505-0
file: data/en.wikipedia.org/wiki/Shower-curtain_effect-0.md
category: reference
title: Shower-curtain effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Shower-curtain_effect
date_saved: 2026-05-05T11:06:15.549332+00:00
instance: kb-cron
parent: shower-curtain-effect-20260505-0
summary:
The shower-curtain effect in physics describes the phenomenon of a shower curtain being blown inward when a shower is running. The problem of identifying the cause of this effect has been featured in Scientific American magazine, with several hypotheses given to explain the phenomenon but no definite conclusion. == Hypotheses == === Buoyancy hypothesis === Also called chimney effect or stack effect, observes that warm air (from the hot shower) rises out over the shower curtain as cooler air (near the floor) pushes in under the curtain to replace the rising air. By pushing the curtain in towards the shower, the (short range) vortex and Coandă effects become more significant. However, the shower-curtain effect persists when cold water is used, implying that this is not the sole mechanism. === Bernoulli effect hypothesis === The most popular explanation given for the shower-curtain effect is Bernoulli's principle. Bernoulli's principle states that an increase in velocity results in a decrease in pressure. This theory presumes that the water flowing out of a shower head causes the air through which the water moves to start flowing in the same direction as the water. This movement would be parallel to the plane of the shower


id: sic-povm-20260505-0
file: data/en.wikipedia.org/wiki/SIC-POVM-0.md
category: reference
title: SIC-POVM
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/SIC-POVM
date_saved: 2026-05-05T11:06:16.798078+00:00
instance: kb-cron
parent: sic-povm-20260505-0
summary:
In the context of quantum mechanics and quantum information theory, symmetric, informationally complete, positive operator-valued measures (SIC-POVMs) are a particular type of generalized measurement (POVM). SIC-POVMs are particularly notable thanks to their defining features of (1) being informationally complete; (2) having the minimal number of outcomes compatible with informational completeness, and (3) being highly symmetric. In this context, informational completeness is the property of a POVM of allowing to fully reconstruct input states from measurement data. The properties of SIC-POVMs make them an interesting candidate for a "standard quantum measurement", utilized in the study of foundational quantum mechanics, most notably in QBism. SIC-POVMs have several applications in the context of quantum state tomography and quantum cryptography, and a possible connection has been discovered with Hilbert's twelfth problem. == Definition == A POVM over a d {\displaystyle d} -dimensional Hilbert space H {\displaystyle {\mathcal {H}}} is a set of m {\displaystyle m} positive-semidefinite operators { F i } i = 1 m {\displaystyle \left\{F_{i}\right\}_{i=1}^{m}} that sum to the identity: ∑ i = 1 m F i = I . {\displaystyle \sum _{i=1}^{m}F_{i}=I.} If a POVM consists of at least d 2 {\displaystyle d^{2}} operators which span the space of self-adjoint operators


id: sic-povm-20260505-1
file: data/en.wikipedia.org/wiki/SIC-POVM-1.md
category: reference
title: SIC-POVM
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/SIC-POVM
date_saved: 2026-05-05T11:06:16.798078+00:00
instance: kb-cron
parent: sic-povm-20260505-0
summary:
ρ = I | ρ ) = ∑ α [ ( d + 1 ) Π α − I ] ( Π α | ρ ) d = ∑ α [ ( d + 1 ) Π α − I ] T r ( Π α ρ ) d = ∑ α p α [ ( d + 1 ) Π α − I ] where p α = T r ( Π α ρ ) / d = − I + ( d + 1 ) ∑ α p α | ψ α ⟩ ⟨ ψ α | = ∑ α [ ( d + 1 ) p α − 1 d ] | ψ α ⟩ ⟨ ψ α | {\displaystyle {\begin{aligned}\rho =I|\rho )&=\displaystyle \sum _{\alpha }\left[(d+1)\Pi _{\alpha }-I\right]{\frac {(\Pi _{\alpha }|\rho )}{d}}\\&=\displaystyle \sum _{\alpha }\left[(d+1)\Pi _{\alpha }-I\right]{\frac {\mathrm {Tr} (\Pi _{\alpha }\rho )}{d}}\\&=\displaystyle \sum _{\alpha }p_{\alpha }\left[(d+1)\Pi _{\alpha }-I\right]\quad {\text{ where }}p_{\alpha }=\mathrm {Tr} (\Pi _{\alpha }\rho )/d\\&=\displaystyle -I+(d+1)\sum _{\alpha }p_{\alpha }|\psi _{\alpha }\rangle \langle \psi _{\alpha }|\\&=\displaystyle \sum _{\alpha }\left[(d+1)p_{\alpha }-{\frac {1}{d}}\right]|\psi _{\alpha }\rangle \langle \psi _{\alpha }|\end{aligned}}} where | ρ ) {\displaystyle |\rho )} is the Dirac notation for the density operator viewed in the


id: sic-povm-20260505-2
file: data/en.wikipedia.org/wiki/SIC-POVM-2.md
category: reference
title: SIC-POVM
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/SIC-POVM
date_saved: 2026-05-05T11:06:16.798078+00:00
instance: kb-cron
parent: sic-povm-20260505-0
summary:
For every dimension d ≥ 2 {\displaystyle d\geq 2} there exists a SIC-POVM whose elements are the orbit of a positive rank-one operator E 0 {\displaystyle E_{0}} under the Weyl–Heisenberg group H d {\displaystyle H_{d}} . What is more, E 0 {\displaystyle E_{0}} commutes with an element T of the Jacobi group J d = H d ⋊ S L ( 2 , Z d ) {\displaystyle J_{d}=H_{d}\rtimes SL(2,\mathbb {Z} _{d})} . The action of T on H d {\displaystyle H_{d}} modulo the center has order three. Utilizing the notion of group covariance on Z d × Z d {\displaystyle \mathbb {Z} _{d}\times \mathbb {Z} _{d}} , this can be restated as For any dimension d ∈ N {\displaystyle d\in \mathbb {N} } , let { k } k = 0 d − 1 {\displaystyle \left\{k\right\}_{k=0}^{d-1}} be an orthonormal basis for C d {\displaystyle \mathbb {C} ^{d}} , and define ω = e 2 π i d , D j , k = ω j k 2 ∑ m = 0 d − 1 ω j m | k + m ( mod d ) ⟩ ⟨ m | {\displaystyle \displaystyle \omega =e^{\frac {2\pi i}{d}},\quad \quad D_{j,k}=\omega ^{\frac {jk}{2}}\sum _{m=0}^{d-1}\omega


id: simon-problems-20260505-0
file: data/en.wikipedia.org/wiki/Simon_problems-0.md
category: reference
title: Simon problems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Simon_problems
date_saved: 2026-05-05T11:06:18.069142+00:00
instance: kb-cron
parent: simon-problems-20260505-0
summary:
In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators that incorporate the Coulomb potential. In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems. Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was, in fact, the Cantor set, a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it. The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984. == Context == Background definitions for the "Coulomb energies" problems ( N {\displaystyle N} non-relativistic particles (electrons) in R 3 {\displaystyle \mathbb {R} ^{3}} with spin 1 / 2 {\displaystyle 1/2} and an infinitely heavy nucleus with charge Z {\displaystyle Z} and Coulombic mutual interaction): H f ( N ) {\displaystyle


id: amorphous-solid-20260505-0
file: data/en.wikipedia.org/wiki/Amorphous_solid-0.md
category: reference
title: Amorphous solid
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Amorphous_solid
date_saved: 2026-05-05T11:06:19.245432+00:00
instance: kb-cron
parent: amorphous-solid-20260505-0
summary:
In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid) is a solid that lacks the long-range order that is a characteristic of a crystal. The terms "glass" and "glassy solid" are sometimes used synonymously with amorphous solid; however, these terms refer specifically to amorphous materials that undergo a glass transition. Examples of amorphous solids include glasses, metallic glasses, and certain types of plastics and polymers. == Etymology == The term "Amorphous" comes from the Greek a ("without"), and morphé ("shape, form"). == Structure == Amorphous materials have an internal structure of molecular-scale structural blocks that can be similar to the basic structural units in the crystalline phase of the same compound. Unlike in crystalline materials, however, no long-range regularity exists: amorphous materials cannot be described by the repetition of a finite unit cell. Statistical measures, such as the atomic density function and radial distribution function, are more useful in describing the structure of amorphous solids. Although amorphous materials lack long range order, they exhibit localized order on small length scales. By convention, short range order extends only to the nearest neighbor shell, typically only 1-2 atomic spacings. Medium range order may extend beyond the short range


id: amorphous-solid-20260505-1
file: data/en.wikipedia.org/wiki/Amorphous_solid-1.md
category: reference
title: Amorphous solid
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Amorphous_solid
date_saved: 2026-05-05T11:06:19.245432+00:00
instance: kb-cron
parent: amorphous-solid-20260505-0
summary:
=== Computational techniques === Simulation and modeling techniques are often combined with experimental methods to characterize structures of amorphous materials. Commonly used computational techniques include density functional theory, molecular dynamics, and reverse Monte Carlo. == Uses and observations == === Amorphous thin films === Amorphous phases are important constituents of thin films. Thin films are solid layers of a few nanometres to tens of micrometres thickness that are deposited onto a substrate. So-called structure zone models were developed to describe the microstructure of thin films as a function of the homologous temperature (Th), which is the ratio of deposition temperature to melting temperature. According to these models, a necessary condition for the occurrence of amorphous phases is that (Th) has to be smaller than 0.3. The deposition temperature must be below 30% of the melting temperature. === Superconductivity === Regarding their applications, amorphous metallic layers played an important role in the discovery of superconductivity in amorphous metals made by Buckel and Hilsch. The superconductivity of amorphous metals, including amorphous metallic thin films, is now understood to be due to phonon-mediated Cooper pairing. The role of structural disorder can be rationalized based on the strong-coupling Eliashberg theory of superconductivity. === Thermal


id: sonoluminescence-20260505-0
file: data/en.wikipedia.org/wiki/Sonoluminescence-0.md
category: reference
title: Sonoluminescence
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonoluminescence
date_saved: 2026-05-05T11:06:20.444802+00:00
instance: kb-cron
parent: sonoluminescence-20260505-0
summary:
Sonoluminescence is luminescence induced by sound waves, such as in the emission of light from imploding bubbles in a liquid when excited by sound. Sonoluminescence is sometimes considered a kind of mechanoluminescence. However, mechanoluminescence is typically defined as pertaining to solids, while sonoluminescence usually pertains to liquids. The related terms acoustoluminescence and sonotriboluminescence have been used to describe sound-induced luminescence in solids (e.g., crystals suspended in slurries). Sonoluminescence was first discovered in 1934 at the University of Cologne. It occurs when a sound wave of sufficient intensity induces a gaseous cavity within a liquid to collapse quickly, emitting a burst of light. The phenomenon can be observed in stable single-bubble sonoluminescence (SBSL) and multi-bubble sonoluminescence (MBSL). In 1960, Peter Jarman proposed that sonoluminescence is thermal in origin and might arise from microshocks within collapsing cavities. Later experiments revealed that the temperature inside the bubble during SBSL could reach up to 12,000 kelvins (11,700 °C; 21,100 °F). The exact mechanism behind sonoluminescence remains unknown, with various hypotheses including hotspot, bremsstrahlung, and collision-induced radiation. Some researchers have even speculated that temperatures in sonoluminescing systems could reach millions of kelvins, potentially causing thermonuclear fusion; this idea, however, has been met with skepticism by


id: sonoluminescence-20260505-1
file: data/en.wikipedia.org/wiki/Sonoluminescence-1.md
category: reference
title: Sonoluminescence
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonoluminescence
date_saved: 2026-05-05T11:06:20.444802+00:00
instance: kb-cron
parent: sonoluminescence-20260505-0
summary:
R R ¨ + 3 2 R ˙ 2 = 1 ρ ( P ∞ ( t ) − P 0 ( t ) − 4 μ R ˙ R − 2 γ R ) {\displaystyle R{\ddot {R}}+{\frac {3}{2}}{\dot {R}}^{2}={\frac {1}{\rho }}\left(P_{\infty }(t)-P_{0}(t)-4\mu {\frac {\dot {R}}{R}}-{\frac {2\gamma }{R}}\right)} This is an approximate equation that is derived from the Navier–Stokes equations (written in spherical coordinate system) and describes the motion of the radius of the bubble R as a function of time t. Here, μ is the viscosity, P ∞ ( t ) {\displaystyle P_{\infty }(t)} is the external pressure infinitely far from the bubble, P 0 ( t ) {\displaystyle P_{0}(t)} is the internal pressure of the bubble, ρ {\displaystyle \rho } is the liquid density, and γ is the surface tension. The over-dots represent time derivatives. This equation, though approximate, has been shown to give good estimates on the motion of the bubble under the acoustically driven field except during the final stages of collapse. Both simulation and experimental measurement show that during the critical final stages of collapse, the bubble wall velocity exceeds the speed of sound of the gas inside the bubble. Thus a more detailed analysis


id: sonoluminescence-20260505-2
file: data/en.wikipedia.org/wiki/Sonoluminescence-2.md
category: reference
title: Sonoluminescence
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonoluminescence
date_saved: 2026-05-05T11:06:20.444802+00:00
instance: kb-cron
parent: sonoluminescence-20260505-0
summary:
== Biological sonoluminescence == Pistol shrimp (also called snapping shrimp) produce a type of cavitation luminescence from a collapsing bubble caused by quickly snapping its claw. The animal snaps a specialized claw shut to create a cavitation bubble that generates acoustic pressures of up to 80 kPa at a distance of 4 cm from the claw. As it extends out from the claw, the bubble reaches speeds of 60 miles per hour (97 km/h) and releases a sound reaching 218 decibels. The pressure is strong enough to kill small fish. The light produced is of lower intensity than the light produced by typical sonoluminescence and is not visible to the naked eye. The light and heat produced by the bubble may have no direct significance, as it is the shockwave produced by the rapidly collapsing bubble which these shrimp use to stun or kill prey. However, it is the first known instance of an animal producing light by this effect and was whimsically dubbed "shrimpoluminescence" upon its discovery in 2001. It has subsequently been discovered that another group of crustaceans, the mantis shrimp, contains species whose club-like forelimbs can strike so quickly and with such force as to induce sonoluminescent


id: strange-matter-20260505-0
file: data/en.wikipedia.org/wiki/Strange_matter-0.md
category: reference
title: Strange matter
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Strange_matter
date_saved: 2026-05-05T11:06:21.627423+00:00
instance: kb-cron
parent: strange-matter-20260505-0
summary:
Strange matter (or strange quark matter) is quark matter containing strange quarks. In extreme environments, strange matter is hypothesized to occur in the core of neutron stars, or, more speculatively, as isolated droplets that may vary in size from femtometers (strangelets) to kilometers, as in the hypothetical strange stars. At high enough density, strange matter is expected to be color superconducting. Ordinary matter, also referred to as atomic matter, is composed of atoms, with nearly all matter concentrated in the atomic nuclei. Nuclear matter is a liquid composed of neutrons and protons, and they are themselves composed of up and down quarks. Quark matter is a condensed form of matter composed entirely of quarks. When quark matter does not contain strange quarks, it is sometimes referred to as non-strange quark matter. == Context == In particle physics and astrophysics, the term 'strange matter' is used in two different contexts, one broader and the other more specific and hypothetical: In the broader context, our current understanding of the laws of nature predicts that strange matter could be created when nuclear matter (made of protons and neutrons) is compressed beyond a critical density. At this critical pressure and density, the protons and


id: strangelet-20260505-0
file: data/en.wikipedia.org/wiki/Strangelet-0.md
category: reference
title: Strangelet
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Strangelet
date_saved: 2026-05-05T11:06:22.905505+00:00
instance: kb-cron
parent: strangelet-20260505-0
summary:
A strangelet (pronounced ) is a hypothetical particle consisting of a bound state of roughly equal numbers of up, down, and strange quarks. An equivalent description is that a strangelet is a small fragment of strange matter, small enough to be considered a particle. The size of an object composed of strange matter could, theoretically, range from a few femtometers across (with the mass of a light nucleus) to arbitrarily large. Once the size becomes macroscopic (on the order of meters across), such an object is usually called a strange star. The term "strangelet" originates with Edward Farhi and Robert Jaffe in 1984. It has been theorized that strangelets can convert matter to strange matter on contact. Strangelets have also been suggested as a dark matter candidate. == Theoretical possibility == === Strange matter hypothesis === The known particles with strange quarks are unstable. Because the strange quark is heavier than the up and down quarks, it can spontaneously decay, via the weak interaction, into an up quark, an electron, and an antineutrino. Consequently, particles containing strange quarks, such as the lambda particle, always lose their strangeness, by decaying into lighter particles containing only up and down quarks. However, condensed


id: strangelet-20260505-1
file: data/en.wikipedia.org/wiki/Strangelet-1.md
category: reference
title: Strangelet
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Strangelet
date_saved: 2026-05-05T11:06:22.905505+00:00
instance: kb-cron
parent: strangelet-20260505-0
summary:
=== Accelerator production === At heavy ion accelerators like the Relativistic Heavy Ion Collider (RHIC), nuclei are collided at relativistic speeds, creating strange and antistrange quarks that could conceivably lead to strangelet production. The experimental signature of a strangelet would be its very high ratio of mass to charge, which would cause its trajectory in a magnetic field to be very nearly, but not quite, straight. The STAR collaboration has searched for strangelets produced at the RHIC, but none were found. The Large Hadron Collider (LHC) is even less likely to produce strangelets, but searches are planned for the LHC ALICE detector. === Space-based detection === The Alpha Magnetic Spectrometer (AMS), an instrument that is mounted on the International Space Station, could detect strangelets. === Possible seismic detection === In May 2002, a group of researchers at Southern Methodist University reported the possibility that strangelets may have been responsible for seismic events recorded on 22 October and 24 November 1993. The authors later retracted their claim, after finding that the clock of one of the seismic stations had a large error during the relevant period. It has been suggested that the International Monitoring System be set up to verify the


id: strangelet-20260505-2
file: data/en.wikipedia.org/wiki/Strangelet-2.md
category: reference
title: Strangelet
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Strangelet
date_saved: 2026-05-05T11:06:22.905505+00:00
instance: kb-cron
parent: strangelet-20260505-0
summary:
== In fiction == One episode of the TV series Odyssey 5 featured an attempt to destroy the planet by intentionally creating negatively charged strangelets in a particle accelerator. The BBC docudrama End Day features a scenario where a particle accelerator in New York City explodes. This creates a strangelet which creates a chain reaction which destroys Earth. The Robert L. Forward story "A Matter Most Strange" included ins collection Indistinguishable from Magic deals with the making of a strangelet in a particle accelerator. In Douglas Preston's 2010 novel Impact, an alien machine creates strangelets. The machine's strangelets impact the Earth and Moon and pass through them. Steve Alten's 2011 novel Phobos, written as the third and final part of his Domain trilogy, presents a fictional story where strangelets are unintentionally created at the LHC and escape from it to destroy the Earth. In Donald E. Westlake's 1992 black-comedy novel Humans, an irritated God sends an angel to Earth to bring about Armageddon by means of using a strangelet created in a particle accelerator to convert the Earth into a quark star. In the 2010 film Quantum Apocalypse, a strangelet approaches the Earth from space. In Hannu Rajaniemi's novel The


id: strong-cp-problem-20260505-0
file: data/en.wikipedia.org/wiki/Strong_CP_problem-0.md
category: reference
title: Strong CP problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Strong_CP_problem
date_saved: 2026-05-05T11:06:24.092448+00:00
instance: kb-cron
parent: strong-cp-problem-20260505-0
summary:
The strong CP problem is a question in particle physics, which brings up the following quandary: why does quantum chromodynamics (QCD) seem to preserve CP-symmetry? In particle physics, CP stands for the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). According to the current mathematical formulation of quantum chromodynamics, a violation of CP-symmetry in strong interactions could occur. However, no violation of the CP-symmetry has ever been seen in any experiment involving only the strong interaction. As there is no known reason in QCD for it to necessarily be conserved, this is a "fine tuning" problem known as the strong CP problem. The strong CP problem is sometimes regarded as an unsolved problem in physics, and has been referred to as "the most underrated puzzle in all of physics." There are several proposed solutions to solve the strong CP problem. The most well-known is Peccei–Quinn theory, involving new pseudoscalar particles called axions. == Theory == CP-symmetry states that physics should be unchanged if particles were swapped with their antiparticles and then left-handed and right-handed particles were also interchanged. This corresponds to performing a charge conjugation transformation and then a parity transformation. The symmetry is known to be broken


id: superconductivity-20260505-0
file: data/en.wikipedia.org/wiki/Superconductivity-0.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T11:06:25.375736+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source. The superconductivity phenomenon was discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes. Like ferromagnetism and atomic spectral lines, superconductivity is a phenomenon which can only be explained by quantum mechanics. It is characterized by the Meissner effect, the complete cancellation of the magnetic field in the interior of the superconductor during its transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics. In 1986, it was discovered that some cuprate-perovskite ceramic materials have a critical temperature above 35 K (−238 °C). It was shortly found (by Ching-Wu Chu) that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K (−181 °C), which was


id: superconductivity-20260505-1
file: data/en.wikipedia.org/wiki/Superconductivity-1.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T11:06:25.375736+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
=== Niobium === The first practical application of superconductivity was developed in 1954 with Dudley Allen Buck's invention of the cryotron. Two superconductors with greatly different values of the critical magnetic field are combined to produce a fast, simple switch for computer elements. Soon after discovering superconductivity in 1911, Kamerlingh Onnes attempted to make an electromagnet with superconducting windings but found that relatively low magnetic fields destroyed superconductivity in the materials he investigated. Much later, in 1955, G. B. Yntema succeeded in constructing a small 0.7-tesla iron-core electromagnet with superconducting niobium wire windings. Then, in 1961, J. E. Kunzler, E. Buehler, F. S. L. Hsu, and J. H. Wernick made the startling discovery that, at 4.2 kelvin, niobium–tin, a compound consisting of three parts niobium and one part tin, was capable of supporting a current density of more than 100,000 amperes per square centimeter in a magnetic field of 8.8 tesla. The alloy was brittle and difficult to fabricate, but niobium–tin proved useful for generating magnetic fields as high as 20 tesla. In 1962, T. G. Berlincourt and R. R. Hake discovered that more ductile alloys of niobium and titanium are suitable for applications up to 10 tesla. Commercial production


id: superconductivity-20260505-2
file: data/en.wikipedia.org/wiki/Superconductivity-2.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T11:06:25.375736+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
=== Theory of operation === A superconductor is conventional if it is driven by electron–phonon interaction and explained by the BCS theory or its extension, the Eliashberg theory. Otherwise, it is unconventional. Alternatively, a superconductor is called unconventional if the superconducting order parameter transforms according to a non-trivial irreducible representation of the system's point group or space group. === Critical temperature === A superconductor is generally considered high-temperature if it reaches a superconducting state above a temperature of 30 K (−243.15 °C); as in the initial discovery by Georg Bednorz and K. Alex Müller. It may also reference materials that transition to superconductivity when cooled using liquid nitrogen – that is, at only Tc > 77 K, although this is generally used only to emphasize that liquid nitrogen coolant is sufficient. Low temperature superconductors refer to materials with a critical temperature below 30 K, and are cooled mainly by liquid helium (Tc > 4.2 K). One exception to this rule is the iron pnictide group of superconductors that display behaviour and properties typical of high-temperature superconductors, yet some of the group have critical temperatures below 30 K. === Material === Superconductor material classes include chemical elements (e.g. mercury or lead),


id: superconductivity-20260505-3
file: data/en.wikipedia.org/wiki/Superconductivity-3.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T11:06:25.375736+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature Tc. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from around 20 K to less than 1 K. Solid mercury, for example, has a critical temperature of 4.2 K. As of 2015, the highest critical temperature found for a conventional superconductor is 203 K for H2S, although high pressures of approximately 90 gigapascals were required. Cuprate superconductors can have much higher critical temperatures: YBa2Cu3O7, one of the first cuprate superconductors to be discovered, has a critical temperature above 90 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The basic physical mechanism responsible for the high critical temperature is not yet clear. However, it is clear that a two-electron pairing is involved, although the nature of the pairing ( s {\displaystyle s} wave vs. d {\displaystyle d} wave) remains controversial. Similarly, at a fixed temperature below the critical temperature, superconducting materials cease to superconduct when an external magnetic field is applied which is greater than the critical magnetic field. This is because the Gibbs free energy


id: superconductivity-20260505-4
file: data/en.wikipedia.org/wiki/Superconductivity-4.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T11:06:25.375736+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
When a superconductor is placed in a weak external magnetic field Ba=Ha, and cooled below its transition temperature, the magnetic field is ejected. The Meissner effect does not cause the field to be completely ejected but instead, the field penetrates the superconductor but only to a very small distance, characterized by a parameter λ, called the London penetration depth, decaying exponentially to zero within the bulk of the material. The Meissner effect is a defining characteristic of superconductivity. For most superconductors, the London penetration depth is on the order of 100 nm. The Meissner effect is sometimes confused with the kind of diamagnetism one would expect in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is applied to a conductor, it will induce an electric current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field. The Meissner effect is distinct from this – it is the spontaneous expulsion that occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled


id: superconductivity-20260505-5
file: data/en.wikipedia.org/wiki/Superconductivity-5.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T11:06:25.375736+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
Superconductors are promising candidate materials for devising fundamental circuit elements of electronic, spintronic, and quantum technologies. One such example is a superconducting diode, in which supercurrent flows along one direction only, that promise dissipationless superconducting and semiconducting-superconducting hybrid technologies. Superconducting magnets are some of the most powerful electromagnets known. They are used in MRI/NMR machines, mass spectrometers, the beam-steering magnets used in particle accelerators and plasma confining magnets in some tokamaks. They can also be used for magnetic separation, where weakly magnetic particles are extracted from a background of less or non-magnetic particles, as in the pigment industries. They can also be used in large wind turbines to overcome the restrictions imposed by high electrical currents, with an industrial grade 3.6 megawatt superconducting windmill generator having been tested successfully in Denmark. In the 1950s and 1960s, superconductors were used to build experimental digital computers using cryotron switches. More recently, superconductors have been used to make digital circuits based on rapid single flux quantum technology and RF and microwave filters for mobile phone base stations. Superconductors are used to build Josephson junctions which are the building blocks of SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. SQUIDs are used


id: tunguska-event-20260505-0
file: data/en.wikipedia.org/wiki/Tunguska_event-0.md
category: reference
title: Tunguska event
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tunguska_event
date_saved: 2026-05-05T11:06:27.907118+00:00
instance: kb-cron
parent: tunguska-event-20260505-0
summary:
The Tunguska event was a large explosion of between 3–50 megatons TNT equivalent that occurred near the Podkamennaya Tunguska River in Yeniseysk Governorate (now Krasnoyarsk Krai), Russia, on the morning of 30 June [O.S. 17 June] 1908. The explosion over the sparsely populated East Siberian taiga felled a large number of trees, over an area of 2,150 km2 (830 sq mi) of forest, and eyewitness accounts suggest up to three people may have died. The explosion is attributed to a meteor air burst, the atmospheric explosion of a stony asteroid about 50–60 m (160–200 ft) wide. The asteroid approached from the east-south-east, probably with a relatively high speed of about 27 km/s; 98,004 km/h (Mach 80). Though the incident is classified as an impact event, the object is thought to have exploded at an altitude of 5–10 km (3–6 mi) rather than hitting the Earth's surface, leaving no impact crater. The Tunguska event is the largest impact event on Earth in recorded history, though much larger impacts are believed to have occurred in prehistoric times, including the Chicxulub impact that ended the Cretaceous period. An explosion of the Tunguska magnitude would be capable of destroying a large metropolitan area. The


id: tunguska-event-20260505-1
file: data/en.wikipedia.org/wiki/Tunguska_event-1.md
category: reference
title: Tunguska event
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tunguska_event
date_saved: 2026-05-05T11:06:27.907118+00:00
instance: kb-cron
parent: tunguska-event-20260505-0
summary:
We had a hut by the river with my brother Chekaren. We were sleeping. Suddenly we both woke up at the same time. Somebody shoved us. We heard whistling and felt strong wind. Chekaren said "Can you hear all those birds flying overhead?" We were both in the hut, couldn't see what was going on outside. Suddenly, I got shoved again, this time so hard I fell into the fire. I got scared. Chekaren got scared too. We started crying out for father, mother, brother, but no one answered. There was noise beyond the hut, we could hear trees falling down. Chekaren and I got out of our sleeping bags and wanted to run out, but then the thunder struck. This was the first thunder. The Earth began to move and rock, the wind hit our hut and knocked it over. My body was pushed down by sticks, but my head was in the clear. Then I saw a wonder: trees were falling, the branches were on fire, it became mighty bright, how can I say this, as if there was a second sun, my eyes were hurting, I even closed them. It was like what the Russians call lightning.


id: tunguska-event-20260505-2
file: data/en.wikipedia.org/wiki/Tunguska_event-2.md
category: reference
title: Tunguska event
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tunguska_event
date_saved: 2026-05-05T11:06:27.907118+00:00
instance: kb-cron
parent: tunguska-event-20260505-0
summary:
== Scientific investigation == Since the 1908 event, an estimated 1,000 scholarly papers (most in Russian) have been published about the Tunguska explosion. Owing to the site's remoteness and the limited instrumentation available at the time of the event, modern scientific interpretations of its cause and magnitude have relied chiefly on damage assessments and geological studies conducted many years after the event. Estimates of its energy have ranged from 3–30 megatons of TNT (13–126 PJ). Not until more than a decade after the event did any scientific analysis of the region take place, in part due to the area's isolation and significant political upheaval affecting Russia in the 1910s. In 1921, the Russian mineralogist Leonid Kulik led a team to the Podkamennaya Tunguska River basin to conduct a survey for the Soviet Academy of Sciences. Although they never visited the central blast area, the many local accounts of the event led Kulik to believe that a giant meteorite impact had caused the event. Upon returning, he persuaded the Soviet government to fund an expedition to the suspected impact zone, based on the prospect of salvaging meteoric iron. Kulik led a scientific expedition to the Tunguska blast site in 1927. He


id: tunguska-event-20260505-3
file: data/en.wikipedia.org/wiki/Tunguska_event-3.md
category: reference
title: Tunguska event
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tunguska_event
date_saved: 2026-05-05T11:06:27.907118+00:00
instance: kb-cron
parent: tunguska-event-20260505-0
summary:
Researcher John Anfinogenov has suggested that a boulder found at the event site, known as "John's stone", is a remnant of the meteorite, but oxygen isotope analysis of the quartzite suggests that it is of hydrothermal origin, and probably related to Permian-Triassic Siberian Traps magmatism. In 2013, a team of researchers published the results of an analysis of micro-samples from a peat bog near the centre of the affected area, which show fragments that may be of extraterrestrial origin. Although it is widely claimed the impact resulted in the felling of over 80 million trees, this was based on a preliminary guess multiplying tree density by impacted area that overestimated the area of devastation by a factor of four, so is likely to be incorrect. The largest accurately recorded felled trees are around 44 cm (17 in) in trunk diameter and not around 1 m (3.3 ft) that has been claimed by some sources. The observations of decreased atmospheric transparency at the Mount Wilson Observatory in California have been used to calculate that roughly a million tons of dust were released into the stratosphere. Further modelling suggests that shock waves from the falling meteor generated up to 30 Mt of


id: tunguska-event-20260505-4
file: data/en.wikipedia.org/wiki/Tunguska_event-4.md
category: reference
title: Tunguska event
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tunguska_event
date_saved: 2026-05-05T11:06:27.907118+00:00
instance: kb-cron
parent: tunguska-event-20260505-0
summary:
==== Asteroid or comet ==== In 1930, the British meteorologist and mathematician F. J. W. Whipple suggested that the Tunguska body was a small comet. A comet is composed of dust and volatiles, such as water ice and frozen gases, and could have been completely vaporised by the impact with Earth's atmosphere, leaving no obvious traces. The comet hypothesis was further supported by the glowing skies (or "skyglows" or "bright nights") observed across Eurasia for several evenings after the impact, which are possibly explained by dust and ice that had been dispersed from the comet's tail across the upper atmosphere. The cometary hypothesis gained a general acceptance among Soviet Tunguska investigators by the 1960s. In 1978, Slovak astronomer Ľubor Kresák suggested that the body was a fragment of Comet Encke, a periodic comet with a period of just over three years that stays entirely within Jupiter's orbit. It is also responsible for the Beta Taurids, an annual meteor shower with a maximum activity around 28–29 June. The Tunguska event coincided with that shower's peak activity, the Tunguska object's approximate trajectory is consistent with what would be expected from a fragment of Comet Encke, and a hypothetical risk corridor has now


id: tunguska-event-20260505-5
file: data/en.wikipedia.org/wiki/Tunguska_event-5.md
category: reference
title: Tunguska event
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tunguska_event
date_saved: 2026-05-05T11:06:27.907118+00:00
instance: kb-cron
parent: tunguska-event-20260505-0
summary:
==== Chelyabinsk meteor ==== The February 2013 Chelyabinsk bolide event provided ample data for scientists to create new models for the Tunguska event. Researchers used data from both Tunguska and Chelyabinsk to perform a statistical study of over 50 million combinations of bolide and entry properties that could produce Tunguska-scale damage when breaking apart or exploding at similar altitudes. Some models focused on combinations of properties which created scenarios with similar effects to the tree-fall pattern as well as the atmospheric and seismic pressure waves of Tunguska. Four different computer models produced similar results; they concluded that the likeliest candidate for the Tunguska impactor was a stony body between 50–80 m (164–262 ft) in diameter, entering the atmosphere at roughly 55,000 km/h (34,000 mph), exploding at 10–14 km (6–9 mi) altitude, and releasing explosive energy equivalent to between 10–30 megatons. This is similar to the blast energy equivalent of the 1980 volcanic eruption of Mount St. Helens. The researchers also concluded impactors of this size hit the Earth only at an average interval scale of millennia. ==== Lake Cheko ==== In June 2007, scientists from the University of Bologna identified a lake in the Tunguska region as a possible impact


id: tunguska-event-20260505-6
file: data/en.wikipedia.org/wiki/Tunguska_event-6.md
category: reference
title: Tunguska event
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Tunguska_event
date_saved: 2026-05-05T11:06:27.907118+00:00
instance: kb-cron
parent: tunguska-event-20260505-0
summary:
=== Geophysical hypotheses === Though scientific consensus is that the Tunguska explosion was caused by the impact of a small asteroid, there are some dissenters. Astrophysicist Wolfgang Kundt has proposed that the Tunguska event was caused by the release and subsequent explosion of 10 million tons of natural gas from within the Earth's crust. The basic idea is that natural gas leaked out of the crust and then rose to its equal-density height in the atmosphere; from there, it drifted downwind, in a sort of wick, which eventually found an ignition source such as lightning. Once the gas was ignited, the fire streaked along the wick, and then down to the source of the leak in the ground, whereupon there was an explosion. The similar verneshot hypothesis has also been proposed as a possible cause of the Tunguska event. Other research has proposed a geophysical mechanism for the event. == Similar event == A smaller air burst occurred over a populated area on 15 February 2013, at Chelyabinsk in the Ural district of Russia. The exploding meteoroid was determined to have been an asteroid that measured about 17–20 m (56–66 ft) across. It had an estimated initial mass of 11,000


id: unified-field-theory-20260505-0
file: data/en.wikipedia.org/wiki/Unified_field_theory-0.md
category: reference
title: Unified field theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Unified_field_theory
date_saved: 2026-05-05T11:06:29.038086+00:00
instance: kb-cron
parent: unified-field-theory-20260505-0
summary:
In physics, a Unified Field Theory (UFT) is a type of field theory that allows all fundamental forces of nature, including gravity, and all elementary particles to be written in terms of a single physical field. According to quantum field theory, particles are themselves the quanta of fields. Different fields in physics include vector fields such as the electromagnetic field, spinor fields whose quanta are fermionic particles such as electrons, and tensor fields such as the metric tensor field that describes the shape of spacetime and gives rise to gravitation in general relativity. Unified field theories attempt to organize these fields into a single mathematical structure. For over a century, the unified field theory has remained an open line of research. The term was coined by Albert Einstein, who attempted to unify his general theory of relativity with electromagnetism. Einstein attempted to create a classical unified field theory. Among other difficulties, this required a new explanation of particles as singularities or solitons instead of field quanta. Later attempts to unify general relativity with other forces incorporate quantum mechanics. The concept of a "Theory of Everything" or Grand Unified Theory are closely related to unified field theory. A theory of everything


id: unified-field-theory-20260505-1
file: data/en.wikipedia.org/wiki/Unified_field_theory-1.md
category: reference
title: Unified field theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Unified_field_theory
date_saved: 2026-05-05T11:06:29.038086+00:00
instance: kb-cron
parent: unified-field-theory-20260505-0
summary:
=== Modern progress === In 1963, American physicist Sheldon Glashow proposed that the weak nuclear force, electricity, and magnetism could arise from a partially unified electroweak theory. In 1967, Pakistani Abdus Salam and American Steven Weinberg independently revised Glashow's theory by having the masses for the W particle and Z particle arise through spontaneous symmetry breaking with the Higgs mechanism. This unified theory modelled the electroweak interaction as a force mediated by four particles: the photon for the electromagnetic aspect, a neutral Z particle, and two charged W particles for the weak aspect. As a result of the spontaneous symmetry breaking, the weak force becomes short-range and the W and Z bosons acquire masses of 80.4 and 91.2 GeV/c2, respectively. Their theory was first given experimental support by the discovery of weak neutral currents in 1973. In 1983, the Z and W bosons were first produced at CERN by Carlo Rubbia's team. For their insights, Glashow, Salam, and Weinberg were awarded the Nobel Prize in Physics in 1979. Carlo Rubbia and Simon van der Meer received the Prize in 1984. After Gerardus 't Hooft showed the Glashow–Weinberg–Salam electroweak interactions to be mathematically consistent, the electroweak theory became a template for


id: yang-mills-existence-and-mass-gap-20260505-0
file: data/en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap-0.md
category: reference
title: Yang–Mills existence and mass gap
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap
date_saved: 2026-05-05T11:06:30.271614+00:00
instance: kb-cron
parent: yang-mills-existence-and-mass-gap-20260505-0
summary:
The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution. The problem is phrased as follows: Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on R 4 {\displaystyle \mathbb {R} ^{4}} and has a mass gap Δ > 0. Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975) [citations adapted]. In this statement, a quantum Yang–Mills theory is a non-abelian quantum field theory similar to that underlying the Standard Model of particle physics; R 4 {\displaystyle \mathbb {R} ^{4}} is Euclidean 4-space; the mass gap Δ is the mass of the least massive particle predicted by the theory. Therefore, the winner must prove that: Yang–Mills theory exists and satisfies the standard of rigor that characterizes contemporary mathematical physics, in particular constructive quantum field theory, and The mass of all particles of the force field predicted by the theory are strictly positive.


id: yang-mills-existence-and-mass-gap-20260505-1
file: data/en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap-1.md
category: reference
title: Yang–Mills existence and mass gap
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap
date_saved: 2026-05-05T11:06:30.271614+00:00
instance: kb-cron
parent: yang-mills-existence-and-mass-gap-20260505-0
summary:
⟨ ϕ ( 0 , t ) ϕ ( 0 , 0 ) ⟩ ∼ ∑ n A n exp ⁡ ( − Δ n t ) {\displaystyle \langle \phi (0,t)\phi (0,0)\rangle \sim \sum _{n}A_{n}\exp \left(-\Delta _{n}t\right)} with Δ 0 > 0 {\displaystyle \Delta _{0}>0} being the lowest energy value in the spectrum of the Hamiltonian and thus the mass gap. This quantity, easy to generalize to other fields, is what is generally measured in lattice computations. It was proved in this way that Yang–Mills theory develops a mass gap on a lattice. == Importance of Yang–Mills theory == Most known and nontrivial (i.e. interacting) quantum field theories in 4 dimensions are effective field theories with a cutoff scale. Since the beta function is positive for most models, it appears that most such models have a Landau pole as it is not at all clear whether or not they have nontrivial UV fixed points. This means that if such a QFT is well-defined at all scales, as it has to be to satisfy the axioms of axiomatic quantum field theory, it would have to be trivial (i.e. a free field theory). Quantum Yang–Mills theory with a non-abelian gauge group and


id: list-of-quantum-computing-journals-20260505-0
file: data/en.wikipedia.org/wiki/List_of_quantum_computing_journals-0.md
category: reference
title: List of quantum computing journals
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_quantum_computing_journals
date_saved: 2026-05-05T11:06:31.825492+00:00
instance: kb-cron
parent: list-of-quantum-computing-journals-20260505-0
summary:
This is a list of quantum computing journals which is a collection of peer-reviewed scientific journals that publish research in the field of quantum computing, including topics such as quantum algorithms, quantum information theory, quantum cryptography, and quantum hardware. == Journals == Quantum (journal) npj Quantum Information Quantum Information Processing International Journal of Quantum Information Entropy (journal) Physical Review A New Journal of Physics Nature Physics Nature Communications == See also == List of computer science journals List of physics journals List of scientific journals List of cryptography journals List of computer science conferences Quantum information science Quantum Computation and Quantum Information — textbook Quantum engineering Quantum programming List of quantum algorithms Glossary of quantum computing


id: adiabatic-quantum-computation-20260505-0
file: data/en.wikipedia.org/wiki/Adiabatic_quantum_computation-0.md
category: reference
title: Adiabatic quantum computation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adiabatic_quantum_computation
date_saved: 2026-05-05T11:06:32.974566+00:00
instance: kb-cron
parent: adiabatic-quantum-computation-20260505-0
summary:
Adiabatic quantum computation (AQC) is a form of quantum computing which relies on the adiabatic theorem to perform calculations and is closely related to quantum annealing. == Description == First, a (potentially complicated) Hamiltonian is found whose ground state describes the solution to the problem of interest. Next, a system with a simple Hamiltonian is prepared and initialized to the ground state. Finally, the simple Hamiltonian is adiabatically evolved to the desired complicated Hamiltonian. By the adiabatic theorem, the system remains in the ground state, so at the end, the state of the system describes the solution to the problem. Adiabatic quantum computing has been shown to be polynomially equivalent to conventional quantum computing in the circuit model. The time complexity for an adiabatic algorithm is the time taken to complete the adiabatic evolution which is dependent on the gap in the energy eigenvalues (spectral gap) of the Hamiltonian. Specifically, if the system is to be kept in the ground state, the energy gap between the ground state and the first excited state of H ( t ) {\displaystyle H(t)} provides an upper bound on the rate at which the Hamiltonian can be evolved at time t {\displaystyle t} .


id: adiabatic-quantum-computation-20260505-1
file: data/en.wikipedia.org/wiki/Adiabatic_quantum_computation-1.md
category: reference
title: Adiabatic quantum computation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Adiabatic_quantum_computation
date_saved: 2026-05-05T11:06:32.974566+00:00
instance: kb-cron
parent: adiabatic-quantum-computation-20260505-0
summary:
H ~ ( s ) = ( 1 − s ) H B + s H P {\displaystyle {\tilde {H}}(s)=(1-s)H_{B}+sH_{P}} , which is the adiabatic evolution Hamiltonian of the algorithm. In accordance with the adiabatic theorem, start from the ground state of Hamiltonian H B {\displaystyle H_{B}} at the beginning, proceed through an adiabatic process, and end in the ground state of problem Hamiltonian H P {\displaystyle H_{P}} . Then measure the z-component of each of the n spins in the final state. This will produce a string z 1 , z 2 , … , z n {\displaystyle z_{1},z_{2},\dots ,z_{n}} which is highly likely to be the result of the satisfiability problem. The run time T must be sufficiently long to assure correctness of the result. According to the adiabatic theorem, T is about ε / g m i n 2 {\displaystyle \varepsilon /g_{\mathrm {min} }^{2}} , where g m i n = min 0 ≤ s ≤ 1 ( E 1 ( s ) − E 0 ( s ) ) {\displaystyle g_{\mathrm {min} }=\min _{0\leq s\leq 1}(E_{1}(s)-E_{0}(s))} is the minimum energy gap between ground state and first excited state. == Comparison to gate-based quantum computing == Adiabatic


id: algorithmic-qubits-20260505-0
file: data/en.wikipedia.org/wiki/Algorithmic_qubits-0.md
category: reference
title: Algorithmic qubits
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Algorithmic_qubits
date_saved: 2026-05-05T11:06:34.178639+00:00
instance: kb-cron
parent: algorithmic-qubits-20260505-0
summary:
Algorithmic Qubits (AQ) are an application based benchmark of quantum computers. Introduced by IonQ in 2020, the goal was to define a "single number figure of merit to evaluate the performance of quantum computers for solving a representative set of quantum algorithms." While other benchmarks such as IBM's Quantum volume are run on random quantum circuits that do not necessarily have practical applications, AQ is measured on specific algorithms which are known to have value by industry, such as those defined by the Quantum Economic Development Consortium. [1] == Definition == IonQ published code for calculating AQ in a Git code repository. [2] The formal definition of calculating AQ is composed of several steps: Let the set of circuits in the benchmark suite be denoted by C. Locate each circuit c ∈ C as a point on the 2D plot by its Width, wc (Number of qubits), and Depth, dc (Number of Controlled NOT (CX) gates) Define success probability for a Quantum circuit c, Fc The circuit passes if Fc - ϵc > t, where ϵc is the statistical error based on the number of shots, ϵ c = √ ( F c ( q − F c ) )


id: amaravati-quantum-valley-20260505-0
file: data/en.wikipedia.org/wiki/Amaravati_Quantum_Valley-0.md
category: reference
title: Amaravati Quantum Valley
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Amaravati_Quantum_Valley
date_saved: 2026-05-05T11:06:35.480296+00:00
instance: kb-cron
parent: amaravati-quantum-valley-20260505-0
summary:
Amaravati Quantum Valley is a planned quantum technology park and hub dedicated for innovations and researches in the field of quantum computing and technologies in India. It is located in Amaravati city of Andhra Pradesh state in India. It is planned that the quantum technology hub will attract huge investments of worth 1 billion USD dollar. It is alignment with the goals of the National Quantum Mission to increase productivity and create wealth through the advanced technologies going to be developed from the Amaravati Quantum Valley. The foreign company IBM and the Indian company Tata Consultancy Services have planned to establish India’s largest quantum computer at the tech park of the Amaravati Quantum Valley, featuring a 156-qubit IBM Heron processor. The planned Amaravati Quantum Valley is seen as a historic opportunity for the state of Andhra Pradesh to become a global hub for the future advanced quantum technologies. It is also considered as the first dedicated "Quantum Valley" tech park in the region of Southern asia. == History == In the March month of 2025, the Government of Andhra Pradesh planned to establish Quantum Valley in the capital city Amaravati as part of National Quantum Mission in India. On 4


id: bacon-shor-code-20260505-0
file: data/en.wikipedia.org/wiki/Bacon–Shor_code-0.md
category: reference
title: Bacon–Shor code
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Bacon–Shor_code
date_saved: 2026-05-05T11:06:36.713955+00:00
instance: kb-cron
parent: bacon-shor-code-20260505-0
summary:
The Bacon–Shor code is a subsystem error correcting code. In a subsystem code, information is encoded in a subsystem of a Hilbert space. Subsystem codes lend to simplified error correcting procedures unlike codes which encode information in the subspace of a Hilbert space. This simplicity led to the first claim of fault tolerant circuit demonstration on a quantum computer. It is named after Dave Bacon and Peter Shor. Given the stabilizer generators of Shor's code: ⟨ X 0 X 1 X 2 X 3 X 4 X 5 , X 0 X 1 X 2 X 6 X 7 X 8 , Z 0 Z 1 , Z 1 Z 2 , Z 3 Z 4 , Z 4 Z 5 , Z 6 Z 7 , Z 7 Z 8 ⟩ {\displaystyle \langle X_{0}X_{1}X_{2}X_{3}X_{4}X_{5},X_{0}X_{1}X_{2}X_{6}X_{7}X_{8},Z_{0}Z_{1},Z_{1}Z_{2},Z_{3}Z_{4},Z_{4}Z_{5},Z_{6}Z_{7},Z_{7}Z_{8}\rangle } , 4 stabilizers can be removed from this generator by recognizing gauge symmetries in the code to get: ⟨ X 0 X 1 X 2 X 3 X 4 X 5 , X 0 X 1 X 2 X 6 X 7 X 8 , Z 0 Z 1 Z 3 Z 4 Z 6 Z 7 , Z 1 Z 2 Z 4


id: stefanie-barz-20260505-0
file: data/en.wikipedia.org/wiki/Stefanie_Barz-0.md
category: reference
title: Stefanie Barz
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stefanie_Barz
date_saved: 2026-05-05T11:06:37.846175+00:00
instance: kb-cron
parent: stefanie-barz-20260505-0
summary:
Stefanie Barz is a German physicist and Professor of Quantum Information and Technology at the University of Stuttgart working in the field of photonic quantum technology. == Early life and education == Barz studied at the Johannes Gutenberg University Mainz, with a stay at the KTH Royal Institute of Technology within the Erasmus Programme. She earned her PhD from the University of Vienna under the supervision of Anton Zeilinger, working on various aspects of photonic quantum computing, including 'blind' quantum computing using entangled photons, where the sender knows the initial state of entanglement while companies in control of data processing do not, making it impossible for them to decode the information without destroying it. For her dissertation she was awarded the Laudimaxima Prize of the University of Vienna, and her work has been featured in New Scientist and covered by the BBC and NBC. In 2013 Barz was awarded the Maria Schaumayer Prize and the Loschmidt Prize. From 2014 to 2017, Barz was a Marie Skłodowska-Curie Fellow as well as a Millard and Lee Alexander Fellow in the Christ Church College at the University of Oxford. She worked with Ian Walmsley on three-photon interference, during which project she created integrated


id: paul-benioff-20260505-0
file: data/en.wikipedia.org/wiki/Paul_Benioff-0.md
category: reference
title: Paul Benioff
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paul_Benioff
date_saved: 2026-05-05T11:06:40.105692+00:00
instance: kb-cron
parent: paul-benioff-20260505-0
summary:
Paul Anthony Benioff (May 1, 1930 – March 29, 2022) was an American physicist who helped pioneer the field of quantum computing. Benioff was best known for his research in quantum information theory during the 1970s and 80s that demonstrated the theoretical possibility of quantum computers by describing the first quantum mechanical model of a computer. In this work, Benioff showed that a computer could operate under the laws of quantum mechanics by describing a Schrödinger equation description of Turing machines. Benioff's body of work in quantum information theory encompassed quantum computers, quantum robots, and the relationship between foundations in logic, math, and physics. == Early life and education == Benioff was born on May 1, 1930, in Pasadena, California. His father, Hugo Benioff, was a professor of seismology at the California Institute of Technology, and his mother, Alice Pauline Silverman, received a master's degree in English from the University of California, Berkeley. Benioff also attended Berkeley, where he earned an undergraduate degree in botany in 1951. After a two-year stint working in nuclear chemistry for Tracerlab, he returned to Berkeley. In 1959, he obtained his PhD in nuclear chemistry. == Career and later life == In 1960, Benioff spent


id: paul-benioff-20260505-1
file: data/en.wikipedia.org/wiki/Paul_Benioff-1.md
category: reference
title: Paul Benioff
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paul_Benioff
date_saved: 2026-05-05T11:06:40.105692+00:00
instance: kb-cron
parent: paul-benioff-20260505-0
summary:
== Selected scientific works == ”Cosmic-ray production rate and mean removal time of beryllium-7 from the atmosphere," Physical Review, Vol. 104, 1956, pp. 1122–1130. ”Information theory in quantum statistical mechanics," Physics Letters, Vol. 14, 1965, pp. 196–197. ”Some aspects of the relationship between mathematical logic and physics. I," Journal of Mathematical Physics, Vol. 11, 1970, pp. 2553–2569. ”Some aspects of the relationship between mathematical logic and physics. II," Journal of Mathematical Physics, Vol. 12, 1971, pp. 360–376. ”Operator valued measures in quantum mechanics: finite and infinite processes," Journal of Mathematical Physics, Vol. 13, 1972, pp. 231–242. ”Decision procedures in quantum mechanics," Journal of Mathematical Physics, Vol. 13, 1972, pp. 908–915. ”Procedures in quantum mechanics without Von Neumann's projection axiom," Journal of Mathematical Physics, Vol. 13, 1972, pp. 1347–1355. ”Some consequences of the strengthened interpretative rules of quantum mechanics," Journal of Mathematical Physics, Vol. 15, 1974, pp. 552–559. ”Models of Zermelo Frankel set theory as carriers for the mathematics of physics. I", Journal of Mathematical Physics, Vol. 17, 1976, pp. 618–628. ”Models of Zermelo Frankel set theory as carriers for the mathematics of physics. II," Journal of Mathematical Physics, Vol. 17, 1976, pp. 629–640. ”Finite and infinite measurement sequences in quantum


id: bqp-20260505-0
file: data/en.wikipedia.org/wiki/BQP-0.md
category: reference
title: BQP
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/BQP
date_saved: 2026-05-05T11:06:41.292100+00:00
instance: kb-cron
parent: bqp-20260505-0
summary:
In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. It is the quantum analogue to the complexity class BPP. A decision problem is a member of BQP if there exists a quantum algorithm (an algorithm that runs on a quantum computer) that solves the decision problem with high probability and is guaranteed to run in polynomial time. A run of the algorithm will correctly solve the decision problem with a probability of at least 2/3. == Definition == BQP can be viewed as the languages associated with certain bounded-error uniform families of quantum circuits. A language L is in BQP if and only if there exists a polynomial-time uniform family of quantum circuits { Q n : n ∈ N } {\displaystyle \{Q_{n}\colon n\in \mathbb {N} \}} , such that For all n ∈ N {\displaystyle n\in \mathbb {N} } , Qn takes n qubits as input and outputs 1 bit For all x in L, P r ( Q | x | ( x ) = 1 ) ≥ 2 3 {\displaystyle \mathrm {Pr}


id: bqp-20260505-1
file: data/en.wikipedia.org/wiki/BQP-1.md
category: reference
title: BQP
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/BQP
date_saved: 2026-05-05T11:06:41.292100+00:00
instance: kb-cron
parent: bqp-20260505-0
summary:
==== APPROX-QCIRCUIT-PROB ==== The APPROX-QCIRCUIT-PROB problem is complete for efficient quantum computation, and the version presented below is complete for the Promise-BQP complexity class (and not for the total BQP complexity class, for which no complete problems are known). APPROX-QCIRCUIT-PROB's completeness makes it useful for proofs showing the relationships between other complexity classes and BQP. Given a description of a quantum circuit C acting on n qubits with m gates, where m is a polynomial in n and each gate acts on one or two qubits, and two numbers α , β ∈ [ 0 , 1 ] , α > β {\displaystyle \alpha ,\beta \in [0,1],\alpha >\beta } , distinguish between the following two cases: measuring the first qubit of the state C | 0 ⟩ ⊗ n {\displaystyle C|0\rangle ^{\otimes n}} yields | 1 ⟩ {\displaystyle |1\rangle } with probability ≥ α {\displaystyle \geq \alpha } measuring the first qubit of the state C | 0 ⟩ ⊗ n {\displaystyle C|0\rangle ^{\otimes n}} yields | 1 ⟩ {\displaystyle |1\rangle } with probability ≤ β {\displaystyle \leq \beta } Here, there is a promise on the inputs as the problem does not specify the behavior if an instance is


id: bqp-20260505-2
file: data/en.wikipedia.org/wiki/BQP-2.md
category: reference
title: BQP
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/BQP
date_saved: 2026-05-05T11:06:41.292100+00:00
instance: kb-cron
parent: bqp-20260505-0
summary:
Consider a quantum circuit C, which consists of t gates, g 1 , g 2 , ⋯ , g m {\displaystyle g_{1},g_{2},\cdots ,g_{m}} , where each g j {\displaystyle g_{j}} comes from a universal gate set and acts on at most two qubits. To understand what the sum of histories is, we visualize the evolution of a quantum state given a quantum circuit as a tree. The root is the input | 0 ⟩ ⊗ n {\displaystyle |0\rangle ^{\otimes n}} , and each node in the tree has 2 n {\displaystyle 2^{n}} children, each representing a state in C n {\displaystyle \mathbb {C} ^{n}} . The weight on a tree edge from a node in j-th level representing a state | x ⟩ {\displaystyle |x\rangle } to a node in j + 1 {\displaystyle j+1} -th level representing a state | y ⟩ {\displaystyle |y\rangle } is ⟨ y | g j + 1 | x ⟩ {\displaystyle \langle y|g_{j+1}|x\rangle } , the amplitude of | y ⟩ {\displaystyle |y\rangle } after applying g j + 1 {\displaystyle g_{j+1}} on | x ⟩ {\displaystyle |x\rangle } . The transition amplitude of a root-to-leaf path is the product of all the


id: cat-qubit-quantum-computer-20260505-0
file: data/en.wikipedia.org/wiki/Cat_qubit_quantum_computer-0.md
category: reference
title: Cat qubit quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cat_qubit_quantum_computer
date_saved: 2026-05-05T11:06:42.433230+00:00
instance: kb-cron
parent: cat-qubit-quantum-computer-20260505-0
summary:
A cat qubit quantum computer is one proposed approach to a large-scale quantum computer based on Schrödinger cat states. Cat states are superpositions of two coherent states of light. Cat qubits encode quantum information in these states. They are designed to provide built in protection against certain types of errors, particularly bit flips, making quantum error correction more efficient in superconducting circuits. The approach is being developed by Alice & Bob and Amazon Web Services (AWS), among others. == Background == Cat qubits use coherent states of a quantum harmonic oscillator—microwave photons trapped in a superconducting resonator—as their logical 0 and 1 states. The name derives from the Schrödinger's cat thought experiment, in which a system exists in a superposition of two macroscopically distinct states. Errors in quantum computation generally occur as bit-flip errors — changing a qubit's logical state from 0 to 1 or vice versa — and phase-flip errors, which alter the relative phase between superposed states. The key property of cat qubits is that the probability of a bit-flip decreases exponentially with the number of photons in the coherent state. In conventional superconducting transmon-based architectures using surface codes, correcting both types of errors can require a significant


id: chemical-computer-20260505-0
file: data/en.wikipedia.org/wiki/Chemical_computer-0.md
category: reference
title: Chemical computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Chemical_computer
date_saved: 2026-05-05T11:06:43.894478+00:00
instance: kb-cron
parent: chemical-computer-20260505-0
summary:
A chemical computer, also called a reaction-diffusion computer, Belousov–Zhabotinsky (BZ) computer, or gooware computer, is an unconventional computer based on a semi-solid chemical "soup" where data are represented by varying concentrations of chemicals. The computations are performed by naturally occurring chemical reactions. == Background == Originally chemical reactions were seen as a simple move towards a stable equilibrium which was not very promising for computation. This was changed by a discovery made by Boris Belousov, a Soviet scientist, in the 1950s. He created a chemical reaction between different salts and acids that swing back and forth between being yellow and clear because the concentration of the different components changes up and down in a cyclic way. At the time this was considered impossible because it seemed to go against the second law of thermodynamics, which says that in a closed system the entropy will only increase over time, causing the components in the mixture to distribute themselves until equilibrium is gained and making any changes in the concentration impossible. But modern theoretical analyses shows sufficiently complicated reactions can indeed comprise wave phenomena without breaking the laws of nature. (A convincing directly visible demonstration was achieved by Anatol Zhabotinsky with the


id: cirac-zoller-controlled-not-gate-20260505-0
file: data/en.wikipedia.org/wiki/Cirac–Zoller_controlled-NOT_gate-0.md
category: reference
title: Cirac–Zoller controlled-NOT gate
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cirac–Zoller_controlled-NOT_gate
date_saved: 2026-05-05T11:06:45.070213+00:00
instance: kb-cron
parent: cirac-zoller-controlled-not-gate-20260505-0
summary:
The Cirac–Zoller controlled-NOT gate is an implementation of the controlled-NOT (CNOT) quantum logic gate using cold trapped ions that was proposed by Ignacio Cirac and Peter Zoller in 1995 and represents the central ingredient of the Cirac–Zoller proposal for a trapped-ion quantum computer. The key idea of the Cirac–Zoller proposal is to mediate the interaction between the two qubits through the joint motion of the complete chain of trapped ions. The quantum CNOT gate acts on two qubits and can entangle them. It forms part of the standard universal set of gates, meaning that any gate (unitary transformation) on the N {\displaystyle N} -qubit Hilbert space can be approximated to arbitrary precision by a sequence of gates from the universal set. The Cirac–Zoller gate was experimentally first realized in 2003 (in slightly modified form) at the University of Innsbruck, Austria by Ferdinand Schmidt-Kaler and coworkers in the group of Rainer Blatt using two calcium ions. == Procedure == The qubits on which the Cirac–Zoller gate operates are represented by two internal states, ground state and excited state (called in the following g and e) of trapped ions. An additional auxiliary excited state a is used to implement the gate. Due


id: circuit-layer-operations-per-second-20260505-0
file: data/en.wikipedia.org/wiki/Circuit_Layer_Operations_per_Second-0.md
category: reference
title: Circuit Layer Operations per Second
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Circuit_Layer_Operations_per_Second
date_saved: 2026-05-05T11:06:46.190126+00:00
instance: kb-cron
parent: circuit-layer-operations-per-second-20260505-0
summary:
Circuit Layer Operations per Second (CLOPS) is a benchmarking metric of quantum computers developed by IBM in 2021. While Quantum volume is more indicative of a qubit's performance and quality, CLOPS is a measure of a quantum computer’s execution speed. CLOPS incorporates both the time to run a circuit as well as the real-time and near-time classical computation, enabling it to serve as a holistic single measure of speed. CLOPS in conjunction with the number of qubits and the quantum volume was originally envisioned by IBM to be the 3 core metrics for comparing quantum devices. == Redefinition == Originally CLOPS was designed to be related to quantum volume, in the sense that each circuit layer was idealized square quantum volume circuits. However, in 2023 IBM created a new definition of CLOPS which is related to a specific hardware layer. The different versions are differentiated with a subscript: CLOPSv for virtual and CLOPSh for hardware. Functionally, the core difference is that instead of using quantum volume in the calculation, a different metric known as layer fidelity is used instead, measured by the error per layered gate (ELPG) protocol. This enables different hardware with different quantum volumes to be more accurately


id: classical-shadow-20260505-0
file: data/en.wikipedia.org/wiki/Classical_shadow-0.md
category: reference
title: Classical shadow
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Classical_shadow
date_saved: 2026-05-05T11:06:47.340833+00:00
instance: kb-cron
parent: classical-shadow-20260505-0
summary:
In quantum computing, classical shadow is a protocol for predicting expectation values of a quantum state using only a logarithmic number of measurements. Given an unknown state ρ {\displaystyle \rho } , a tomographically complete set of gates U {\displaystyle U} (e.g. Clifford gates), a set of M {\displaystyle M} observables { O i } {\displaystyle \{O_{i}\}} and a quantum channel E {\displaystyle {\mathcal {E}}} defined by randomly sampling from U {\displaystyle U} , applying it to ρ {\displaystyle \rho } and measuring the resulting state, predict the expectation values tr ⁡ ( O i ρ ) {\displaystyle \operatorname {tr} (O_{i}\rho )} . A list of classical shadows S {\displaystyle S} is created using ρ {\displaystyle \rho } , U {\displaystyle U} and E {\displaystyle {\mathcal {E}}} by running a Shadow generation algorithm. When predicting the properties of ρ {\displaystyle \rho } , a Median-of-means estimation algorithm is used to deal with the outliers in S {\displaystyle S} . Classical shadow is useful for direct fidelity estimation, entanglement verification, estimating correlation functions, and predicting entanglement entropy. Recently, researchers have built on classical shadow to devise provably efficient classical machine learning algorithms for a wide range of quantum many-body problems. For


id: cloud-based-quantum-computing-20260505-0
file: data/en.wikipedia.org/wiki/Cloud-based_quantum_computing-0.md
category: reference
title: Cloud-based quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cloud-based_quantum_computing
date_saved: 2026-05-05T11:06:48.511879+00:00
instance: kb-cron
parent: cloud-based-quantum-computing-20260505-0
summary:
Cloud-based quantum computing refers to the remote access of quantum computing resources—such as quantum emulators, simulators, or processors—via the internet. Cloud access enables users to develop, test, and execute quantum algorithms without the need for direct interaction with specialized hardware, facilitating broader participation in quantum software development and experimentation. In 2016, IBM launched the IBM Quantum Experience, one of the first publicly accessible quantum processors connected to the cloud. In early 2017, researchers at Rigetti Computing demonstrated programmable quantum cloud access through their software platform Forest, which included the pyQuil Python library. Since the early-2020s, cloud-based quantum computing has grown significantly, with multiple providers offering access to a variety of quantum hardware modalities, including superconducting qubits, trapped ions, neutral atoms, and photonic systems. Major platforms such as Amazon Braket, Azure Quantum, and qBraid aggregate quantum devices from hardware developers like IonQ, Rigetti Computing, QuEra, Pasqal, Oxford Quantum Circuits, and IBM Quantum. These platforms provide unified interfaces for users to write and execute quantum algorithms across diverse backends, often supporting open-source SDKs such as Qiskit, Cirq, and PennyLane. The proliferation of cloud-based access has played a key role in accelerating quantum education, algorithm research, and early-stage application development by lowering the


id: list-of-companies-involved-in-quantum-computing-communication-or-sensing-20260505-0
category: reference
title: List of companies involved in quantum computing, communication or sensing
tags: science, encyclopedia
date_saved: 2026-05-05T11:06:49.720687+00:00
instance: kb-cron
parent: list-of-companies-involved-in-quantum-computing-communication-or-sensing-20260505-0
file:
data/en.wikipedia.org/wiki/List_of_companies_involved_in_quantum_computing,_communication_or_sensing-0.md

summary:
This article lists the companies worldwide engaged in the development of quantum computing, quantum communication and quantum sensing. Quantum computing and communication are two sub-fields of quantum information science, which describes and theorizes information science in terms of quantum physics. While the fundamental unit of classical information is the bit, the basic unit of quantum information is the qubit. Quantum sensing is the third main sub-field of quantum technologies and it focus consists in taking advantage of the quantum states sensitivity to the surrounding environment to perform atomic scale measurements. == Company details == == See also == Quantum programming Quantum supremacy List of quantum processors == References == == Further reading == Quantum Computing Report's list of quantum players The Quantum Insider's list of quantum computing companies

source_url:
https://en.wikipedia.org/wiki/List_of_companies_involved_in_quantum_computing,_communication_or_sensing


id: cross-entropy-benchmarking-20260505-0
file: data/en.wikipedia.org/wiki/Cross-entropy_benchmarking-0.md
category: reference
title: Cross-entropy benchmarking
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cross-entropy_benchmarking
date_saved: 2026-05-05T11:06:50.850403+00:00
instance: kb-cron
parent: cross-entropy-benchmarking-20260505-0
summary:
Cross-entropy benchmarking (XEB) is a statistical measure used to evaluate the performance in random circuit sampling experiments. It quantifies how strongly experimental samples correlate with the ideal output distribution and has been used in demonstrations of quantum supremacy. == Definition == Let C {\displaystyle C} be an n {\displaystyle n} -qubit quantum circuit. The output probability for bitstrings x ∈ { 0 , 1 } n {\displaystyle x\in \{0,1\}^{n}} for C {\displaystyle C} acting on all 0 input 0 n {\displaystyle 0^{n}} is P ( x ) = | ⟨ x | C | 0 n ⟩ | 2 {\displaystyle P(x)=|\langle x|C|0^{n}\rangle |^{2}} . Given k {\displaystyle k} samples { x i } i = 1 k {\displaystyle \{x_{i}\}_{i=1}^{k}} obtained from an experimental device, the (linear) cross-entropy benchmarking fidelity is defined as F X E B = 2 n ⟨ P ( x i ) ⟩ k − 1 = 2 n k ( ∑ i = 1 k | ⟨ 0 n | C | x i ⟩ | 2 ) − 1 {\displaystyle F_{\rm {XEB}}=2^{n}\langle P(x_{i})\rangle _{k}-1={\frac {2^{n}}{k}}\left(\sum _{i=1}^{k}|\langle 0^{n}|C|x_{i}\rangle |^{2}\right)-1} == Interpretation == If F X E B = 1 {\displaystyle F_{XEB}=1} , the samples were collected


id: d-wave-systems-20260505-0
file: data/en.wikipedia.org/wiki/D-Wave_Systems-0.md
category: reference
title: D-Wave Systems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/D-Wave_Systems
date_saved: 2026-05-05T11:06:52.071639+00:00
instance: kb-cron
parent: d-wave-systems-20260505-0
summary:
D-Wave Quantum Inc. is a quantum computing company with locations in Palo Alto, California and Burnaby, British Columbia. D-Wave claims to be the world's first company to sell computers that exploit quantum effects in their operation. D-Wave's early customers include Lockheed Martin, the University of Southern California, Google/NASA, and Los Alamos National Laboratory. D-Wave does not implement a generic, universal quantum computer; instead, their computers implement specialized quantum annealing. == History == D-Wave was founded by Haig Farris, Geordie Rose, Bob Wiens, and Alexandre Zagoskin in 1999. Farris taught a business course at the University of British Columbia (UBC), where Rose obtained his PhD, and Zagoskin was a postdoctoral fellow. The company name refers to their first qubit designs, which used d-wave superconductors. D-Wave operated from various locations in Vancouver, British Columbia, and laboratory spaces at UBC before moving to its current location in the neighboring suburb of Burnaby. D-Wave also has offices in Palo Alto, California and Vienna, California, USA. D-Wave operated as an offshoot from UBC, while maintaining ties with the Department of Physics and Astronomy. It funded academic research in quantum computing, thus building a collaborative network of research scientists. The company collaborated with several universities and


id: d-wave-systems-20260505-1
file: data/en.wikipedia.org/wiki/D-Wave_Systems-1.md
category: reference
title: D-Wave Systems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/D-Wave_Systems
date_saved: 2026-05-05T11:06:52.071639+00:00
instance: kb-cron
parent: d-wave-systems-20260505-0
summary:
=== Orion prototype === On February 13, 2007, D-Wave demonstrated the Orion system, running three different applications at the Computer History Museum in Mountain View, California. This marked the first public demonstration of, supposedly, a quantum computer and associated service. The first application, an example of pattern matching, performed a search for a similar compound to a known drug within a database of molecules. The next application computed a seating arrangement for an event subject to compatibilities and incompatibilities between guests. The last involved solving a Sudoku puzzle. The processors at the heart of D-Wave's "Orion quantum computing system" are designed for use as hardware accelerator processors rather than general-purpose computer microprocessors. The system is designed to solve a particular NP-complete problem related to the two-dimensional Ising model in a magnetic field. D-Wave terms the device as a 16-qubit superconducting adiabatic quantum computer processor. According to the company, a conventional front-end running an application that requires the solution of an NP-complete problem, such as pattern matching, passes the problem to the Orion system. According to Geordie Rose, founder and Chief Technology Officer of D-Wave, NP-complete problems "are probably not exactly solvable, no matter how big, fast or advanced computers get";


id: d-wave-systems-20260505-2
file: data/en.wikipedia.org/wiki/D-Wave_Systems-2.md
category: reference
title: D-Wave Systems
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/D-Wave_Systems
date_saved: 2026-05-05T11:06:52.071639+00:00
instance: kb-cron
parent: d-wave-systems-20260505-0
summary:
== Incidents and criticisms == Despite its pioneering role in quantum annealing, D-Wave has faced criticism regarding the practical utility and commercial viability of its systems. In March 2025, D-Wave announced that it had achieved what it described as "quantum supremacy," reporting that its latest quantum annealer solved a specialized optimization problem faster than the world's most powerful classical supercomputers could replicate the result. The Wall Street Journal noted that while the experiment demonstrated a performance gap favoring D-Wave's hardware, skeptics argued the problem was carefully chosen to highlight the system's strengths and did not reflect general-purpose computational tasks. Critics further observed that advances in classical algorithms might soon close this benchmark gap, suggesting that D-Wave's claimed supremacy may be limited to narrow, contrived applications rather than broad, real-world problems. In April 2025, independent investment research firm Kerrisdale Capital argued that D-Wave's market valuation was "disconnected from its stagnating revenue and lack of broad commercial adoption," highlighting concerns over significant share dilution and questioning the company's path to profitability. == See also == List of companies involved in quantum computing or communication Adiabatic quantum computation Analog computer AQUA@home Flux qubit Quantum annealing Superconducting quantum computing IBM Q System One ==


id: david-deutsch-20260505-0
file: data/en.wikipedia.org/wiki/David_Deutsch-0.md
category: reference
title: David Deutsch
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/David_Deutsch
date_saved: 2026-05-05T11:06:53.298460+00:00
instance: kb-cron
parent: david-deutsch-20260505-0
summary:
David Elieser Deutsch ( DOYTCH; born 18 May 1953) is a British physicist at the University of Oxford who is often described as the "father of quantum computing". He is a visiting professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation (CQC) in the Clarendon Laboratory of the University of Oxford. He pioneered the field of quantum computation by formulating a description for a quantum Turing machine, as well as specifying an algorithm designed to run on a quantum computer. He is a proponent of the many-worlds interpretation of quantum mechanics. == Education == Deutsch was born to a Jewish family in Haifa, Israel, on 18 May 1953, the son of Oskar and Tikva Deutsch. David attended Geneva House school in Cricklewood, London. His parents owned and ran the Alma restaurant on Cricklewood Broadway. He later attended William Ellis School in Highgate before reading Natural Sciences at Clare College, Cambridge, and taking Part III of the Mathematical Tripos. He went on to Wolfson College, Oxford for his doctorate in theoretical physics on quantum field theory in curved space-time, supervised by Dennis Sciama and Philip Candelas. == Career and research == His work on quantum


id: david-deutsch-20260505-1
file: data/en.wikipedia.org/wiki/David_Deutsch-1.md
category: reference
title: David Deutsch
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/David_Deutsch
date_saved: 2026-05-05T11:06:53.298460+00:00
instance: kb-cron
parent: david-deutsch-20260505-0
summary:
== Personal life == Deutsch is a founding member of the parenting and educational method Taking Children Seriously. === Views on Antisemitism and Zionism === Deutsch describes antisemitism as a recurring pattern of irrational thinking, present in many cultures, whose function is to justify harming Jews simply for being Jews. He argues that "the pattern" persists because, when old justifications for hating Jews lose relevance, new ones are invented to take their place. Deutsch compares this phenomenon to the way gold retains its high value, not because of any inherent quality, but because people know that other people value it. He regards Zionism as the contemporary Jewish response to this pattern and identifies himself as an atheist Zionist. === Views on Brexit === Deutsch supported Brexit, with his advocacy quoted by then-government adviser, Dominic Cummings, and reported by The New Yorker in January 2020. Michael Gove mentioned Deutsch's viewpoint during a BBC Brexit debate. Regarding the debate, Deutsch later commented: In Britain there is a clear path if you have a grievance, you can join a pressure-group, the pressure-group will pressure the government, or you can see your MP, and the MP will see the grievance building up, and so-on.


id: andrew-dzurak-20260505-0
file: data/en.wikipedia.org/wiki/Andrew_Dzurak-0.md
category: reference
title: Andrew Dzurak
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Andrew_Dzurak
date_saved: 2026-05-05T11:06:54.451250+00:00
instance: kb-cron
parent: andrew-dzurak-20260505-0
summary:
Andrew Dzurak is an Australian physicist and engineer, known for his work in quantum computing. He is the CEO and founder of Diraq, a start-up that is developing a scalable quantum computer based on single electron spins in silicon. He is a Scientia Professor in Quantum Engineering at the University of New South Wales (UNSW), an ARC Laureate Fellow and a member of the executive board of the Sydney Quantum Academy. == Education == Dzurak completed his Bachelor of Science at the University of Sydney in 1987. He then earned his PhD in experimental physics from the University of Cambridge in 1993, under the supervision of Professor Sir Michael Pepper, FRS. == Research == While in Cambridge, Dzurak studied hot electron and ballistic transport in various semiconductor nanostructures, including quantum point contact and quantum dot systems, which were then newly discovered. He also became an expert in the fabrication and low-temperature measurement of nanoelectronic devices, skills that he applied upon his return to Australia. In 1994, Dzurak took up a Vice-Chancellor's Research Fellowship in the School of Physics at the UNSW, followed by an ARC Postdoctoral Research Fellowship in 1996. He was the founding Director (2007–2022) of ANFF–NSW, the NSW


id: eastin-knill-theorem-20260505-0
file: data/en.wikipedia.org/wiki/Eastin–Knill_theorem-0.md
category: reference
title: Eastin–Knill theorem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Eastin–Knill_theorem
date_saved: 2026-05-05T11:06:55.634034+00:00
instance: kb-cron
parent: eastin-knill-theorem-20260505-0
summary:
The Eastin–Knill theorem is a no-go theorem that states: "No quantum error correcting code can have a continuous symmetry which acts transversely on physical qubits". In other words, no quantum error correcting code can transversely implement a universal gate set that contains only unitary gates, where a transversal logical gate is one that can be implemented on a logical qubit by the independent action of separate physical gates on corresponding physical qubits. In addition to investigating fault tolerant quantum computation, the Eastin–Knill theorem is also useful for studying quantum gravity via the AdS/CFT correspondence and in condensed matter physics via quantum reference frame or many-body theory. The theorem is named after Bryan Eastin and Emanuel Knill, who published it in 2009. == Description == Since quantum computers are inherently noisy, quantum error correcting codes are used to correct errors that affect information due to decoherence and dissipation. Decoding error corrected data in order to perform gates on the qubits makes it prone to errors. Fault tolerant quantum computation avoids this by performing gates on encoded data. Transversal gates, which perform a gate between two logical qubits each of which is encoded in N physical qubits by pairing up the physical


id: electron-on-helium-qubit-20260505-0
file: data/en.wikipedia.org/wiki/Electron-on-helium_qubit-0.md
category: reference
title: Electron-on-helium qubit
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Electron-on-helium_qubit
date_saved: 2026-05-05T11:06:56.851379+00:00
instance: kb-cron
parent: electron-on-helium-qubit-20260505-0
summary:
An electron-on-helium qubit is a quantum bit for which the orthonormal basis states |0⟩ and |1⟩ are defined by quantized motional states or alternatively the spin states of an electron trapped above the surface of liquid helium. The electron-on-helium qubit was proposed as the basic element for building quantum computers with electrons on helium by Platzman and Dykman in 1999. == History of electrons on helium == The electrostrictive binding of electrons to the surface of liquid helium was first demonstrated experimentally by Bruschi and co-workers in 1966. A theoretical treatment of the electron-helium interaction was developed by Cole and Cohen in 1969 and, independently, by Shikin in 1970. An electron close to the surface of liquid helium experiences an attractive force due to the formation of a weak (~0.01e) image charge in the dielectric liquid. However, the electron is prevented from entering the liquid by a high (~1 eV) barrier formed at the surface due to the hard-core repulsion of the electron by the helium atoms. As a result, the electron remains trapped outside the liquid. The energy of the electron in this potential well is quantised in a Hydrogen-like series with the modified Rydberg constant RHe ≈ {\displaystyle


id: electron-on-helium-qubit-20260505-1
file: data/en.wikipedia.org/wiki/Electron-on-helium_qubit-1.md
category: reference
title: Electron-on-helium qubit
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Electron-on-helium_qubit
date_saved: 2026-05-05T11:06:56.851379+00:00
instance: kb-cron
parent: electron-on-helium-qubit-20260505-0
summary:
== Decoherence == In any quantum computer the decoherence of the qubit wavefunction, due to energy relaxation or dephasing effects, must be limited to a suitably low rate. For electron-on-helium qubits, deformations of the helium surface due to surface or bulk excitations (ripplons or phonons) modify the image charge potential and distort the electron wavefunction. Therefore, for Rydberg and orbital states, the primary source of decoherence is expected to be the emission of ripplons or phonons in the helium substrate. However, the decay rate due to these processes is expected to be slow (~100 μs) compared with the rate at which qubit operations can be performed (~10 ns). For the spin state, the inherent purity of the qubit environment and the weak spin orbit interaction for an electron moving above the helium surface results in predicted coherence times > {\displaystyle >} 1 s. == Current developments == The first trapping and detection of single electrons on helium was demonstrated by Lea and co-workers in 2005, using a micrometer-scale helium-filled trap and a single electron transistor beneath the surface to count the electrons. This experiment also demonstrated the first coupling between an electron on helium and a superconducting quantum circuit. Subsequently,


id: marcos-eduardo-elias-20260505-0
file: data/en.wikipedia.org/wiki/Marcos_Eduardo_Elias-0.md
category: reference
title: Marcos Eduardo Elias
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Marcos_Eduardo_Elias
date_saved: 2026-05-05T11:06:57.999873+00:00
instance: kb-cron
parent: marcos-eduardo-elias-20260505-0
summary:
Marcos Eduardo Elias (São Paulo, May 16, 1971) is a Brazilian entrepreneur with a background in mathematics, engineering, and financial markets. He has worked in investment and financial analysis and has been associated with initiatives related to quantum computing in Brazil. == Career == Elias built his career in the financial sector, working as an investment analyst and later as a fund manager and entrepreneur. He held positions at institutions including Banco Bozano Simonsen and BNP Paribas, where he became chief analyst in Brazil. He was later involved in founding and development of investment and research firms such as Empiricus and other financial ventures. He has also worked in academia, teaching at institutions including Insper and Fundação Getulio Vargas. == Legal Issues == In 2018, Elias was arrested in Switzerland at the request of United States authorities in connection with an investigation into financial fraud. According to the United States Department of Justice, he was accused of participating in a scheme involving international bank transfers, the use of false identities, and offshore companies. He was later extradited to the United States, where he faced charges related to wire fraud and aggravated identity theft. In 2019, he pleasded guilty and was


id: entanglement-swapping-20260505-0
file: data/en.wikipedia.org/wiki/Entanglement_swapping-0.md
category: reference
title: Entanglement swapping
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Entanglement_swapping
date_saved: 2026-05-05T11:06:59.127187+00:00
instance: kb-cron
parent: entanglement-swapping-20260505-0
summary:
In quantum mechanics, entanglement swapping is a protocol to transfer quantum entanglement from one pair of particles to another, even if the second pair of particles have never interacted. This process may have application in quantum communication networks and quantum computing. == Concept == === Basic principles === Entanglement swapping has two pairs of entangled particles: (A, B) and (C, D). Pair of particles (A, B) is initially entangled, as is the pair (C, D). The pair (B, C) taken from the original pairs, is projected onto one of the four possible Bell states, a process called a Bell state measurement. The unmeasured pair of particles (A, D) can become entangled. This effect happens without any previous direct interaction between particles A and D. Entanglement swapping is a form of quantum teleportation. In quantum teleportation, the unknown state of a particle can be sent from one location to another using the combination of a quantum and classical channel. The unknown state is projected by Alice onto a Bell state and the result is communicated to Bob through the classical channel. In entanglement swapping, the state from one of the two sources is the quantum channel of teleportation and the state


id: fault-tolerant-quantum-computing-20260505-0
file: data/en.wikipedia.org/wiki/Fault_tolerant_quantum_computing-0.md
category: reference
title: Fault tolerant quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fault_tolerant_quantum_computing
date_saved: 2026-05-05T11:07:00.326482+00:00
instance: kb-cron
parent: fault-tolerant-quantum-computing-20260505-0
summary:
In quantum information, fault-tolerant quantum computing (FTQC) is a regime of quantum processors that are both large-scale and that effectively incorporate quantum error correction to achieve arbitrarily low error rates (i.e. their logical error rate is much lower than their physical error rate). Full-FTQC processors are theoretically possible, but have not yet been realized experimentally. They are often seen as the primary end goal of quantum processor development, and are used to contrast with existing noisy intermediate-scale quantum (NISQ) quantum processors, which are subject to noise and decoherence preventing scalable error correction. One way FTQC devices can be realized is by grouping together multiple physical qubits to create a single logical qubit, and using error correction methods such as the surface code so that the combined system is fault-tolerant. Proposed FTQC devices generally include hundreds of logical (error-corrected) qubits, which would mean thousands of physical qubits at minimum. The transition from NISQ-era devices to the FTQC regime is an open research topic in quantum information. It is likely that advances at both the hardware and algorithm level are necessary for the transition to occur. == History == When quantum computers were initially theorized, it was unclear whether they would be


id: richard-feynman-20260505-0
file: data/en.wikipedia.org/wiki/Richard_Feynman-0.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He shared the 1965 Nobel Prize in Physics with Julian Schwinger and Shin'ichirō Tomonaga "for their fundamental work in quantum electrodynamics (QED), with deep-ploughing consequences for the physics of elementary particles". He is also known for his work in the path integral formulation of quantum mechanics, the theory of the physics of the superfluidity of supercooled liquid helium, and the parton model. Feynman developed a pictorial representation scheme for the mathematical expressions describing the behavior of subatomic particles, which later became known as Feynman diagrams and remains widely used. He assisted in the development of the atomic bomb during World War II and became known to the wider public in the 1980s as a member of the Rogers Commission, the panel that investigated the Space Shuttle Challenger disaster. Along with his work in theoretical physics, Feynman has been credited with having pioneered the field of quantum computing and introducing the concept of nanotechnology. He held the Richard C. Tolman professorship in theoretical physics at the California Institute of Technology. In a 1999 poll of 130 leading physicists worldwide by the British journal Physics World,


id: richard-feynman-20260505-1
file: data/en.wikipedia.org/wiki/Richard_Feynman-1.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
== Education == Feynman attended Far Rockaway High School, which was also attended by fellow Nobel laureates Burton Richter and Baruch Samuel Blumberg. Upon starting high school, Feynman was quickly promoted to a higher math class. An IQ test administered in high school estimated his IQ at 125—high but "merely respectable", according to biographer James Gleick. His sister Joan, who scored one point higher, later jokingly claimed to an interviewer that she was smarter. Years later he declined to join Mensa International, saying that his IQ was too low. When Feynman was 15, he taught himself trigonometry, advanced algebra, infinite series, analytic geometry, and both differential and integral calculus. Before entering college, he was experimenting with mathematical topics such as the half-derivative using his own notation. He created special symbols for logarithm, sine, cosine and tangent functions so they did not look like three variables multiplied together, and for the derivative, to remove the temptation of canceling out the d {\displaystyle d} s in d / d x {\displaystyle d/dx} . A member of the Arista Honor Society, in his last year in high school he won the New York University Math Championship. His habit of direct characterization sometimes rattled


id: richard-feynman-20260505-2
file: data/en.wikipedia.org/wiki/Richard_Feynman-2.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
In 1941, with World War II occurring in Europe but the United States not yet at war, Feynman spent the summer working on ballistics problems at the Frankford Arsenal in Pennsylvania. After the attack on Pearl Harbor brought the United States into the war, Feynman was recruited by Robert R. Wilson, who was working on means to produce enriched uranium for use in an atomic bomb, as part of what would become the Manhattan Project. At the time, Feynman had not earned a graduate degree. Wilson's team at Princeton was working on a device called an isotron, intended to electromagnetically separate uranium-235 from uranium-238. This was done in a quite different manner from that used by the calutron that was under development by a team under Wilson's former mentor, Ernest O. Lawrence, at the Radiation Laboratory of the University of California. On paper, the isotron was many times more efficient than the calutron, but Feynman and Paul Olum struggled to determine whether it was practical. Ultimately, on Lawrence's recommendation, the isotron project was abandoned. At this juncture, in early 1943, Robert Oppenheimer was establishing the Los Alamos Laboratory, a secret laboratory on a mesa in New Mexico where atomic bombs


id: richard-feynman-20260505-3
file: data/en.wikipedia.org/wiki/Richard_Feynman-3.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
Informed that Arline was dying, Feynman drove to Albuquerque and sat with her for hours until she died on June 16, 1945. He then immersed himself in work on the project and was present at the Trinity nuclear test. Feynman claimed to be the only person to see the explosion without the very dark glasses or welder's lenses provided, reasoning that it was safe to look through a truck windshield, as it would screen out the harmful ultraviolet radiation. The immense brightness of the explosion made him duck to the truck's floor, where he saw a temporary "purple splotch" afterimage. == Cornell (1945–1949) == Feynman nominally held an appointment at the University of Wisconsin–Madison as an assistant professor of physics, but was on unpaid leave during his involvement in the Manhattan Project. In 1945, he received a letter from Dean Mark Ingraham of the College of Letters and Science requesting his return to the university to teach in the coming academic year. His appointment was not extended when he did not commit to returning. In a talk given there several years later, Feynman quipped, "It's great to be back at the only university that ever had the good sense to


id: richard-feynman-20260505-4
file: data/en.wikipedia.org/wiki/Richard_Feynman-4.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
Feynman was not the only frustrated theoretical physicist in the early post-war years. Quantum electrodynamics suffered from infinite integrals in perturbation theory. These were clear mathematical flaws in the theory, which Feynman and Wheeler had tried, unsuccessfully, to work around. "Theoreticians", noted Murray Gell-Mann, "were in disgrace". In June 1947, leading American physicists met at the Shelter Island Conference. For Feynman, it was his "first big conference with big men ... I had never gone to one like this one in peacetime." The problems plaguing quantum electrodynamics were discussed, but the theoreticians were completely overshadowed by the achievements of the experimentalists, who reported the discovery of the Lamb shift, the measurement of the magnetic moment of the electron, and Robert Marshak's two-meson hypothesis. Bethe took the lead from the work of Hans Kramers, and derived a renormalized non-relativistic quantum equation for the Lamb shift. The next step was to create a relativistic version. Feynman thought that he could do this, but when he went back to Bethe with his solution, it did not converge. Feynman carefully worked through the problem again, applying the path integral formulation that he had used in his thesis. Like Bethe, he made the integral finite


id: richard-feynman-20260505-5
file: data/en.wikipedia.org/wiki/Richard_Feynman-5.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
=== Personal and political life === Feynman did not return to Cornell. Bacher, who had been instrumental in bringing Feynman to Cornell, had lured him to the California Institute of Technology (Caltech). Part of the deal was that he could spend his first year on sabbatical in Brazil. He had become smitten by Mary Louise Bell from Neodesha, Kansas. They had met in a cafeteria in Cornell, where she had studied the history of Mexican art and textiles. She later followed him to Caltech, where he gave a lecture. While he was in Brazil, she taught classes on the history of furniture and interiors at Michigan State University. He proposed to her by mail from Rio de Janeiro, and they married in Boise, Idaho, on June 28, 1952, shortly after he returned. They frequently quarreled and she was frightened by what she described as "a violent temper". Their politics were different; although he registered and voted as a Republican, she was more conservative, and her opinion on the 1954 Oppenheimer security hearing ("Where there's smoke there's fire") offended him. They separated on May 20, 1956. An interlocutory decree of divorce was entered on June 19, 1956, on the grounds of


id: richard-feynman-20260505-6
file: data/en.wikipedia.org/wiki/Richard_Feynman-6.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
=== Physics === At Caltech, Feynman investigated the physics of the superfluidity of supercooled liquid helium, where helium seems to display a complete lack of viscosity when flowing. Feynman provided a quantum-mechanical explanation for the Soviet physicist Lev Landau's theory of superfluidity. Applying the Schrödinger equation to the question showed that the superfluid was displaying quantum mechanical behavior observable on a macroscopic scale. This helped with the problem of superconductivity, but the solution eluded Feynman. It was solved with the BCS theory of superconductivity, proposed by John Bardeen, Leon Neil Cooper, and John Robert Schrieffer in 1957. Feynman, inspired by a desire to quantize the Wheeler–Feynman absorber theory of electrodynamics, laid the groundwork for the path integral formulation and Feynman diagrams. With Murray Gell-Mann, Feynman developed a model of weak decay, which showed that the current coupling in the process is a combination of vector and axial currents (an example of weak decay is the decay of a neutron into an electron, a proton, and an antineutrino). Although E. C. George Sudarshan and Robert Marshak developed the theory nearly simultaneously, Feynman's collaboration with Gell-Mann was seen as seminal because the weak interaction was neatly described by the vector and axial


id: richard-feynman-20260505-7
file: data/en.wikipedia.org/wiki/Richard_Feynman-7.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
In the early 1960s, Feynman acceded to a request to "spruce up" the teaching of undergraduates at Caltech. After three years devoted to the task, he produced a series of lectures that later became The Feynman Lectures on Physics. Accounts vary about how successful the original lectures were. Feynman's own preface, written just after an exam on which the students did poorly, was somewhat pessimistic. His colleagues David L. Goodstein and Gerry Neugebauer said later that the intended audience of first-year students found the material intimidating while older students and faculty found it inspirational, so the lecture hall remained full even as the first-year students dropped away. In contrast, physicist Matthew Sands recalled the student attendance as being typical for a large lecture course. Converting the lectures into books occupied Matthew Sands and Robert B. Leighton as part-time co-authors for several years. Feynman suggested that the book cover should have a picture of a drum with mathematical diagrams about vibrations drawn upon it, in order to illustrate the application of mathematics to understanding the world. Instead, the publishers gave the books plain red covers, though they included a picture of Feynman playing drums in the foreword. Even though the books


id: richard-feynman-20260505-8
file: data/en.wikipedia.org/wiki/Richard_Feynman-8.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
=== Surely You're Joking, Mr. Feynman! === In the 1960s, Feynman began thinking of writing an autobiography, and he began granting interviews to historians. In the 1980s, working with Ralph Leighton (Robert Leighton's son), he recorded chapters on audio tape that Ralph transcribed. The book was published in 1985 as Surely You're Joking, Mr. Feynman! and became a best-seller. Gell-Mann was upset by Feynman's account in the book of the weak interaction work, and threatened to sue, resulting in a correction being inserted in later editions. This incident was just the latest provocation in decades of bad feeling between the two scientists. Gell-Mann often expressed frustration at the attention Feynman received; he remarked: "[Feynman] was a great scientist, but he spent a great deal of his effort generating anecdotes about himself." Feynman has been criticized for a chapter in the book entitled "You Just Ask Them?", where he describes how he learned to seduce women at a bar he went to in the summer of 1946. A mentor taught him to ask a woman if she would sleep with him before buying her anything. He describes seeing women at the bar as "bitches" in his thoughts, and tells a story


id: richard-feynman-20260505-9
file: data/en.wikipedia.org/wiki/Richard_Feynman-9.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
Aspects of Feynman's life have been portrayed in various media. Feynman was portrayed by Matthew Broderick in the 1996 biopic Infinity. Actor Alan Alda commissioned playwright Peter Parnell to write a two-character play about a fictional day in the life of Feynman set two years before Feynman's death. The play, QED, premiered at the Mark Taper Forum in Los Angeles in 2001 and was later presented at the Vivian Beaumont Theater on Broadway, with both productions starring Alda as Richard Feynman. Real Time Opera premiered its opera Feynman at the Norfolk (Connecticut) Chamber Music Festival in June 2005. In 2011, Feynman was the subject of a biographical graphic novel entitled simply Feynman, written by Jim Ottaviani and illustrated by Leland Myrick. In 2013, Feynman's role on the Rogers Commission was dramatized by the BBC in The Challenger (US title: The Challenger Disaster), with William Hurt playing Feynman. In 2016, Oscar Isaac performed a public reading of Feynman's 1946 love letter to the late Arline. In the 2023 American film Oppenheimer, directed by Christopher Nolan and based on American Prometheus, Feynman is portrayed by actor Jack Quaid. On May 4, 2005, the United States Postal Service issued the "American Scientists" commemorative


id: richard-feynman-20260505-10
file: data/en.wikipedia.org/wiki/Richard_Feynman-10.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
=== Selected scientific works === Feynman, Richard P. (1942). Laurie M. Brown (ed.). The Principle of Least Action in Quantum Mechanics. PhD Dissertation, Princeton University. World Scientific (with title "Feynman's Thesis: a New Approach to Quantum Theory") (published 2005). ISBN 978-981-256-380-4 Wheeler, John A.; Feynman, Richard P. (1945). "Interaction with the Absorber as the Mechanism of Radiation". Reviews of Modern Physics. 17 (2–3): 157–181. Bibcode:1945RvMP...17..157W. doi:10.1103/RevModPhys.17.157. Archived from the original on April 17, 2020. Retrieved May 20, 2019. Feynman, Richard P. (1946). A Theorem and its Application to Finite Tampers. Los Alamos Scientific Laboratory, Atomic Energy Commission. doi:10.2172/4341197. OSTI 4341197. Feynman, Richard P.; Welton, T. A. (1946). Neutron Diffusion in a Space Lattice of Fissionable and Absorbing Materials. Los Alamos Scientific Laboratory, Atomic Energy Commission. doi:10.2172/4381097. OSTI 4381097. Feynman, Richard P.; Metropolis, N.; Teller, E. (1947). Equations of State of Elements Based on the Generalized Fermi-Thomas Theory (PDF). Los Alamos Scientific Laboratory, Atomic Energy Commission. doi:10.2172/4417654. OSTI 4417654. Feynman, Richard P. (1948). "Space-time approach to non-relativistic quantum mechanics". Reviews of Modern Physics. 20 (2): 367–387. Bibcode:1948RvMP...20..367F. doi:10.1103/RevModPhys.20.367. Archived from the original on September 17, 2020. Retrieved May 20, 2019. Feynman, Richard P. (1948). "A Relativistic Cut-Off for Classical Electrodynamics". Physical


id: richard-feynman-20260505-11
file: data/en.wikipedia.org/wiki/Richard_Feynman-11.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (2005) [1970]. The Feynman Lectures on Physics: The Definitive and Extended Edition (2nd ed.). Addison Wesley. ISBN 0-8053-9045-6. Includes Feynman's Tips on Physics (with Michael Gottlieb and Ralph Leighton), which includes four previously unreleased lectures on problem solving, exercises by Robert Leighton and Rochus Vogt, and a historical essay by Matthew Sands. Three volumes; originally published as separate volumes in 1964 and 1966. Feynman, Richard P. (1961). Theory of Fundamental Processes. Addison Wesley. Feynman, Richard P. (1962). Quantum Electrodynamics. Addison Wesley. Feynman, Richard P.; Hibbs, Albert (1965). Quantum Mechanics and Path Integrals. McGraw Hill. ISBN 0-07-020650-3. Feynman, Richard P. (1967). The Character of Physical Law: The 1964 Messenger Lectures. MIT Press. ISBN 0-262-56003-8. Feynman, Richard P. (1972). Statistical Mechanics: A Set of Lectures. Reading, Mass: W. A. Benjamin. ISBN 0-8053-2509-3. Feynman, Richard P. (1972). Photon-Hadron interactions. Reading, Mass: W. A. Benjamin. ISBN 0-201-36074-8. Feynman, Richard P. (1985b). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 0-691-02417-0. Feynman, Richard P. (1987). Elementary Particles and the Laws of Physics: The 1986 Dirac Memorial Lectures. Cambridge University Press. ISBN 0-521-34000-4. Feynman, Richard P. (1995). Brian Hatfield (ed.). Lectures on Gravitation. Addison


id: richard-feynman-20260505-12
file: data/en.wikipedia.org/wiki/Richard_Feynman-12.md
category: reference
title: Richard Feynman
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Richard_Feynman
date_saved: 2026-05-05T11:07:01.571261+00:00
instance: kb-cron
parent: richard-feynman-20260505-0
summary:
== Sources == Bashe, Charles J.; Johnson, Lyle R.; Palmer, John H.; Pugh, Emerson W. (1986). IBM's Early Computers. Cambridge, Massachusetts: MIT. ISBN 0-262-02225-7. OCLC 12021988. Bethe, Hans A. (1991). The Road from Los Alamos. Masters of Modern Physics. Vol. 2. New York: Simon and Schuster. ISBN 0-671-74012-1. OCLC 24734608. Brian, Denis (2001). The Voice of Genius: Conversations with Nobel Scientists and Other Luminaries. Cambridge, Massachusetts: Perseus. ISBN 978-0-7382-0447-5. OCLC 751292707. Carroll, John Bissell (1996). Sternberg, Robert J.; Ben-Zeev, Talia (eds.). The Nature of Mathematical Thinking. Mahwah, New Jersey: L. Erlbaum Associates. ISBN 978-0-8058-1799-7. OCLC 34513302. Chown, Marcus (May 2, 1985). "Strangeness and Charm". New Scientist: 34. ISSN 0262-4079. Close, Frank (2011). The Infinity Puzzle: The Personalities, Politics, and Extraordinary Science Behind the Higgs Boson. Oxford University Press. ISBN 978-0-19-959350-7. OCLC 840427493. Deutsch, David (June 1, 1992). "Quantum computation". Physics World. 5 (6): 57–61. doi:10.1088/2058-7058/5/6/38. ISSN 0953-8585. Friedman, Jerome (2004). "A Student's View of Fermi". In Cronin, James W. (ed.). Fermi Remembered. Chicago, Illinois: University of Chicago Press. ISBN 978-0-226-12111-6. OCLC 835230762. Galison, Peter (1998). "Feynman's War: Modelling Weapons, Modelling Nature". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 29 (3):


id: fibonacci-anyons-20260505-0
file: data/en.wikipedia.org/wiki/Fibonacci_anyons-0.md
category: reference
title: Fibonacci anyons
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fibonacci_anyons
date_saved: 2026-05-05T11:07:02.742403+00:00
instance: kb-cron
parent: fibonacci-anyons-20260505-0
summary:
In condensed matter physics, a Fibonacci anyon is a type of anyon which lives in two-dimensional topologically ordered systems. The Fibonacci anyon τ {\displaystyle \tau } is distinguished uniquely by the fact that it satisfies the fusion rule τ ⊗ τ = 1 ⊕ τ {\displaystyle \tau \otimes \tau ={\bf {1}}\oplus \tau } . Alternatively, the Fibonacci anyon can be defined by fact that it is algebraically described by the unique non-trivial simple object in the Fibonacci category. Experimentally, it has been proposed that Fibonacci anyons could be hosted in the fractional quantum Hall system. In particular, it is possible that Fibonacci anyons are present in the system with filling factor ν = 12 / 5 {\displaystyle \nu =12/5} . Fibonacci anyons have primary been developed in the context of topological quantum computing. This is because these anyons allow for universal quantum computing based entirely on braiding and performing topological charge measurements, and hence form a natural setting for topological quantum computing. This is in contrast to anyons based on discrete gauge theory, which require a more subtle use of ancillas to perform universal quantum computation. == The Fibonacci category == Mathematically, the Fibonacci anyons are identified by the fact


id: fibonacci-anyons-20260505-1
file: data/en.wikipedia.org/wiki/Fibonacci_anyons-1.md
category: reference
title: Fibonacci anyons
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fibonacci_anyons
date_saved: 2026-05-05T11:07:02.742403+00:00
instance: kb-cron
parent: fibonacci-anyons-20260505-0
summary:
== Relationship to topological quantum field theory == In the context of topological quantum field theory, the Fibonacci category corresponds to the quantum Chern–Simons theory with gauge group G = S O ( 3 ) {\displaystyle G=SO(3)} at level k = 5 {\displaystyle k=5} . Seeing as SO ( 3 ) {\displaystyle {\text{SO}}(3)} is a double cover of SU ( 2 ) {\displaystyle {\text{SU}}(2)} , the Fibonacci category can alternatively be described as the even sectors in the Chern–Simons theory with gauge group G = SU ( 2 ) {\displaystyle G={\text{SU}}(2)} at level k = 3 {\displaystyle k=3} . From this perspective, one can see a connection between Fibonacci anyons and the Jones polynomial polynomial using the classical techniques of Edward Witten. In his seminal 1989 paper, Witten demonstrated that the link and manifold invariants of quantum Chern–Simons theory with gauge group G = S U ( 2 ) {\displaystyle G=SU(2)} are related intimately to the Jones polynomial evaluated at roots of unity. Since the Fibonacci category is related to G = SU ( 2 ) {\displaystyle G={\text{SU}}(2)} Chern–Simons theory, this gives a relation between the Fibonacci category and the Jones polynomial. A key insight of Michael Freedman in 1997


id: fibonacci-anyons-20260505-2
file: data/en.wikipedia.org/wiki/Fibonacci_anyons-2.md
category: reference
title: Fibonacci anyons
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fibonacci_anyons
date_saved: 2026-05-05T11:07:02.742403+00:00
instance: kb-cron
parent: fibonacci-anyons-20260505-0
summary:
== Method for universal quantum computing == The pipeline for universal quantum computing with Fibonacci anyons can be described as follows. First, one is given an instance of a decision problem which is in the complexity class BQP (for instance, a large integer whose factorization one wishes to determine). Since the problem of additively approximating a normalization of the Jones polynomial at a third root of unity is BQP complete, this means by definition that there is a polynomial time classical algorithm for taking any efficient quantum circuit an assigning to it a framed link such that an additive approximation of the Jones invariant (or really, Kauffman bracket) of that link evaluated at e 3 π i / 5 {\displaystyle e^{3\pi i/5}} encodes the solution of the decision problem. For example, using this procedure, Shor's algorithm for factoring an integer would correspond to some large link. To relate the Kauffman bracket of this link evaluated at e 3 π i / 5 {\displaystyle e^{3\pi i/5}} to the physical world, one would take some material which hosts Fibonacci anyons, and perform a series of creation, braiding, and fusion operators such that the spacetime trajectories of the Fibonacci anyons in this process


id: five-qubit-error-correcting-code-20260505-0
file: data/en.wikipedia.org/wiki/Five-qubit_error_correcting_code-0.md
category: reference
title: Five-qubit error correcting code
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Five-qubit_error_correcting_code
date_saved: 2026-05-05T11:07:03.873413+00:00
instance: kb-cron
parent: five-qubit-error-correcting-code-20260505-0
summary:
The five-qubit error correcting code, [[5,1,3]] code, or Laflamme–Miquel–Paz–Zurek code is the smallest quantum error correcting code that can protect a logical qubit from any arbitrary single qubit error. In this code, 5 physical qubits are used to encode the logical qubit. With X {\displaystyle X} and Z {\displaystyle Z} being Pauli matrices and I {\displaystyle I} the Identity matrix, this code's generators are ⟨ X Z Z X I , I X Z Z X , X I X Z Z , Z X I X Z ⟩ {\displaystyle \langle XZZXI,IXZZX,XIXZZ,ZXIXZ\rangle } . Its logical operators are X ¯ = X X X X X {\displaystyle {\bar {X}}=XXXXX} and Z ¯ = Z Z Z Z Z {\displaystyle {\bar {Z}}=ZZZZZ} . Once the logical qubit is encoded, errors on the physical qubits can be detected via stabilizer measurements. A lookup table that maps the results of the stabilizer measurements to the types and locations of the errors gives the control system of the quantum computer enough information to correct errors. == History == Peter Shor's original quantum error correcting code of 1995 used nine qubits. The five-qubit error correcting code was published independently by two groups in 1996: by


id: fluxonium-20260505-0
file: data/en.wikipedia.org/wiki/Fluxonium-0.md
category: reference
title: Fluxonium
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fluxonium
date_saved: 2026-05-05T11:07:05.111266+00:00
instance: kb-cron
parent: fluxonium-20260505-0
summary:
In quantum computing, the fluxonium is a type of superconducting qubit architecture used for gate-based quantum computation that is insensitive to offset charge noise. It is constructed from a Josephson junction, a capacitor, and a “superinductor” (a type of inductor) arranged in a loop. The fluxonium was first proposed as a candidate for a qubit by an experimental group at Yale University led by Michel Devoret in 2009. It is a flux-like qubit, meaning that its energy levels correspond to integer numbers of magnetic flux/phase states. This architecture has long coherence times and high anharmonicity (or nonlinearity), both of which are important for successful qubit architectures. By changing the relative values of the different circuit components, fluxoniums can be engineered to have other properties, such as resistance to noise. However, the design requires complex fabrication methods, and is therefore difficult to scale. The fluxonium architecture has achieved among the strongest coherence for any solid-state superconducting qubit, with millisecond-level coherence times. Fluxoniums are a candidate for a qubit in a quantum processor, with some companies like D-Wave, Atlantic Quantum, and Qilimanjaro focused specifically on developing fluxonium-based quantum computing hardware. == Background == The first successful superconducting qubits were charge qubits, also


id: google-quantum-ai-20260505-0
file: data/en.wikipedia.org/wiki/Google_Quantum_AI-0.md
category: reference
title: Google Quantum AI
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Google_Quantum_AI
date_saved: 2026-05-05T11:07:06.284469+00:00
instance: kb-cron
parent: google-quantum-ai-20260505-0
summary:
Google Quantum AI is a research division of Google focused on developing quantum computing technologies. Its plan is to build large-scale, error-corrected quantum computers and advance quantum hardware, software, and algorithms for scientific and practical applications beyond the capacities of classical computers. == References ==


id: google-research-20260505-0
file: data/en.wikipedia.org/wiki/Google_Research-0.md
category: reference
title: Google Research
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Google_Research
date_saved: 2026-05-05T11:07:07.470932+00:00
instance: kb-cron
parent: google-research-20260505-0
summary:
Google Research (also known as Research at Google) is the research division of Google, a subsidiary of Alphabet Inc.. According to its official website, Google Research publishes findings, releases open-source software, and applies research results within Google products and services as well as within the wider scientific community. == Notable contributions == The 2017 landmark paper Attention Is All You Need, which introduced the Transformer architecture, which has subsequently been used to build modern large language models. Advances in neural machine translation powering Google Translate. Time series forecasting. Development of scalable learning systems and infrastructure for large-model training. Flood forecasting. Research into computational discovery via Google Accelerated Science including demonstrating the first below-threshold quantum calculations. == See also == Google AI Google Brain Google DeepMind == References == == External links == Official website Google AI portal


id: gottesman-kitaev-preskill-code-20260505-0
file: data/en.wikipedia.org/wiki/Gottesman–Kitaev–Preskill_code-0.md
category: reference
title: Gottesman–Kitaev–Preskill code
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gottesman–Kitaev–Preskill_code
date_saved: 2026-05-05T11:07:08.673257+00:00
instance: kb-cron
parent: gottesman-kitaev-preskill-code-20260505-0
summary:
The Gottesman–Kitaev–Preskill (GKP) code is a quantum error correcting code that encodes logical qubits into the continuous degrees of freedom of a quantum system. It is named after Daniel Gottesman, Alexei Kitaev and John Preskill who published it together in 2001. The code is used in continuous variable (CV) photonic quantum computing, in which logical qubits are encoded into the field quadratures of an optical mode. These modes can be thought of as the quantum harmonic oscillator with conjugate position and momentum operators. By encoding logical qubits into a single optical mode, the GKP code demonstrates greater hardware efficiency than traditional qubit codes. Instead of needing many qubits to act as redundancy for a single qubit, the GKP code instead requires a precisely constructed optical state. GKP codes are able to protect against both small shifts in the quadratures, but also loss channels such as photon loss in a photonic system. == Overview == GKP codes protects against random shifts in the quadratures, which can be modeled as a Gaussian random displacement channel. N ( ρ ) = ∫ d x e − | | x | | 2 / 2 σ ~ 2 D ( x ) ρ D


id: gottesman-kitaev-preskill-code-20260505-1
file: data/en.wikipedia.org/wiki/Gottesman–Kitaev–Preskill_code-1.md
category: reference
title: Gottesman–Kitaev–Preskill code
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gottesman–Kitaev–Preskill_code
date_saved: 2026-05-05T11:07:08.673257+00:00
instance: kb-cron
parent: gottesman-kitaev-preskill-code-20260505-0
summary:
== Experimental realization == Physically, GKP states are realized in the following way. First, cat states are generated via Gaussian boson sampling (GBS) techniques, then, the cat states are squeezed and interfered at a beam splitter. Homodyne detection is performed at one output of the beam splitter, and depending on the outcome, an approximate GKP state is created. The output can be further interfered to produce better approximations Cat states are superpositions of out of phase coherent states. They can be written as | ψ ⟩ = N ( | α ⟩ + e i ϕ | − α ⟩ ) {\displaystyle |\psi \rangle ={\mathcal {N}}(|\alpha \rangle +e^{i\phi }|-\alpha \rangle )} Where N {\displaystyle {\mathcal {N}}} is a normalization factor defined as N = [ 2 + 2 e ( − 2 α 2 ) cos ⁡ ϕ ] − 1 / 2 {\displaystyle {\mathcal {N}}=[2+2e^{(-2\alpha ^{2})}\cos {\phi }]^{-1/2}} . These states can be generated in a variety of ways with varying efficiencies. Photon subtraction is one approach, which uses squeezed vacuum states, beam splitters, and photon number resolving (PNR) detectors. The beam splitters must be tuned with a high transmissivity however, making this process impractical for state preparation. The


id: hadamard-test-20260505-0
file: data/en.wikipedia.org/wiki/Hadamard_test-0.md
category: reference
title: Hadamard test
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hadamard_test
date_saved: 2026-05-05T11:07:09.911487+00:00
instance: kb-cron
parent: hadamard-test-20260505-0
summary:
In quantum computation, the Hadamard test is a method used to create a random variable whose expected value is the expected real part R e ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Re} \langle \psi |U|\psi \rangle } , where | ψ ⟩ {\displaystyle |\psi \rangle } is a quantum state and U {\displaystyle U} is a unitary gate acting on the space of | ψ ⟩ {\displaystyle |\psi \rangle } . The Hadamard test produces a random variable whose image is in { ± 1 } {\displaystyle \{\pm 1\}} and whose expected value is exactly R e ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Re} \langle \psi |U|\psi \rangle } . It is possible to modify the circuit to produce a random variable whose expected value is I m ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Im} \langle \psi |U|\psi \rangle } by applying an S † {\displaystyle S^{\dagger }} gate after the first Hadamard gate. == Description of the circuit == To perform the Hadamard test we first calculate the state 1 2 ( | 0 ⟩ + | 1 ⟩ ) ⊗ | ψ ⟩ {\displaystyle {\frac {1}{\sqrt {2}}}\left(\left|0\right\rangle +\left|1\right\rangle \right)\otimes


id: hamiltonian-quantum-computation-20260505-0
file: data/en.wikipedia.org/wiki/Hamiltonian_quantum_computation-0.md
category: reference
title: Hamiltonian quantum computation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hamiltonian_quantum_computation
date_saved: 2026-05-05T11:07:11.125771+00:00
instance: kb-cron
parent: hamiltonian-quantum-computation-20260505-0
summary:
Hamiltonian quantum computation is a form of quantum computing. Unlike methods of quantum computation such as the adiabatic, measurement-based and circuit model where eternal control is used to apply operations on a register of qubits, Hamiltonian quantum computers operate without external control. == Background == Hamiltonian quantum computation was the pioneering model of quantum computation, first proposed by Paul Benioff in 1980. Benioff's motivation for building a quantum mechanical model of a computer was to have a quantum mechanical description of artificial intelligence and to create a computer that would dissipate the least amount of energy allowable by the laws of physics. However, his model was not time-independent and local. Richard Feynman, independent of Benioff, also wanted to provide a description of a computer based on the laws of quantum physics. He solved the problem of a time-independent and local Hamiltonian by proposing a continuous-time quantum walk that could perform universal quantum computation. Superconducting qubits, Ultracold atoms and non-linear photonics have been proposed as potential experimental implementations of Hamiltonian quantum computers. == Definition == Given a list of quantum gates described as unitaries U 1 , U 2 . . . U k {\displaystyle U_{1},U_{2}...U_{k}} , define a hamiltonian H


id: hanyuan-1-20260505-0
file: data/en.wikipedia.org/wiki/Hanyuan-1-0.md
category: reference
title: Hanyuan-1
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hanyuan-1
date_saved: 2026-05-05T11:07:12.258464+00:00
instance: kb-cron
parent: hanyuan-1-20260505-0
summary:
Hanyuan-1, or Hanyuan No. 1, is China's first quantum computer. It was developed by the Chinese Academy of Sciences’ Innovation Academy for Precision Measurement Science and Technology. It is able to operate at room temperature and uses cold atoms as qubits. It is commercially available with current orders totalling 40 million yuan. The Hanyuan-1 contains 100 qubits. It can fit within three standard equipment racks, and can manage complex applications in the area of logistics optimization and financial modeling. == References ==


id: hidden-subgroup-problem-20260505-0
file: data/en.wikipedia.org/wiki/Hidden_subgroup_problem-0.md
category: reference
title: Hidden subgroup problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hidden_subgroup_problem
date_saved: 2026-05-05T11:07:13.896259+00:00
instance: kb-cron
parent: hidden-subgroup-problem-20260505-0
summary:
The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. It is a generalization of problems including factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important in the theory of quantum computing because Shor's algorithms for factoring and finding discrete logarithms in quantum computing are instances of the hidden subgroup problem for finite abelian groups, while the other problems correspond to finite groups that are not abelian. == Problem statement == Given a group G {\displaystyle G} , a subgroup H ≤ G {\displaystyle H\leq G} , and a set X {\displaystyle X} , we say a function f : G → X {\displaystyle f:G\to X} hides the subgroup H {\displaystyle H} if for all g 1 , g 2 ∈ G , f ( g 1 ) = f ( g 2 ) {\displaystyle g_{1},g_{2}\in G,f(g_{1})=f(g_{2})} if and only if g 1 H = g 2 H {\displaystyle g_{1}H=g_{2}H} . Equivalently, f {\displaystyle f} is constant on each coset of H, while it is different between the different cosets of H. Hidden subgroup problem: Let G {\displaystyle G} be a group, X {\displaystyle X} a finite set,


id: hidden-subgroup-problem-20260505-1
file: data/en.wikipedia.org/wiki/Hidden_subgroup_problem-1.md
category: reference
title: Hidden subgroup problem
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hidden_subgroup_problem
date_saved: 2026-05-05T11:07:13.896259+00:00
instance: kb-cron
parent: hidden-subgroup-problem-20260505-0
summary:
==== Procedure ==== The set of characters of G {\displaystyle G} forms a group G ^ {\displaystyle {\widehat {G}}} called the dual group of G {\displaystyle G} . We also have a subgroup H ⊥ ≤ G ^ {\displaystyle H^{\perp }\leq {\widehat {G}}} of size | G | / | H | {\displaystyle |G|/|H|} defined by H ⊥ = { χ g : χ g ( h ) = 1 for all h ∈ H } {\displaystyle H^{\perp }=\{\chi _{g}:\chi _{g}(h)=1{\text{ for all }}h\in H\}} For each iteration of the algorithm, the quantum circuit outputs an element g ∈ G {\displaystyle g\in G} corresponding to a character χ g ∈ H ⊥ {\displaystyle \chi _{g}\in H^{\perp }} , and since χ g ( h ) = 1 {\displaystyle \chi _{g}(h)={1}} for all h ∈ H {\displaystyle h\in H} , it helps to pin down what H {\displaystyle H} is. The algorithm is as follows: Start with the state | 0 ⟩ | 0 ⟩ {\displaystyle |0\rangle |0\rangle } , where the left register's basis states are each element of G {\displaystyle G} , and the right register's basis states are each element of X {\displaystyle X} . Create a superposition


id: horse-ridge-chip-20260505-0
file: data/en.wikipedia.org/wiki/Horse_Ridge_(chip)-0.md
category: reference
title: Horse Ridge (chip)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Horse_Ridge_(chip)
date_saved: 2026-05-05T11:07:15.088356+00:00
instance: kb-cron
parent: horse-ridge-chip-20260505-0
summary:
Intel "Horse Ridge" is a cryogenic control chip that presented at the International Solid State Circuits Conference 2020 of San Francisco. Horse Ridge is based on Intel's 22nm FFL (FinFET Low Power) CMOS technology. Intel and QuTech published a study in Nature in which they demonstrate that they have been able to operate qubits at temperatures above 1 degree Kelvin (-272.15 degrees Celsius). In December 2020, Intel released Horse Ridge II, adding enhanced capabilities and higher levels of integration for sophisticated control of the quantum system. New features include the ability to manipulate and read qubit states (and drive up to 16 spin qubits with a direct digital synthesis (DDS) architecture) and control the potential of multiple gates needed to correlate multiple qubits (features 22 high-speed digital-to-analog converters (DACs)). Horse Ridge II is also implemented using Intel's low-power 22 nm FinFET technology (22FFL) and its operation has been tested at a temperature of 4 degree Kelvin. == References ==


id: elanor-huntington-20260505-0
file: data/en.wikipedia.org/wiki/Elanor_Huntington-0.md
category: reference
title: Elanor Huntington
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Elanor_Huntington
date_saved: 2026-05-05T11:07:16.224202+00:00
instance: kb-cron
parent: elanor-huntington-20260505-0
summary:
Elanor H. Huntington is an Australian scientist and engineer who is Deputy Chief Executive at the Commonwealth Scientific and Industrial Research Organisation and a professor of Quantum Cybernetics at the Australian National University. She led a research program in the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology. == Early life and education == Huntington studied physics at the Australian National University and graduated in 1996 with a University Medal. She decided that she enjoyed using science to help others, and switched to engineering. She earned her PhD in 1999 working in experimental quantum optics. Huntington joined the Australian Defence Science and Technology Organisation after graduating, where she worked for 18 months before joining the University of New South Wales Canberra at the Australian Defence Force Academy. == Research == Huntington specialises in high speed measurements and the generation of non-classical states. She works on quantum computation, creating optical microchips that can detect, generate and manipulate states of light. She is interested in the intersection of quantum theory and applications. She joined the University of New South Wales in 2000. She has worked in the School of Engineering and Information Technology at the Australian Defence Force


id: ibm-condor-20260505-0
file: data/en.wikipedia.org/wiki/IBM_Condor-0.md
category: reference
title: IBM Condor
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IBM_Condor
date_saved: 2026-05-05T11:07:17.441239+00:00
instance: kb-cron
parent: ibm-condor-20260505-0
summary:
IBM Condor is a 1,121-qubit quantum processor created by IBM, unveiled during the IBM Quantum Summit 2023, which occurred on December 4, 2023. It is the 2nd largest quantum processor (in terms of qubits), just shy of the 1,125-qubit quantum processor by the company Atom, created in October 2023. It has a similar performance to its predecessor, the IBM Osprey. It has a 50% increase in qubit density compared to the IBM Osprey, and over a mile of high-density cryogenic flex IO wiring. It is not as fast as the IBM Heron, unveiled during the same event. == References ==


id: ibm-eagle-20260505-0
file: data/en.wikipedia.org/wiki/IBM_Eagle-0.md
category: reference
title: IBM Eagle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IBM_Eagle
date_saved: 2026-05-05T11:07:18.628984+00:00
instance: kb-cron
parent: ibm-eagle-20260505-0
summary:
IBM Eagle is a 127-qubit quantum processor. IBM claims that it can not be simulated by any classical computer. It is two times bigger than China's Jiuzhang 2. It was revealed on November 16, 2021, and was claimed to be the most powerful quantum processor ever made until November 2022, when the IBM Osprey overtook it with 433 qubits. It is almost twice as powerful as their last processor, the 'Hummingbird', which had 65 quantum bits and was created in 2020. IBM believes that the processes used in creating the 'Eagle', will be the backbone for their future processors. == References == == External links == IBM’s roadmap for scaling quantum technology


id: ibm-heron-20260505-0
file: data/en.wikipedia.org/wiki/IBM_Heron-0.md
category: reference
title: IBM Heron
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IBM_Heron
date_saved: 2026-05-05T11:07:19.792248+00:00
instance: kb-cron
parent: ibm-heron-20260505-0
summary:
IBM Heron is a 156-qubit tunable-coupler quantum processor created by IBM, originally unveiled during the IBM Quantum Summit 2023, which occurred on December 4, 2023, and is the highest performance quantum processor IBM has ever built. It is currently in use on the IBM Quantum System Two, unveiled during the same event. IBM claims that this processor eliminates cross-talk errors that emerged in their previous quantum processors, and that this processor is being made available for users via the cloud. The first version is reportedly 5 times faster than their previous best record set by the IBM Eagle. == IBM Heron r2 == During the IBM Quantum Developer Conference, a second revision (called r2) was released, which increased the qubit count from 133 to 156, and introduced a two-level system mitigation to reduce the impact of an important source of noise. == References ==


id: ibm-osprey-20260505-0
file: data/en.wikipedia.org/wiki/IBM_Osprey-0.md
category: reference
title: IBM Osprey
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IBM_Osprey
date_saved: 2026-05-05T11:07:20.943188+00:00
instance: kb-cron
parent: ibm-osprey-20260505-0
summary:
IBM Osprey is a 433-qubit quantum processor created by IBM, revealed during the IBM Quantum Summit 2022, which occurred on November 9, 2022, in New York, United States. It is 3 times larger than its predecessor, the IBM Eagle. It needs to be cooled down to a temperature of ~0.02 K (-273.13 °C). == References ==


id: ibm-q-system-one-20260505-0
file: data/en.wikipedia.org/wiki/IBM_Q_System_One-0.md
category: reference
title: IBM Q System One
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IBM_Q_System_One
date_saved: 2026-05-05T11:07:22.201870+00:00
instance: kb-cron
parent: ibm-q-system-one-20260505-0
summary:
IBM Quantum System One is the first circuit-based commercial quantum computer, introduced by IBM in January 2019. This integrated quantum computing system is housed in an airtight borosilicate glass cube that maintains a controlled physical environment. Each face of the cube is 9 feet (2.7 m) wide and tall. A cylindrical protrusion from the center of the ceiling is a dilution refrigerator, containing a 20-qubit transmon quantum processor. It was tested for the first time in the summer of 2018, for two weeks, in Milan, Italy. IBM Quantum System One was developed by IBM Research, with assistance from the Map Project Office and Universal Design Studio. CERN, ExxonMobil, Fermilab, Argonne National Laboratory, and Lawrence Berkeley National Laboratory are among the clients signed up to access the system remotely. From April 6 to May 31, 2019, the Boston Museum of Science hosted an exhibit featuring a replica of the IBM Quantum System One. On June 15, 2021, IBM deployed the first unit of Quantum System One in Germany at its headquarters in Ehningen. On April 5, 2024, IBM unveiled a Quantum System One at the Rensselaer Polytechnic Institute, the first IBM quantum system on a university campus. == See also ==


id: ibm-q-system-two-20260505-0
file: data/en.wikipedia.org/wiki/IBM_Q_System_Two-0.md
category: reference
title: IBM Q System Two
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IBM_Q_System_Two
date_saved: 2026-05-05T11:07:23.407768+00:00
instance: kb-cron
parent: ibm-q-system-two-20260505-0
summary:
IBM Quantum System Two is the first modular utility-scaled quantum computer system, unveiled by IBM on December 4, 2023. It is a successor to the IBM Quantum System One. It contains three IBM Quantum Heron processors, which can be scaled up due to its modularity, and later upgraded for newer quantum processing units, as it is upgradeable. For its maximum efficiency, it has to be cooled to a temperature of a few hundredths of degrees above absolute zero (10–20 mK), using dilution technology. == Current usage == IBM has stated that their clients and partners are using their 100+ qubit systems to advance science. == Future == IBM has stated that their quantum coupling technology will allow multiple Quantum System Two units to connect together, to create systems capable of running 100 million operations in a single quantum circuit, and later a billion operations, by 2033. == References ==


id: ibm-quantum-platform-20260505-0
file: data/en.wikipedia.org/wiki/IBM_Quantum_Platform-0.md
category: reference
title: IBM Quantum Platform
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IBM_Quantum_Platform
date_saved: 2026-05-05T11:07:24.589299+00:00
instance: kb-cron
parent: ibm-quantum-platform-20260505-0
summary:
IBM Quantum Platform (previously known as IBM Quantum Experience) is an online platform allowing public and premium access to cloud-based quantum computing services provided by IBM. This includes access to a set of IBM's quantum processors, a set of tutorials on quantum computation, and access to interactive courses. As of June 2025, there are 12 devices on the service, all of which are freely accessible by the public. This service can be used to run algorithms and experiments, and explore tutorials and simulations around what might be possible with quantum computing. IBM's quantum processors are made up of superconducting transmon qubits, located in dilution refrigerators at the IBM Research headquarters at the Thomas J. Watson Research Center. Users interact with a quantum processor through the quantum circuit model of computation, typically through code written in Qiskit. This code can be compiled down to OpenQASM for execution on real quantum systems. Circuits can be created either graphically with the Quantum Composer, or programmatically through Jupyter notebooks on IBM's approved platforms for cloud-based quantum computing: qBraid and OVHCloud. == History == The service was launched in May 2016 as the IBM Quantum Experience with a five-qubit quantum processor and matching simulator connected


id: illinois-quantum-and-microelectronics-park-20260505-0
file: data/en.wikipedia.org/wiki/Illinois_Quantum_and_Microelectronics_Park-0.md
category: reference
title: Illinois Quantum and Microelectronics Park
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Illinois_Quantum_and_Microelectronics_Park
date_saved: 2026-05-05T11:07:25.761440+00:00
instance: kb-cron
parent: illinois-quantum-and-microelectronics-park-20260505-0
summary:
The Illinois Quantum and Microelectronics Park (IQMP) is a planned 128-acre technology campus on the site of the former U.S. Steel South Works on the south side of Chicago. It will focus on quantum computing and is not an AI data center. Plans for the IQMP are part of the larger “Quantum Shore Chicago” redevelopment of the former U.S. Steel South Works site, a long-vacant industrial area in Chicago’s South Shore neighborhood. The broader project is expected to include advanced manufacturing facilities, research centers, housing, and a replacement hospital, with an initial phase estimated at about $9 billion in investment. The overall park is expected to cost $9 billion to construct. Work is expected to begin in 2026 and be complete in 2028. == Tenants == PsiQuantum of Palo Alto, California has been announced as the anchor tenant of the IQMP, PsiQuantum intends to build and deploy America’s first million-qubit scale, fault-tolerant quantum computer. Other tenants include the DARPA-Illinois Quantum Proving Ground, IBM, Diraq, Quantum Machines, and Infleqtion. French quantum computing company Pasqal will invest more than $65 million to build its U.S. headquarters there. == History == President of Cook County Board of Commissioners Toni Preckwinkle, Chicago Mayor Brandon


id: india-s-quantum-computer-20260505-0
file: data/en.wikipedia.org/wiki/India's_quantum_computer-0.md
category: reference
title: India's quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/India's_quantum_computer
date_saved: 2026-05-05T11:07:26.974850+00:00
instance: kb-cron
parent: india-s-quantum-computer-20260505-0
summary:
India's quantum computer is the proposed and planned quantum computer to be developed in India by 2026. A quantum computer is a computer based on quantum phenomena and governed by the principles of quantum mechanics in physics. The development in the field of quantum computing in the world is also intricately linked to India. The legacy of quantum computing in India can be traced back from the period of Indian theoretical physicist Satyendra Nath Bose. His last four publication on quantum statistics and condensed matter physics led to the foundation of quantum mechanics. It was published in the year 1924. The first quantum computer India launch was of 7 qubits developed at Tata Institute of Fundamental Research, Mumbai. In April 2025, An Indian startup named QpiAi unveiled a 25 qubit Quantum Computer named Indus, this quantum computer launched, is the first full-stack quantum computing system in the country selected under National Quantum Mission India (NQM), Government of India scheme. In the next five years, it is expected that India will invest around one billion dollars in the programs related to the development of the quantum computer. The Government of India has launched an initiative called as National Quantum Mission to


id: india-s-quantum-computer-20260505-1
file: data/en.wikipedia.org/wiki/India's_quantum_computer-1.md
category: reference
title: India's quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/India's_quantum_computer
date_saved: 2026-05-05T11:07:26.974850+00:00
instance: kb-cron
parent: india-s-quantum-computer-20260505-0
summary:
== Research and development == The Ministry of Electronics and Information Technology (MeitY) in collaboration with Amazon Web Services (AWS) established a Quantum Computing Applications Lab to facilitate research and development related to quantum computing in the month of January in 2021. Similarly in the month of March, the Department of Science and Technology (Government of India) and 13 research groups from the Indian Institute of Science Education and Research (IISER) launched I-HUB Quantum Technology Foundation (I-HUB QTF) at Pune for the development of quantum technologies. On the 22nd day of the same month, the Indian Space Research Organisation (ISRO) successfully demonstrated free-space Quantum Communication over a distance of 300 metre. A number of indigenous key technologies were developed to achieve it. It used the indigenous NAVIC receiver for time synchronization between the transmitter and receiver modules, and gimbal mechanism systems. A live videoconferencing was demonstrated using Quantum Key Distribution (QKD) link. It was demonstrated at the campus of Space Applications Centre (SAC) in Ahmedabad. The demonstration was between the two line-of-sight buildings within the campus. It was conducted at night to prevent the interference of the direct sunlight in the demonstration. The experiment is considered as a major achievement


id: india-s-quantum-computer-20260505-2
file: data/en.wikipedia.org/wiki/India's_quantum_computer-2.md
category: reference
title: India's quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/India's_quantum_computer
date_saved: 2026-05-05T11:07:26.974850+00:00
instance: kb-cron
parent: india-s-quantum-computer-20260505-0
summary:
== Startups companies == In the race of the development of quantum technologies, some startups companies in India are emerging to boost research and development projects of quantum computing in India. Bangalore based startup company QpiAI was founded in 2019 for advancements in quantum computing and generative AI technologies. It was founded by Nagendra Nagaraja who is presently the CEO of the company. The company has planned to establish a 25-qubit quantum computer at its headquarter in Bangalore very soon within this year. Similarly another quantum computing startup company BosonQ Psi was also established in Bangalore. It is a simulation software company utilizing quantum computing. It was named after the famous Indian quantum physicist Satyendra Nath Bose and the fundamental quantity Psi. It is also onboard with the US-based IT company IBM's quantum networks. The Government of India under its two flagship initiatives National Quantum Mission and National Mission on Interdisciplinary Cyber-Physical Systems has selected eight major startups companies for innovation of advanced technologies in the areas of quantum computing, communication, sensing, and advanced materials. These eight major startups companies are QNu Labs (Bengaluru), QPiAI India Private Limited (Bengaluru), Dimira Technologies Private Limited (IIT Mumbai), Prenishq Private Limited (IIT Delhi),


id: integrated-quantum-photonics-20260505-0
file: data/en.wikipedia.org/wiki/Integrated_quantum_photonics-0.md
category: reference
title: Integrated quantum photonics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Integrated_quantum_photonics
date_saved: 2026-05-05T11:07:28.243511+00:00
instance: kb-cron
parent: integrated-quantum-photonics-20260505-0
summary:
Integrated quantum photonics, uses photonic integrated circuits to control photonic quantum states for applications in quantum technologies. As such, integrated quantum photonics provides a promising approach to the miniaturisation and scaling up of optical quantum circuits. The major application of integrated quantum photonics is Quantum technology:, for example quantum computing, quantum communication, quantum simulation, quantum walks and quantum metrology. == History == Linear optics was not seen as a potential technology platform for quantum computation until the seminal work of Knill, Laflamme, and Milburn, which demonstrated the feasibility of linear optical quantum computers using detection and feed-forward to produce deterministic two-qubit gates. Following this there were several experimental proof-of-principle demonstrations of two-qubit gates performed in bulk optics. It soon became clear that integrated optics could provide a powerful enabling technology for this emerging field. Early experiments in integrated optics demonstrated the feasibility of the field via demonstrations of high-visibility non-classical and classical interference. Typically, linear optical components such as directional couplers (which act as beamsplitters between waveguide modes), and phase shifters to form nested Mach–Zehnder interferometers are used to encode a qubit in the spatial degree of freedom. That is, a single photon is in superposition between two waveguides, where


id: integrated-quantum-photonics-20260505-1
file: data/en.wikipedia.org/wiki/Integrated_quantum_photonics-1.md
category: reference
title: Integrated quantum photonics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Integrated_quantum_photonics
date_saved: 2026-05-05T11:07:28.243511+00:00
instance: kb-cron
parent: integrated-quantum-photonics-20260505-0
summary:
=== Silicon === A big advantage of using silicon is that the circuits can be tuned actively using integrated thermal microheaters or p-i-n modulators, after the devices have been fabricated. The other big benefit of silicon is its compatibility with CMOS technology, which allows leveraging the mature fabrication infrastructure of the semiconductor electronics industry. The structures differ from modern electronic ones, however, as they are readily scalable. Silicon has a really high refractive index of ~3.5 at the 1550 nm wavelength commonly used in optical telecommunications. It therefore offers one of the highest component densities in integrated photonics. The large contrast in refractive index with glass (1.44) allows waveguides formed of silicon surrounded by glass to have very tight bends, which allows for a high component density and reduced system size. Large silicon-on-insulator (SOI) wafers up to 300 mm in diameter can be obtained commercially, making the technology both available and reproducible. Many of the largest systems (up to several hundred components) have been demonstrated on the silicon photonics platform, with up to eight simultaneous photons, generation of graph states (cluster states), and up to 15 dimensional qubits). Photon sources in silicon waveguide circuits leverage silicon's third-order nonlinearity to produce


id: intelligence-advanced-research-projects-activity-20260505-0
file: data/en.wikipedia.org/wiki/Intelligence_Advanced_Research_Projects_Activity-0.md
category: reference
title: Intelligence Advanced Research Projects Activity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Intelligence_Advanced_Research_Projects_Activity
date_saved: 2026-05-05T11:07:29.453328+00:00
instance: kb-cron
parent: intelligence-advanced-research-projects-activity-20260505-0
summary:
The Intelligence Advanced Research Projects Activity (IARPA) is an organization, within the Office of the Director of National Intelligence (ODNI), that is responsible for leading research to overcome difficult challenges facing the United States Intelligence Community. IARPA characterizes its mission as follows: "To envision and lead high-risk, high-payoff research that delivers innovative technology for future overwhelming intelligence advantage." IARPA funds academic and industry research across a broad range of technical areas, including mathematics, computer science, physics, chemistry, biology, neuroscience, linguistics, political science, and cognitive psychology. Most IARPA research is unclassified and openly published. IARPA transfers successful research results and technologies to other government agencies. Notable IARPA investments include quantum computing, superconducting computing, machine learning, and forecasting tournaments. == Mission == IARPA characterizes its mission as "to envision and lead high-risk, high-payoff research that delivers innovative technology for future overwhelming intelligence advantage". == History == In 1958, the first Advanced Research Projects Agency, or ARPA, was created in response to an unanticipated surprise—the Soviet Union's successful launch of Sputnik on October 4, 1957. The ARPA model was designed to anticipate and pre-empt such technological surprises. As then-Secretary of Defense Neil McElroy said, "I want an agency that makes sure no important


id: intelligence-advanced-research-projects-activity-20260505-1
file: data/en.wikipedia.org/wiki/Intelligence_Advanced_Research_Projects_Activity-1.md
category: reference
title: Intelligence Advanced Research Projects Activity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Intelligence_Advanced_Research_Projects_Activity
date_saved: 2026-05-05T11:07:29.453328+00:00
instance: kb-cron
parent: intelligence-advanced-research-projects-activity-20260505-0
summary:
=== Past research === Aggregative Contingent Estimation (ACE) Program aimed "to dramatically enhance the accuracy, precision, and timeliness of intelligence forecasts for a broad range of event types, through the development of advanced techniques that elicit, weight, and combine the judgments of many intelligence analysts." ATHENA Program was a research program about cybersecurity. It aimed "to provide an early warning system for detecting precursors to cyberattacks". Babel Program developed "agile and robust speech recognition technology that can be rapidly applied to any human language in order to provide effective search capability for analysts to efficiently process massive amounts of real-world recorded speech". The program tried to develop software that could transcribe and search among all the languages. Biometrics Exploitation Science & Technology (BEST) Program focused on trying to "significantly advance the state-of-the-science for biometrics technologies". It was to discover techniques on utilizing biometrics from a subject in a less controlled environment which could produce a similar result to that in a controlled environment. Synthetic Holographic Observation (SHO) Program's stated goal was "to enable full-parallax, full-color, high-resolution display of dynamic 3D data without head-gear, and possessing visually continuous perspectives without artifacts over wide viewing angles." === Current research === Creation of


id: ionq-20260505-0
file: data/en.wikipedia.org/wiki/IonQ-0.md
category: reference
title: IonQ
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IonQ
date_saved: 2026-05-05T11:07:30.727625+00:00
instance: kb-cron
parent: ionq-20260505-0
summary:
IonQ, Inc. is an American quantum computing hardware and software company headquartered in College Park, Maryland. The company develops general-purpose trapped ion quantum computers and accompanying software to generate, optimize, and execute quantum circuits. == History == IonQ was co-founded by Christopher Monroe and Jungsang Kim, professors at Duke University, in 2015, with the help of venture firm New Enterprise Associates. The company is an offshoot of the co-founders’ 25 years of academic research in quantum information science. Monroe's quantum computing research began as a Staff Researcher at the National Institute of Standards and Technology (NIST) with physicist David Wineland where he led a team using trapped ions to produce the first controllable qubits and the first controllable quantum logic gate, culminating in a proposed architecture for a large-scale trapped ion computer. Kim and Monroe, who was at the time a professor at the University of Maryland, College Park (UMD), began collaborating formally as a result of larger research initiatives funded by the Intelligence Advanced Research Projects Activity (IARPA). They wrote a review paper for Science Magazine entitled Scaling the Ion Trap Quantum Processor, pairing Monroe's research at UMD in trapped ions with Kim's focus on scalable quantum information processing


id: iqm-quantum-computers-20260505-0
file: data/en.wikipedia.org/wiki/IQM_Quantum_Computers-0.md
category: reference
title: IQM Quantum Computers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/IQM_Quantum_Computers
date_saved: 2026-05-05T11:07:31.919551+00:00
instance: kb-cron
parent: iqm-quantum-computers-20260505-0
summary:
IQM Quantum Computers is a Finnish quantum computing hardware and software company headquartered in Espoo, Finland. The company develops and commercializes quantum computers based on superconducting technology. Their goal is to become the leading European company in quantum computing hardware. == Funding == IQM Quantum Computers has secured a total of over €600 million in capital as of 2025, ranking among the most highly funded quantum computing companies in Europe. The company announced a €275 million Series B round in September 2025. This round was led by Ten Eleven Ventures, a U.S.-based cybersecurity-focused investment firm, and Tesi, Finland's state-owned investment fund. It was the largest quantum computing funding round in Europe and the fourth largest round ever for a Finnish growth company to date. The Series B round attracted a diverse group of investors, including Finnish pension funds such as Elo Mutual and Varma Mutual Pension Insurance, the European Innovation Council (EIC). Previous major private funding rounds included a €128 million Series A2 round in 2022 led by World Fund, which brought additional international capital and advanced the company's R&D and scaling activities. Other early investors have included Maki.vc, OpenOcean, MIG Funds, Vito Ventures, and Matadero QED. Public and governmental


id: jiuzhang-quantum-computer-20260505-0
file: data/en.wikipedia.org/wiki/Jiuzhang_(quantum_computer)-0.md
category: reference
title: Jiuzhang (quantum computer)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Jiuzhang_(quantum_computer)
date_saved: 2026-05-05T11:07:33.045556+00:00
instance: kb-cron
parent: jiuzhang-quantum-computer-20260505-0
summary:
Jiuzhang (Chinese: 九章) is the first photonic quantum computer to claim quantum supremacy. Previously quantum supremacy has been achieved only once, in 2019, by Google's Sycamore; however, Google's computer was based on superconducting materials, and not photons. Jiuzhang was developed by a team from University of Science and Technology of China (USTC) led by Pan Jianwei and Lu Chao-Yang. The computer is named after Jiuzhang suanshu, an ancient Chinese mathematical classic book. On 3 December 2020, USTC announced in Science that Jiuzhang successfully performed Gaussian boson sampling in 200 seconds (3 minutes 20 seconds), with a maximum of 76 detected photons. The USTC group estimated that it would take 2.5 billion years for the Sunway TaihuLight supercomputer to perform the same calculation. == Experimental setup == The setup involves a Verdi-pumped Mira 900 Ti:sapphire laser which is split into 13 paths of equal intensity and then shone on 25 PPKTP crystals to produce 25 two-mode squeezed states. Through a hybrid encoding this is equivalent to 50 single-mode squeezed states. The purity is increased from 98% to 99% by 12 nm filtering. The 50 single-mode squeezed states are sent into a 100-mode interferometer and sampled by 100 single-photon detectors with an


id: kane-quantum-computer-20260505-0
file: data/en.wikipedia.org/wiki/Kane_quantum_computer-0.md
category: reference
title: Kane quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Kane_quantum_computer
date_saved: 2026-05-05T11:07:34.231560+00:00
instance: kb-cron
parent: kane-quantum-computer-20260505-0
summary:
The Kane quantum computer is a proposal for a scalable quantum computer proposed by Bruce Kane in 1998, who was then at the University of New South Wales. Often thought of as a hybrid between quantum dot and nuclear magnetic resonance (NMR) quantum computers, the Kane computer is based on an array of individual phosphorus donor atoms embedded in a pure silicon lattice. Both the nuclear spins of the donors and the spins of the donor electrons participate in the computation. Unlike many quantum computation schemes, the Kane quantum computer is in principle scalable to an arbitrary number of qubits. This is possible because qubits may be individually addressed by electrical means. == Description == The original proposal calls for phosphorus donors to be placed in an array with a spacing of 20 nm, approximately 20 nm below the surface. An insulating oxide layer is grown on top of the silicon. Metal A gates are deposited on the oxide above each donor, and J gates between adjacent donors. The phosphorus donors are isotopically pure 31P, which have a nuclear spin of 1/2. The silicon substrate is isotopically pure 28Si which has nuclear spin 0. Using the nuclear spin of the


id: g-peter-lepage-20260505-0
file: data/en.wikipedia.org/wiki/G._Peter_Lepage-0.md
category: reference
title: G. Peter Lepage
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/G._Peter_Lepage
date_saved: 2026-05-05T11:07:35.424839+00:00
instance: kb-cron
parent: g-peter-lepage-20260505-0
summary:
G. Peter Lepage (born 13 April 1952) is a Canadian American theoretical physicist and an academic administrator. He was the Harold Tanner Dean of the College of Arts and Sciences at Cornell University from 2003 to 2013. == Early life and education == Gerard Peter Lepage was born in Canada in 1952. Lepage studied at McGill University and graduated with a bachelor's degree in honours physics in 1972 and the University of Cambridge with a master's degree (M.A.St - Part III of the Mathematical Tripos) in 1973. In 1978, he received his PhD in theoretical physics from Stanford University. == Academic career == Lepage was a research associate at the Stanford Linear Accelerator Center in 1978. He was a postdoctoral research associate at the Laboratory of Nuclear Studies, Cornell University from 1978 to 1980. In 1980, he joined the physics faculty at Cornell University where he became a professor. He received academic tenure in 1984 after only four years on the university faculty. From 1999 to 2003, he was the chair of Cornell's physics department. He was appointed the Harold Tanner Dean of the College of Arts and Sciences, serving from 2003 to 2013. He is a Fellow of the


id: list-of-proposed-quantum-registers-20260505-0
file: data/en.wikipedia.org/wiki/List_of_proposed_quantum_registers-0.md
category: reference
title: List of proposed quantum registers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_proposed_quantum_registers
date_saved: 2026-05-05T11:07:36.666347+00:00
instance: kb-cron
parent: list-of-proposed-quantum-registers-20260505-0
summary:
A practical quantum computer must use a physical system as a programmable quantum register. Researchers are exploring several technologies as candidates for reliable qubit implementations. Superconducting quantum computing (qubit implemented by the state of nonlinear resonant superconducting circuits containing Josephson junctions) Trapped ion quantum computer (qubit implemented by the internal state of trapped ions) Neutral atom quantum computer (qubit implemented by internal states of neutral atoms trapped in an optical lattice or an array of dipole traps, i.e. optical tweezers) Quantum dot computer, spin-based (e.g. the Loss-DiVincenzo quantum computer) (qubit given by the spin states of trapped electrons) Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot) Quantum computing using engineered quantum wells, which could in principle enable the construction of a quantum computer that operates at room temperature Coupled quantum wire (qubit implemented by a pair of quantum wires coupled by a quantum point contact) Nuclear magnetic resonance quantum computer (NMRQC) implemented with the nuclear magnetic resonance of molecules in solution, where qubits are provided by nuclear spins within the dissolved molecule and probed with radio waves Solid-state NMR Kane quantum computer (qubit realized by the nuclear spin state of phosphorus donors in silicon) Vibrational


id: list-of-quantum-logic-gates-20260505-0
file: data/en.wikipedia.org/wiki/List_of_quantum_logic_gates-0.md
category: reference
title: List of quantum logic gates
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_quantum_logic_gates
date_saved: 2026-05-05T11:07:38.104837+00:00
instance: kb-cron
parent: list-of-quantum-logic-gates-20260505-0
summary:
In gate-based quantum computing, various sets of quantum logic gates are commonly used to express quantum operations. The following tables list several unitary quantum logic gates, together with their common name, how they are represented, and some of their properties. Controlled or conjugate transpose (adjoint) versions of some of these gates may not be listed. == Identity gate and global phase == The identity gate is the identity operation I | ψ ⟩ = | ψ ⟩ {\displaystyle I|\psi \rangle =|\psi \rangle } , most of the times this gate is not indicated in circuit diagrams, but it is useful when describing mathematical results. It has been described as being a "wait cycle", and a NOP. The global phase gate introduces a global phase e i φ {\displaystyle e^{i\varphi }} to the whole qubit quantum state. A quantum state is uniquely defined up to a phase. Because of the Born rule, a phase factor has no effect on a measurement outcome: | e i φ | = 1 {\displaystyle |e^{i\varphi }|=1} for any φ {\displaystyle \varphi } . Because e i δ | ψ ⟩ ⊗ | ϕ ⟩ = e i δ ( | ψ ⟩ ⊗ | ϕ


id: list-of-quantum-logic-gates-20260505-1
file: data/en.wikipedia.org/wiki/List_of_quantum_logic_gates-1.md
category: reference
title: List of quantum logic gates
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_quantum_logic_gates
date_saved: 2026-05-05T11:07:38.104837+00:00
instance: kb-cron
parent: list-of-quantum-logic-gates-20260505-0
summary:
The rotation operator gates R x ( θ ) , R y ( θ ) {\displaystyle R_{x}(\theta ),R_{y}(\theta )} and R z ( θ ) {\displaystyle R_{z}(\theta )} are the analog rotation matrices in three Cartesian axes of SO(3), along the x, y or z-axes of the Bloch sphere projection. As Pauli matrices are related to the generator of rotations, these rotation operators can be written as matrix exponentials with Pauli matrices in the argument. Any 2 × 2 {\displaystyle 2\times 2} unitary matrix in SU(2) can be written as a product (i.e. series circuit) of three rotation gates or less. Note that for two-level systems such as qubits and spinors, these rotations have a period of 4π. A rotation of 2π (360 degrees) returns the same statevector with a different phase. We also have R b ( − θ ) = R b ( θ ) † {\displaystyle R_{b}(-\theta )=R_{b}(\theta )^{\dagger }} and R b ( 0 ) = I {\displaystyle R_{b}(0)=I} for all b ∈ { x , y , z } . {\displaystyle b\in \{x,y,z\}.} The rotation matrices are related to the Pauli matrices in the following way: R x ( π ) = − i X


id: list-of-quantum-logic-gates-20260505-2
file: data/en.wikipedia.org/wiki/List_of_quantum_logic_gates-2.md
category: reference
title: List of quantum logic gates
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_quantum_logic_gates
date_saved: 2026-05-05T11:07:38.104837+00:00
instance: kb-cron
parent: list-of-quantum-logic-gates-20260505-0
summary:
The √SWAP gate performs half-way of a two-qubit swap (see Clifford gates). It is universal such that any many-qubit gate can be constructed from only √SWAP and single qubit gates. More than one application of the √SWAP is required to produce a Bell state from product states. The √SWAP gate arises naturally in systems that exploit exchange interaction. For systems with Ising like interactions, it is sometimes more natural to introduce the imaginary swap or iSWAP. Note that i SWAP = R x x ( − π / 2 ) R y y ( − π / 2 ) {\displaystyle i{\mbox{SWAP}}=R_{xx}(-\pi /2)R_{yy}(-\pi /2)} and i SWAP = R x x ( − π / 4 ) R y y ( − π / 4 ) {\displaystyle {\sqrt {i{\mbox{SWAP}}}}=R_{xx}(-\pi /4)R_{yy}(-\pi /4)} , or more generally i SWAP n = R x x ( − π / 2 n ) R y y ( − π / 2 n ) {\displaystyle {\sqrt[{n}]{i{\mbox{SWAP}}}}=R_{xx}(-\pi /2n)R_{yy}(-\pi /2n)} for all real n except 0. SWAPα arises naturally in spintronic quantum computers. The Fredkin gate (also CSWAP or CS gate), named after Edward Fredkin, is a 3-bit gate that performs a controlled swap. It is universal for


id: list-of-quantum-processors-20260505-0
file: data/en.wikipedia.org/wiki/List_of_quantum_processors-0.md
category: reference
title: List of quantum processors
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_quantum_processors
date_saved: 2026-05-05T11:07:39.418674+00:00
instance: kb-cron
parent: list-of-quantum-processors-20260505-0
summary:
This list contains quantum processors, also known as quantum processing units (QPUs). Some devices listed below have only been announced at press conferences so far, with no actual demonstrations or scientific publications characterizing the performance. Quantum processors are difficult to compare due to the different architectures and approaches. Due to this, published physical qubit numbers do not reflect the performance levels of the processor. This is instead achieved through the number of logical qubits or benchmarking metrics such as quantum volume, randomized benchmarking or circuit layer operations per second (CLOPS). == Circuit-based quantum processors == These QPUs are based on the quantum circuit and quantum logic gate-based model of computing. == Annealing quantum processors == These QPUs are based on quantum annealing, not to be confused with digital annealing. == Analog quantum processors == These QPUs are based on analog Hamiltonian simulation. == See also == Quantum programming Timeline of quantum computing and communication == References ==


id: magic-quantum-information-20260505-0
file: data/en.wikipedia.org/wiki/Magic_(quantum_information)-0.md
category: reference
title: Magic (quantum information)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magic_(quantum_information)
date_saved: 2026-05-05T11:07:40.614743+00:00
instance: kb-cron
parent: magic-quantum-information-20260505-0
summary:
In quantum information theory, magic is a property that quantifies the computational resources needed to describe quantum states beyond stabilizer states, which can be efficiently simulated on classical computers. The concept emerged from the Gottesman-Knill theorem proven in the 1990s, which showed that highly entangled stabilizer states offer no quantum computational advantage because they can be simulated just as efficiently on classical computers. In 2014, it was found that magic states are connected to contextuality: in quantum mechanics, it shows that measurement outcomes depend on what other properties are simultaneously measured. Magic is commonly measured using the stabilizer Rényi entropy, which can be experimentally determined through randomized measurement protocols on quantum processors. Without magic, quantum computers cannot perform any computation that classical computers cannot already do, making it essential for achieving quantum computational advantage. In 2024–2025, quantum magic was detected in top quark pairs produced at the Large Hadron Collider; it is the first observation of this property in fundamental particle collisions. The CMS and ATLAS experiments measured correlations between entangled top and anti-top quarks, with the amount of magic depending on the quarks' velocity and direction of travel. Recent theoretical work has revealed a computational phase separation between entanglement-dominated


id: magic-state-distillation-20260505-0
file: data/en.wikipedia.org/wiki/Magic_state_distillation-0.md
category: reference
title: Magic state distillation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magic_state_distillation
date_saved: 2026-05-05T11:07:41.772312+00:00
instance: kb-cron
parent: magic-state-distillation-20260505-0
summary:
Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers. It has also been linked to quantum contextuality, a concept thought to contribute to quantum computers' power. The technique was first proposed by Emanuel Knill in 2004, and further analyzed by Sergey Bravyi and Alexei Kitaev the same year. Thanks to the Gottesman–Knill theorem, it is known that some quantum operations (operations in the Clifford group) can be perfectly simulated in polynomial time on a classical computer. In order to achieve universal quantum computation, a quantum computer must be able to perform operations outside this set. Magic state distillation achieves this, in principle, by concentrating the usefulness of imperfect resources, represented by mixed states, into states that are conducive for performing operations that are difficult to simulate classically. A variety of qubit magic state distillation routines and distillation routines for qubits with various advantages have been proposed. == Stabilizer formalism == The Clifford group consists of a set of n {\displaystyle n} -qubit operations generated by the gates {H, S, CNOT} (where H is Hadamard and S is [ 1 0 0 i ] {\displaystyle


id: majorana-1-20260505-0
file: data/en.wikipedia.org/wiki/Majorana_1-0.md
category: reference
title: Majorana 1
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Majorana_1
date_saved: 2026-05-05T11:07:42.995461+00:00
instance: kb-cron
parent: majorana-1-20260505-0
summary:
Majorana 1 is a quantum computing processor developed by Microsoft. It uses topological superconductors in an attempt to enable topological quantum computing, which is designed to offer enhanced error robustness compared with conventional quantum computing hardware. It is the first device produced by Microsoft intended for use in quantum computing. It is an indium arsenide-aluminium hybrid device that admits superconductivity at low temperatures. Microsoft claims that it shows some signals of hosting boundary Majorana zero modes. The device can fit eight qubits. Majorana zero modes, if confirmed, could have potential application to making topological qubits, and eventually large-scale topological quantum computers. In its February 2025 announcement, Microsoft claimed that the Majorana 1 represents progress in its long-running project to create a quantum computer based on topological qubits. The announcement has generated both excitement and skepticism within the scientific community, in the absence of definitive public evidence that the Majorana 1 device exhibits Majorana zero modes. == Background == Quantum computing research has historically faced challenges in achieving qubit stability and scalability. Traditional qubits, such as those based on superconducting circuits or trapped ions, are highly susceptible to noise and decoherence, which can introduce errors in computations. To overcome these limitations,


id: microsoft-azure-quantum-20260505-0
file: data/en.wikipedia.org/wiki/Microsoft_Azure_Quantum-0.md
category: reference
title: Microsoft Azure Quantum
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Microsoft_Azure_Quantum
date_saved: 2026-05-05T11:07:44.183216+00:00
instance: kb-cron
parent: microsoft-azure-quantum-20260505-0
summary:
Microsoft Azure Quantum is a public cloud-based quantum computing platform developed by Microsoft, that offers quantum hardware, software, and solutions for developers to build quantum applications. It supports variety of quantum hardware architectures from partners including Quantinuum, IonQ, and Atom Computing. To run applications on the cloud platform, Microsoft developed the Q# quantum programming language. Azure Quantum also includes a platform for scientific research, Azure Quantum Elements. It uses artificial intelligence, high-performance computing and quantum processors to run molecular simulations and calculations in computational chemistry and materials science. Azure Quantum was first announced at Microsoft Ignite in 2019. The platform was opened for public preview in 2021, and Azure Quantum Elements was launched in 2023. == Hardware == In addition to its hardware partners on the platform, Microsoft is developing a topological quantum computer with qubits that are inherently resistant to error. The approach is based on Majorana quasiparticles, which act as their own antiparticle and have a charge and energy equal to zero, making qubits that are more resilient to disturbances. In September 2023, Azure Quantum researchers found evidence consistent with the creation and control of Majorana quasiparticles for topological quantum computing. In November 2024, the qubit virtualization system


id: m-lmer-s-rensen-gate-20260505-0
file: data/en.wikipedia.org/wiki/Mølmer–Sørensen_gate-0.md
category: reference
title: Mølmer–Sørensen gate
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mølmer–Sørensen_gate
date_saved: 2026-05-05T11:07:45.564101+00:00
instance: kb-cron
parent: m-lmer-s-rensen-gate-20260505-0
summary:
In quantum computing, Mølmer–Sørensen gate scheme (or MS gate) refers to an implementation procedure for various multi-qubit quantum logic gates used mostly in trapped ion quantum computing. This procedure is based on the original proposition by Klaus Mølmer and Anders Sørensen in 1999–2000. This proposal was an alternative to the 1995 Cirac–Zoller controlled-NOT gate implementation for trapped ions, which requires that the system be restricted to the joint motional ground state of the ions. In an MS gate, entangled states are prepared by illuminating ions with a bichromatic light field. Mølmer and Sørensen identified two regimes in which this is possible: A weak-field regime, where single-photon absorption is suppressed and two-photon processes interfere in a way that makes internal state dynamics insensitive to the vibrational state A strong-field regime where the individual ions are coherently excited, and the motional state is highly entangled with the internal state until all undesirable excitations are deterministically removed toward the end of the interaction. In both regimes, a red and blue sideband interaction are applied simultaneously to each ion, with the red and blue tones symmetrically detuned by δ ′ {\displaystyle \delta '} from the sidebands. This results in laser detunings ± ( ω


id: m-lmer-s-rensen-gate-20260505-1
file: data/en.wikipedia.org/wiki/Mølmer–Sørensen_gate-1.md
category: reference
title: Mølmer–Sørensen gate
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mølmer–Sørensen_gate
date_saved: 2026-05-05T11:07:45.564101+00:00
instance: kb-cron
parent: m-lmer-s-rensen-gate-20260505-0
summary:
The above is equivalent to the Ising coupling gate Ryy(π/2); It can then be shown that this gate (along with arbitrary single-qubit rotation) produces a universal set of gates. An alternative definition of MS gate equates it to Rxx(π/2), and is adopted as IonQ's native gate for two-qubit entanglement. In this definition, CNOT gate can be decomposed as CNOT = e − i π 4 ( I − Z 1 ) ( I − X 2 ) = R y 1 ( − π / 2 ) e − i π 4 ( I − X 1 ) ( I − X 2 ) R y 1 ( π / 2 ) = R y 1 ( − π / 2 ) e − i π 4 e i π 4 ( X 1 + X 2 − X 1 ⊗ X 2 ) R y 1 ( π / 2 ) = e − i π 4 R y 1 ( − π / 2 ) R x 1 ( − π / 2 ) R x 2 ( − π / 2 ) R x x ( π / 2 ) R y 1 ( π / 2


id: m-lmer-s-rensen-gate-20260505-2
file: data/en.wikipedia.org/wiki/Mølmer–Sørensen_gate-2.md
category: reference
title: Mølmer–Sørensen gate
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mølmer–Sørensen_gate
date_saved: 2026-05-05T11:07:45.564101+00:00
instance: kb-cron
parent: m-lmer-s-rensen-gate-20260505-0
summary:
By making a second rotating wave approximation to neglect oscillation terms, each piece can be examined independently. For δ = 0 {\displaystyle \delta =0} , only the first term is kept, and the Hamiltonian becomes H c a r r i e r = Ω 2 ( σ − + σ + ) , {\displaystyle H_{\rm {carrier}}={\frac {\Omega }{2}}(\sigma _{-}+\sigma _{+}),} which alters the spin state of the ion without affecting its motional state. For δ = − ω 0 {\displaystyle \delta =-\omega _{0}} , only the second term is kept since | δ + ω 0 | ≪ | δ | , | δ − ω 0 | {\displaystyle |\delta +\omega _{0}|\ll |\delta |,|\delta -\omega _{0}|} . Then the red sideband (RSB) Hamiltonian is H R S B = − i η Ω 2 ( a † σ − ) e i ( δ + ω 0 ) t + h . c . {\displaystyle H_{\rm {RSB}}=-i\eta {\frac {\Omega }{2}}(a^{\dagger }\sigma _{-})e^{i(\delta +\omega _{0})t}+h.c.} The RSB transition can be thought of as an `exchange' of motion for spin. For an ion with phonon occupation number n {\displaystyle n} , an RSB π {\displaystyle \pi } -pulse will take |


id: m-lmer-s-rensen-gate-20260505-3
file: data/en.wikipedia.org/wiki/Mølmer–Sørensen_gate-3.md
category: reference
title: Mølmer–Sørensen gate
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mølmer–Sørensen_gate
date_saved: 2026-05-05T11:07:45.564101+00:00
instance: kb-cron
parent: m-lmer-s-rensen-gate-20260505-0
summary:
H i n t = i ∑ j , k η j , k Ω j 2 [ e i ( μ k t + ϕ B ) σ − , j a k − e − ( μ k t + ϕ B ) σ + , j a k † + e − i ( μ k t + ϕ R ) σ − , j a k † − e i ( μ k t − ϕ R ) σ + , j a k ] = i ∑ j , k η j , k Ω j 2 [ ( σ − , j e i ϕ s − σ + , j e − i ϕ s ) ( a k e i μ k t e i ϕ m + a k † e − i μ k t e − i ϕ m ) ] ≡ i ∑ j , k η j , k Ω j 2 [ σ ^ j ⊗ A ^ k ( t ) ] {\displaystyle {\begin{aligned}H_{\rm {int}}&=i\sum _{j,k}\eta _{j,k}{\frac {\Omega _{j}}{2}}[e^{i(\mu _{k}t+\phi _{B})}\sigma _{-,j}a_{k}-e^{-(\mu _{k}t+\phi _{B})}\sigma _{+,j}a_{k}^{\dagger }+e^{-i(\mu _{k}t+\phi _{R})}\sigma _{-,j}a_{k}^{\dagger }-e^{i(\mu _{k}t-\phi _{R})}\sigma _{+,j}a_{k}]\\&=i\sum _{j,k}\eta _{j,k}{\frac


id: m-lmer-s-rensen-gate-20260505-4
file: data/en.wikipedia.org/wiki/Mølmer–Sørensen_gate-4.md
category: reference
title: Mølmer–Sørensen gate
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mølmer–Sørensen_gate
date_saved: 2026-05-05T11:07:45.564101+00:00
instance: kb-cron
parent: m-lmer-s-rensen-gate-20260505-0
summary:
Vibrational degrees of freedom will enter the scheme only virtually. They are crucial as intermediate states, but population is never transferred to states with different vibrational excitations. This is because the detuning δ ′ {\displaystyle \delta '} is far enough from the mode frequency ω k {\displaystyle \omega _{k}} that negligible population is transferred to intermediate levels with vibration numbers n ± 1 {\displaystyle n\pm 1} . Transition paths involving different, unpopulated vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on phonon numbers. This is discussed below. ==== Perturbative analysis ==== If we consider two ions, each illuminated by lasers with detunings δ = ± ( ω k + δ ′ ) {\displaystyle \delta =\pm (\omega _{k}+\delta ')} from ω e g {\displaystyle \omega _{eg}} , the only energy-conserving transitions are | g g ⟩ ↔ | e e ⟩ {\displaystyle |gg\rangle \leftrightarrow |ee\rangle } and | g e ⟩ ↔ | e g ⟩ {\displaystyle |ge\rangle \leftrightarrow |eg\rangle } . Under the Lamb-Dicke approximation e − i η ( a † + a ) ≈ 1 − i η ( a † + a ) {\displaystyle e^{-i\eta (a^{\dagger }+a)}\approx 1-i\eta (a^{\dagger }+a)} , we


id: andrea-morello-20260505-0
file: data/en.wikipedia.org/wiki/Andrea_Morello-0.md
category: reference
title: Andrea Morello
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Andrea_Morello
date_saved: 2026-05-05T11:07:46.747981+00:00
instance: kb-cron
parent: andrea-morello-20260505-0
summary:
Andrea Morello (born 26 June 1972, in Pinerolo, Italy) is the Scientia Professor of Quantum Engineering in the School of Electrical Engineering and Telecommunications at the University of New South Wales, and a Program Manager at the ARC Centre of Excellence for Quantum Computation and Communication Technology (CQC2T). Morello is the head of the Fundamental Quantum Technologies Laboratory at UNSW. == Education == Morello completed his undergraduate degree in electrical engineering at the Politecnico di Torino in Italy in 1998. His research career began at the Grenoble High Magnetic Field Laboratory where he investigated the magnetic phase diagram of high T c {\displaystyle T_{c}} superconductors. He obtained his PhD in experimental physics from the Kamerlingh Onnes Laboratory in Leiden in 2004, during which he explored the quantum dynamics of molecular nanomagnets at low temperatures. Morello spent two years at the University of British Columbia before joining UNSW Sydney in 2006. == Research == Morello's research is primarily focused on designing and building the basic components of a quantum computer using the spins of single atoms in silicon. His team were the first in the world to demonstrate the coherent control and readout of the electron and nuclear spin of an


id: multiverse-computing-20260505-0
file: data/en.wikipedia.org/wiki/Multiverse_Computing-0.md
category: reference
title: Multiverse Computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multiverse_Computing
date_saved: 2026-05-05T11:07:47.973282+00:00
instance: kb-cron
parent: multiverse-computing-20260505-0
summary:
Multiverse Computing is a quantum AI software company headquartered in San Sebastián, Spain, with offices in Madrid, Barcelona, Zaragoza, Paris, Munich, London, Milan, Toronto and San Francisco. The company develops compressed AI models and quantum software. The AI model compression platform, CompactifAI, delivers compressed AI models by applying tensor network techniques. With its AI model compression technology, the company offers compressed and optimized versions of leading AI models from providers such as OpenAI, Meta, Microsoft, Qwen, DeepSeek or Mistral. It also offers proprietary open-source AI models such as HyperNova 60B available on HuggingFace. == History == Multiverse was co-founded in 2019 by Enrique Lizaso, Román Orús, Alfonso Rubio-Manzanares and Sam Mugel. Lizaso, treasurer and member of the governing board of the European Quantum Industry Consortium, and Orús, Ikerbasque Research Professor at Donostia International Physics Center and former Marie Curie Fellow at the Max Planck Institute of Quantum Optics, were chatting on WhatsApp when the idea for a quantum computing company for finance was born. In 2021, the company announced €12.5 million in funding from the European_Innovation_Council (EIC) Accelerator program. This was followed by a €25 million funding round in 2024, valuing the startup at €100 million. Later that year, the


id: multiverse-computing-20260505-1
file: data/en.wikipedia.org/wiki/Multiverse_Computing-1.md
category: reference
title: Multiverse Computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Multiverse_Computing
date_saved: 2026-05-05T11:07:47.973282+00:00
instance: kb-cron
parent: multiverse-computing-20260505-0
summary:
== Technology == Multiverse Computing’s algorithms have been implemented across verticals such as energy, manufacturing, logistics, finance, chemistry, space, and cybersecurity. In addition to quantum machine learning and optimization algorithms, the company uses quantum-inspired tensor networks to improve efficiency in solving industrial challenges. Tensor networks are used to model quantum systems, specifically quantum systems of many particles, and more recently are being applied to model artificial intelligence systems. In 2023, the company launched CompactifAI, software that utilizes these networks to reduce the computational costs and energy requirements of training and operating large language models (LLMs). By minimizing size, memory, and storage needs of the models, the tensor networks can enhance efficiency and portability of these models. In 2024, the company secured a $1.4M contract with the German Aerospace Center to develop single photon detectors with applications ranging from quantum computing to deep-space communication and bio-imaging. In 2025, Multiverse Computing launched compressed Llama 3.1 8B and Llama 3.3 70B AI models. Both models have 60% fewer parameters than the original models, 84% greater energy efficiency, 40% faster inference, and yield a 50% cost reduction without sacrificing accuracy. AI developers can plug the models into any application – edge, on-premise, or cloud.


id: national-quantum-computing-centre-20260505-0
file: data/en.wikipedia.org/wiki/National_Quantum_Computing_Centre-0.md
category: reference
title: National Quantum Computing Centre
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/National_Quantum_Computing_Centre
date_saved: 2026-05-05T11:07:49.239056+00:00
instance: kb-cron
parent: national-quantum-computing-centre-20260505-0
summary:
The National Quantum Computing Centre (NQCC) is the United Kingdom's national laboratory for quantum computing, located within the Rutherford Appleton Laboratory, in south Oxfordshire. It is part of UK Research and Innovation (UKRI). Construction began in September 2021 and it was officially opened in 2024-10-25. == References ==


id: national-quantum-initiative-act-20260505-0
file: data/en.wikipedia.org/wiki/National_Quantum_Initiative_Act-0.md
category: reference
title: National Quantum Initiative Act
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/National_Quantum_Initiative_Act
date_saved: 2026-05-05T11:07:50.426425+00:00
instance: kb-cron
parent: national-quantum-initiative-act-20260505-0
summary:
The National Quantum Initiative Act is an Act of Congress passed on December 13, 2018, and signed into law on December 21, 2018. The law gives the United States a plan for advancing quantum technology, particularly quantum computing. == Act == The act was passed unanimously by the United States Senate and was signed into law by President Donald Trump. The National Quantum Initiative (NQI) provides an umbrella under which a number of government agencies develop and operate programs related to improving the climate for quantum science and technology in the US, coordinated by the National Quantum Coordination Office. These agencies include the National Institute of Standards and Technology (NIST), the National Science Foundation (NSF), and the United States Department of Energy (DOE). Under the authority of the NQI, the NSF and the DOE have established new research centers and institutes, and NIST has established the Quantum Economic Development Consortium (QED-C), a consortium of industrial, academic, and governmental entities. == Recent Developments == In May 2025, U.S. lawmakers introduced the bipartisan Quantum Sandbox for Near-Term Applications Act (S.1344), aiming to amend the National Quantum Initiative Act. The proposed legislation seeks to establish a public-private partnership to accelerate the development of


id: national-quantum-mission-india-20260505-0
file: data/en.wikipedia.org/wiki/National_Quantum_Mission_India-0.md
category: reference
title: National Quantum Mission India
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/National_Quantum_Mission_India
date_saved: 2026-05-05T11:07:51.644825+00:00
instance: kb-cron
parent: national-quantum-mission-india-20260505-0
summary:
National Quantum Mission India is an initiative by the Department of Science and Technology, Government of India, to foster quantum technologies related scientific and industrial research and development to support national Digital India, Make India, Skill India and Sustainable development goals. == Background == The union cabinet of Government of India approved the National Quantum Mission with a cost of INR 6003.65 cr ($730,297,000) from 2023–24 to 2030–31. Quantum key distribution (QKD) satellites are being developed by ISRO as part of the National Quantum Mission to provide secure communication. == Selection of Thematic Hubs (T-Hubs) and Technical Groups (TGs) == In January 2024, the National Quantum Mission issued a Call for Proposals (CFP), inviting academic and research institutions to contribute to the development of quantum technologies in the areas of Quantum Computing, Communication, Sensing & Metrology andMaterials & Devices. The initiative received 384 submissions from across the country. == Four T-Hubs and 14 TGs Announced == On September 30, 2024, the National Quantum Mission announced four T-Hubs. After evaluation 17 proposals were selected. == References ==


id: neutral-atom-quantum-computer-20260505-0
file: data/en.wikipedia.org/wiki/Neutral_atom_quantum_computer-0.md
category: reference
title: Neutral atom quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Neutral_atom_quantum_computer
date_saved: 2026-05-05T11:07:52.888479+00:00
instance: kb-cron
parent: neutral-atom-quantum-computer-20260505-0
summary:
A neutral atom quantum computer is a type of quantum computers built out of Rydberg atoms; this type has many commonalities with trapped-ion quantum computers. As of December 2023, the concept has been used to demonstrate a 48 logical qubit processor. To perform computation, the atoms are first trapped in a magneto-optical trap. Qubits are then encoded in the energy levels of the atoms. Initialization and operation of the computer is performed via the application of lasers on the qubits. For example, the laser can accomplish arbitrary single qubit gates and a C Z {\displaystyle CZ} gate for universal quantum computation. The C Z {\displaystyle CZ} gate is carried out by leveraging the Rydberg blockade which leads to strong interactions when the qubits are physically close to each other. To perform a C Z {\displaystyle CZ} gate, a Rydberg π {\displaystyle \pi } pulse is applied to the control qubit, a 2 π {\displaystyle 2\pi } on the target qubit and then a π {\displaystyle \pi } on the control. Measurement is enforced at the end of the computation with a camera that generates an image of the outcome by measuring the fluorescence of the atoms. == Architecture == Neutral


id: neutral-atom-quantum-computer-20260505-1
file: data/en.wikipedia.org/wiki/Neutral_atom_quantum_computer-1.md
category: reference
title: Neutral atom quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Neutral_atom_quantum_computer
date_saved: 2026-05-05T11:07:52.888479+00:00
instance: kb-cron
parent: neutral-atom-quantum-computer-20260505-0
summary:
where, H i = 1 2 ( ( Ω | 1 ⟩ i ⟨ r | + Ω ∗ | r ⟩ i ⟨ 1 | ) − Δ | r ⟩ i ⟨ r | {\displaystyle H_{i}={\frac {1}{2}}((\Omega |1\rangle _{i}\langle r|+\Omega ^{*}|r\rangle _{i}\langle 1|)-\Delta |r\rangle _{i}\langle r|} is the Hamiltonian of i-th atom, Ω {\displaystyle \Omega } is the Rabi frequency of coupling between the Rydberg states and the | 1 ⟩ {\displaystyle |1\rangle } state and Δ {\displaystyle \Delta } is the detuning (see figure to the right for level diagram). When | V r r | >> | Ω | , | Δ | {\displaystyle |V_{rr}|>>|\Omega |,|\Delta |} , we are in the so-called Rydberg Blockade regime. In this regime, the | r r ⟩ {\displaystyle |rr\rangle } state is highly detuned from the rest of the system and thus is effectively decoupled. For the rest of this article, we consider only the Rydberg Blockade regime. The physics of this Hamiltonian can be divided into several subspaces depending on the initial state. The | 00 ⟩ {\displaystyle |00\rangle } state is decoupled and does not evolve. Suppose only the i-th the atom is in | 1 ⟩


id: neutral-atom-quantum-computer-20260505-2
file: data/en.wikipedia.org/wiki/Neutral_atom_quantum_computer-2.md
category: reference
title: Neutral atom quantum computer
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Neutral_atom_quantum_computer
date_saved: 2026-05-05T11:07:52.888479+00:00
instance: kb-cron
parent: neutral-atom-quantum-computer-20260505-0
summary:
==== Adiabatic gate ==== The adiabatic gate was introduced as an alternative to the Jaksch gate. It is global and symmetric and thus it does not require locally focused lasers. Moreover, the Adiabatic Gate prevents the problem of spurious phase accumulation when the atom is in Rydberg state. In the Adiabatic Gate, instead of doing fast pulses, we dress the atom with an adiabatic pulse sequence that takes the atom on a trajectory around the Bloch sphere and back. The levels pick up a phase on this trip due to the so-called "light shift" induced by the lasers. The shapes of pulses can be chosen to control this phase. If both atoms are in the | 00 ⟩ {\displaystyle |00\rangle } state, nothing happens so | 00 ⟩ → | 00 ⟩ {\displaystyle |00\rangle \rightarrow |00\rangle } . If one of them is in the | 0 ⟩ {\displaystyle |0\rangle } state, the other atom picks up a phase due to light shift: | 01 ⟩ → e i ϕ 1 | 01 ⟩ {\displaystyle |01\rangle \rightarrow e^{i\phi _{1}}|01\rangle } and similarly | 10 ⟩ → e i ϕ 1 | 10 ⟩ {\displaystyle |10\rangle \rightarrow e^{i\phi _{1}}|10\rangle } with:


id: nitrogen-vacancy-center-20260505-0
file: data/en.wikipedia.org/wiki/Nitrogen-vacancy_center-0.md
category: reference
title: Nitrogen-vacancy center
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nitrogen-vacancy_center
date_saved: 2026-05-05T11:07:54.043665+00:00
instance: kb-cron
parent: nitrogen-vacancy-center-20260505-0
summary:
The nitrogen-vacancy center (N-V center or NV center) is one of numerous photoluminescent point defects in diamond. It consists of a nearest-neighbor pair of a nitrogen atom, which substitutes for a carbon atom, and a lattice vacancy. The most explored and useful properties of an NV center include its spin-dependent photoluminescence (which enables measurement of the electronic spin state using optically detected magnetic resonance), and its relatively long spin coherence at room temperature, lasting up to milliseconds. The NV center energy levels are modified by magnetic fields, electric fields, temperature, and strain, which allow it to serve as a sensor of a variety of physical phenomena. Its atomic size and spin properties can form the basis for useful quantum sensors. NV centers enable nanoscale measurements of magnetic and electric fields, temperature, and mechanical strain with improved precision. External perturbation sensitivity makes NV centers ideal for applications in biomedicine—such as single-molecule imaging and cellular process modeling. NV centers can also be initialized as qubits and enable the implementation of quantum algorithms and networks. It has also been explored for applications in quantum computing (e.g. for entanglement generation), quantum simulation, and spintronics. == Production == Natural NV centers are randomly oriented within


id: nitrogen-vacancy-center-20260505-1
file: data/en.wikipedia.org/wiki/Nitrogen-vacancy_center-1.md
category: reference
title: Nitrogen-vacancy center
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nitrogen-vacancy_center
date_saved: 2026-05-05T11:07:54.043665+00:00
instance: kb-cron
parent: nitrogen-vacancy-center-20260505-0
summary:
Amplitude and orientation of a static magnetic field splits the ms = ±1 levels in the ground and excited states. Amplitude and orientation of elastic (strain) or electric fields have a much smaller but also more complex effects on the different levels. Continuous-wave microwave radiation (applied in resonance with the transition between ms = 0 and (one of the) ms = ±1 states) changes the population of the sublevels within the ground and excited state. A tunable laser can selectively excite certain sublevels of the ground and excited states. Surrounding spins and spin–orbit interaction will modulate the magnetic field experienced by the NV center. Temperature and pressure affect different parts of the spectrum including the shift between ground and excited states. == Electromagnetic coupling == The Hamiltonian dynamics of a NV center are approximated extremely well by the following sum of interactions with the electromagnetic field: Each term in the Hamiltonian can be measured under the right conditions. === Optical properties === NV centers emit bright red light (3E→3A transitions), if excited off-resonantly by visible green light (3A →3E transitions). This can be done with convenient light sources such as argon or krypton lasers, frequency doubled Nd:YAG lasers, dye lasers,


id: nitrogen-vacancy-center-20260505-2
file: data/en.wikipedia.org/wiki/Nitrogen-vacancy_center-2.md
category: reference
title: Nitrogen-vacancy center
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nitrogen-vacancy_center
date_saved: 2026-05-05T11:07:54.043665+00:00
instance: kb-cron
parent: nitrogen-vacancy-center-20260505-0
summary:
=== Net charge === It is also possible to switch the charge state of the NV center (i.e. between NV−, NV+ and NV0) by applying a gate voltage. The gate voltage electrically shifts the Fermi level at the diamond surface and changes its surface band bending. Upon varying the gate voltage, individual centers are allowed to switch from an unknown non-fluorescent state to the neutral charge state NV0. The ensemble of centers can be transitioned from NV0 to the qubit state NV−. The diamond surface termination additionally influences the charge state of near-surface NV centers. Oxygen termination is known to stabilize the NV−state by reducing surface conductivity and mitigating band bending. This improves charge state stability and coherence. In a similar capacity, nitrogen termination also affects surface properties and can optimize NV centers for specific sensing applications. Optical excitation methods additionally play a role in charge state manipulation. Illumination with specific wavelengths can induce transitions between charge states. Near-infrared light at 1064 nm has been shown to convert NV0 to NV−, enhancing photoluminescence. Additionally, it has been demonstrated that NV+ centers can be switched to NV0 by photons with energies ≥ {\displaystyle \geq } 1.23 eV. == Applications == The


id: nitrogen-vacancy-center-20260505-3
file: data/en.wikipedia.org/wiki/Nitrogen-vacancy_center-3.md
category: reference
title: Nitrogen-vacancy center
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nitrogen-vacancy_center
date_saved: 2026-05-05T11:07:54.043665+00:00
instance: kb-cron
parent: nitrogen-vacancy-center-20260505-0
summary:
== Historical remarks == The microscopic model and most optical properties of ensembles of the NV− centers have been firmly established in the 1970s based on the optical measurements combined with uniaxial stress and on the electron paramagnetic resonance. However, a minor error in EPR results (it was assumed that illumination is required to observe NV− EPR signals) resulted in the incorrect multiplicity assignments in the energy level structure. In 1991 it was shown that EPR can be observed without illumination, which established the energy level scheme shown above. The magnetic splitting in the excited state has been measured only recently. The characterization of single NV− centers has become a very competitive field nowadays, with many dozens of papers published in the most prestigious scientific journals. One of the first results was reported back in 1997. In that paper, it was demonstrated that the fluorescence of single NV− centers can be detected by room-temperature fluorescence microscopy and that the defect shows perfect photostability. Also one of the outstanding properties of the NV center was demonstrated, namely room-temperature optically detected magnetic resonance. Despite extensive efforts, electron paramagnetic resonance signals from NV0 avoided detection for decades until 2008. Optical excitation is required


id: noisy-intermediate-scale-quantum-computing-20260505-0
file: data/en.wikipedia.org/wiki/Noisy_intermediate-scale_quantum_computing-0.md
category: reference
title: Noisy intermediate-scale quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Noisy_intermediate-scale_quantum_computing
date_saved: 2026-05-05T11:07:55.205303+00:00
instance: kb-cron
parent: noisy-intermediate-scale-quantum-computing-20260505-0
summary:
Noisy intermediate-scale quantum (NISQ) computing is characterized by quantum processors containing up to 1,000 qubits which are not advanced enough yet for fault-tolerance or large enough to achieve quantum advantage. These processors, which are sensitive to their environment (noisy) and prone to quantum decoherence, are not yet capable of continuous quantum error correction. This intermediate-scale is defined by the quantum volume, which is based on a moderate number of qubits and gate fidelity. The NISQ era is the current state of quantum computer technology, and the term was coined by John Preskill in 2018. According to Microsoft Azure Quantum's scheme, NISQ computation is considered level 1, the lowest of the quantum computing implementation levels. In October 2023, the 1,000 qubit mark was passed for the first time by Atom Computing's 1,180 qubit quantum processor. However, as of 2024, only two quantum processors have over 1,000 qubits, with sub-1,000 quantum processors still remaining the norm. == Algorithms == NISQ algorithms are quantum algorithms designed for quantum processors in the NISQ era. Common examples are the variational quantum eigensolver (VQE) and quantum approximate optimization algorithm (QAOA), which use NISQ devices but offload some calculations to classical processors. These algorithms have been successful


id: noisy-intermediate-scale-quantum-computing-20260505-1
file: data/en.wikipedia.org/wiki/Noisy_intermediate-scale_quantum_computing-1.md
category: reference
title: Noisy intermediate-scale quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Noisy_intermediate-scale_quantum_computing
date_saved: 2026-05-05T11:07:55.205303+00:00
instance: kb-cron
parent: noisy-intermediate-scale-quantum-computing-20260505-0
summary:
==== Performance benchmarks and quantum advantage ==== Recent theoretical and experimental work has demonstrated QAOA's potential for quantum advantage on specific problem classes. For the Max Cut problem on random graphs, QAOA at depth p=11 has been shown to outperform standard semidefinite programming algorithms. Even more remarkably, QAOA can exploit non-adiabatic quantum effects that classical algorithms cannot access, potentially circumventing fundamental limitations that constrain classical optimization methods. Experimental implementations on quantum hardware have shown promising results for problems with up to 20–30 variables, though current hardware limitations restrict practical applications to relatively small problem sizes. The algorithm's performance improves with circuit depth p, but NISQ constraints limit the achievable depth, creating a fundamental trade-off between solution quality and hardware requirement. == Error mitigation: Making noisy quantum computing practical == Since NISQ devices lack full quantum error correction, error mitigation techniques become essential for extracting meaningful results from noisy quantum computations. These techniques operate through post-processing measured data rather than actively correcting errors during computation, making them suitable for near-term hardware implementations. === Zero-noise extrapolation === Zero-noise extrapolation (ZNE) represents one of the most widely used error mitigation techniques, artificially amplifying circuit noise and extrapolating results to the zero-noise limit. The


id: nqit-20260505-0
file: data/en.wikipedia.org/wiki/NQIT-0.md
category: reference
title: NQIT
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/NQIT
date_saved: 2026-05-05T11:07:56.366460+00:00
instance: kb-cron
parent: nqit-20260505-0
summary:
NQIT (Networked Quantum Information Technologies) is a quantum computing research hub established in 2014 as part of the UK National Quantum Technologies Programme. NQIT is a consortium of 9 UK universities and 30 partners, which received funding of £38m over a 5-year period. By the end of the 5-year programme NQIT aims to produce the Q20:20 engine, a demonstration of a scalable quantum computer demonstrator comprising an optically linked network of 20 cells, each cell being a quantum processor with 20 matter qubits. == Organisation == The UK National Quantum Technologies Programme was initiated by the UK Chancellor of the Exchequer, George Osborne in the Autumn Statement in 2013 in which he pledged a £270 million investment. A £120 million national network of four Quantum Technology Hubs was announced by Greg Clark in 2014. The NQIT Hub is led by a Director, Professor Ian Walmsley, who provides overall leadership and scientific vision, and two co-directors, Professor Dominic O’Brien, who leads the Systems Engineering, and Dr Tim Cook, who leads the Industrial User Engagement activities. NQIT is led by the University of Oxford and academic partners are the University of Bath, the University of Cambridge, the University of Edinburgh, the University


id: one-clean-qubit-20260505-0
file: data/en.wikipedia.org/wiki/One_clean_qubit-0.md
category: reference
title: One clean qubit
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/One_clean_qubit
date_saved: 2026-05-05T11:07:57.586244+00:00
instance: kb-cron
parent: one-clean-qubit-20260505-0
summary:
In quantum information, the one clean qubit model of computation is performed an n {\displaystyle n} qubit system with one pure state and n − 1 {\displaystyle n-1} maximally mixed states. This model was motivated by highly mixed states that are prevalent in nuclear magnetic resonance quantum computers. It's described by the density matrix ρ = | 0 ⟩ ⟨ 0 | ⊗ I 2 n − 1 {\displaystyle \rho =\left|0\right\rangle \langle 0|\otimes {\frac {I}{2^{n-1}}}} , where I {\displaystyle I} is the identity matrix. In computational complexity theory, DQC1; also known as the deterministic quantum computation with one clean qubit is the class of decision problems solvable by a one clean qubit machine in polynomial time, upon measuring the first qubit, with an error probability of at most 1/poly(n) for all instances. == Error bounds and composability == The most standard definition of DQC1 requires that measuring the output qubit correctly accepts or rejects the input, with error at most 1 / q ( n ) {\displaystyle 1/q(n)} for specified some polynomial q, given a gap in acceptance probabilities of [ 0 , 1 / 2 − 1 / q ( n ) ] {\displaystyle [0,1/2-1/q(n)]} for NO instances and


id: openqasm-20260505-0
file: data/en.wikipedia.org/wiki/OpenQASM-0.md
category: reference
title: OpenQASM
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/OpenQASM
date_saved: 2026-05-05T11:07:58.731884+00:00
instance: kb-cron
parent: openqasm-20260505-0
summary:
Open Quantum Assembly Language (OpenQASM; pronounced open kazm) is a programming language designed for describing quantum circuits and algorithms for execution on quantum computers. == Language == It is designed to be an intermediate representation that can be used by higher-level compilers to communicate with quantum hardware, and allows for the description of a wide range of quantum operations, as well as classical feed-forward flow control based on measurement outcomes. The language includes a mechanism for describing explicit timing of instructions, and allows for the attachment of low-level definitions to gates for tasks such as calibration. OpenQASM is not intended for general-purpose classical computation, and hardware implementations of the language may not support the full range of data manipulation described in the specification. Compilers for OpenQASM are expected to support a wide range of classical operations for compile-time constants, but the support for these operations on runtime values may vary between implementations. The language was first described in a paper published in July 2017, and a reference source code implementation was released as part of IBM's Quantum Information Software Kit (Qiskit) for use with their IBM Quantum Experience cloud quantum computing platform. The language has similar qualities to traditional hardware


id: parity-measurement-20260505-0
file: data/en.wikipedia.org/wiki/Parity_measurement-0.md
category: reference
title: Parity measurement
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Parity_measurement
date_saved: 2026-05-05T11:07:59.938826+00:00
instance: kb-cron
parent: parity-measurement-20260505-0
summary:
Parity measurement (also referred to as Operator measurement) is a procedure in quantum information science used for error detection in quantum qubits. A parity measurement checks the equality of two qubits to return a true or false answer, which can be used to determine whether a correction needs to occur. Additional measurements can be made for a system greater than two qubits. Because parity measurement does not measure the state of singular bits but rather gets information about the whole state, it is considered an example of a joint measurement. Joint measurements do not have the consequence of destroying the original state of a qubit as normal quantum measurements do. Mathematically speaking, parity measurements are used to project a state into an eigenstate of an operator and to acquire its eigenvalue. Parity measurement is an essential concept of quantum error correction. From the parity measurement, an appropriate unitary operation can be applied to correct the error without knowing the beginning state of the qubit. == Parity and parity checking == A qubit is a two-level system, and when we measure one qubit, we can have either 1 or 0 as a result. One corresponds to odd parity, and zero corresponds


id: parity-measurement-20260505-1
file: data/en.wikipedia.org/wiki/Parity_measurement-1.md
category: reference
title: Parity measurement
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Parity_measurement
date_saved: 2026-05-05T11:07:59.938826+00:00
instance: kb-cron
parent: parity-measurement-20260505-0
summary:
An easy way to visualize this is in the circuit above. First, the input state | ψ ⟩ {\displaystyle |\psi \rangle } is encoded into 3 bits, and parity checks are performed with subsequent error correction performed based on the results of the ancilla qubits at the bottom. Finally, decoding is performing to put get back to the same basis of the input state. == Parity check matrix == A parity check matrix for a quantum circuit can also be constructed using these principles. For some message x encoded as Gx, where G corresponds to the generator matrix, Hx = 0 where H is the parity matrix containing 0's and 1's for a situation where there is no error. However, if an error occurs at one component, then the pattern in the errors can be used to find which bit is incorrect. == Types of parity measurements == Two types of parity measurement are indirect and direct. Indirect parity measurements coincide with the typical way we think of parity measurement as described above, by measuring an ancilla qubit to determine the parity of the input bits. Direct parity measurements differ from the previous type in that a common mode with


id: phase-kickback-20260505-0
file: data/en.wikipedia.org/wiki/Phase_kickback-0.md
category: reference
title: Phase kickback
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_kickback
date_saved: 2026-05-05T11:08:01.130073+00:00
instance: kb-cron
parent: phase-kickback-20260505-0
summary:
In quantum computing, phase kickback refers to the fact that controlled operations have effects on their controls, in addition to on their targets, and that these effects correspond to phasing operations. When a controlled operation, such as a Controlled NOT (CNOT) gate, is applied to two qubits, the phase of the second (target) qubit is conditioned on the state of the first (control) qubit. Because the phase of the second qubit is being "kicked back" to the first qubit, this phenomenon was coined "phase kickback" in 1997 by Richard Cleve, Artur Ekert, Chiara Macchiavello, and Michele Mosca through a paper that solved the Deutsch-Jozsa problem. For example, when a controlled NOT gate's target qubit is in the state 1 / 2 ( | 0 ⟩ − | 1 ⟩ ) {\displaystyle 1/{\sqrt {2}}(|0\rangle -|1\rangle )} , the effect of the controlled NOT gate is equivalent to the effect of applying a Pauli Z gate to the controlled NOT's control qubit. Phase kickback is one of the key effects that distinguishes quantum computation from classical computation. Phase kickback also provides a justification for why qubits would be disrupted by measurements: a measurement is an operation that flips a classical bit (the


id: phase-kickback-20260505-1
file: data/en.wikipedia.org/wiki/Phase_kickback-1.md
category: reference
title: Phase kickback
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_kickback
date_saved: 2026-05-05T11:08:01.130073+00:00
instance: kb-cron
parent: phase-kickback-20260505-0
summary:
| ψ ⟩ {\displaystyle |\psi \rangle } must be an eigenvector of controlled operator U {\displaystyle U} . When | ψ ⟩ {\displaystyle |\psi \rangle } is an eigenvector of U {\displaystyle U} , U | ψ ⟩ = e i ϕ | ψ ⟩ {\displaystyle U|\psi \rangle =e^{i\phi }|\psi \rangle } . At point B of the above circuit, the system will then have state | 0 ⟩ | ψ ⟩ + | 1 ⟩ e i ϕ | ψ ⟩ 2 = | 0 ⟩ + e i ϕ | 1 ⟩ 2 | ψ ⟩ {\displaystyle {\frac {|0\rangle |\psi \rangle +|1\rangle e^{i\phi }|\psi \rangle }{\sqrt {2}}}={\frac {|0\rangle +e^{i\phi }|1\rangle }{\sqrt {2}}}|\psi \rangle } . Now, e i ϕ {\displaystyle e^{i\phi }} will be associated with the first qubit when this state is factored out into individual states (assuming the system is not entangled). From this, it can be seen that when | ψ ⟩ {\displaystyle |\psi \rangle } is an eigenvector of U {\displaystyle U} , the control qubit is able to change by being multiplied by the phase while the target qubit remains unchanged. Operator U {\displaystyle U} must be used in a controlled way. In


id: physical-and-logical-qubits-20260505-0
file: data/en.wikipedia.org/wiki/Physical_and_logical_qubits-0.md
category: reference
title: Physical and logical qubits
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physical_and_logical_qubits
date_saved: 2026-05-05T11:08:02.278467+00:00
instance: kb-cron
parent: physical-and-logical-qubits-20260505-0
summary:
In quantum computing, a qubit is a unit of information analogous to a bit (binary digit) in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks. Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations. A physical qubit is a physical device that behaves as a two-state quantum system, used as a component of a computer system. A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit subject to unitary transformations, has a long enough coherence time to be usable by quantum logic gates (cf. propagation delay for classical logic gates). Since the development of the first quantum computer in 1998, most technologies used to implement qubits face issues of stability, decoherence, fault tolerance and scalability. Because of this, many physical qubits are needed for the purposes of error-correction to produce an entity which behaves logically as a single qubit would in a quantum circuit or algorithm; this is the


id: planqc-20260505-0
file: data/en.wikipedia.org/wiki/Planqc-0.md
category: reference
title: Planqc
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Planqc
date_saved: 2026-05-05T11:08:03.451786+00:00
instance: kb-cron
parent: planqc-20260505-0
summary:
planqc is a quantum computing company based in Garching. Founded in 2022 as a spin-off from the Max Planck Institute of Quantum Optics, the company develops quantum processors that use neutral atoms trapped in optical lattices of light to perform computations. == History == planqc was founded in 2022 by Alexander Glätzle, Sebastian Blatt, and Johannes Zeiher as the first spin-off from the Max Planck Institute of Quantum Optics within the Munich Quantum Valley initiative. The company is part of broader European efforts to develop locally built quantum computing technologies. The company’s founders and leadership include researchers formerly affiliated with the University of Oxford, Harvard University, and the University of California, Berkeley. In the same year, planqc secured seed funding of approximately €4.6 million from UVC Partners and Speedinvest to support the development of its neutral-atom quantum processors. Among the investors were Hermann Hauser, Ann-Kristin Achleitner, and Markus Wagner, who also joined the company's advisory board. planqc’s scientific advisory board includes researchers in quantum physics, such as Immanuel Bloch, J. Ignacio Cirac, Artur Ekert, Dieter Jaksch, and Markus Müller. In 2023, the company was selected by the German Aerospace Center (DLR) to develop a 1,000-qubit quantum computer under a contract


id: qmill-20260505-0
file: data/en.wikipedia.org/wiki/QMill-0.md
category: reference
title: QMill
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/QMill
date_saved: 2026-05-05T11:08:04.681605+00:00
instance: kb-cron
parent: qmill-20260505-0
summary:
QMill is a quantum computing firm based in Finland that was established in 2024, focusing on creating quantum algorithms that offer immediate, practical advantages for industrial uses. Utilizing upcoming quantum technology, QMill strives to tackle intricate optimization challenges and deliver considerable value across multiple industries. The organization is situated in Espoo, Finland. == References == == External links == Official website


id: qpiai-indus-20260505-0
file: data/en.wikipedia.org/wiki/QpiAI-Indus-0.md
category: reference
title: QpiAI-Indus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/QpiAI-Indus
date_saved: 2026-05-05T11:08:05.842605+00:00
instance: kb-cron
parent: qpiai-indus-20260505-0
summary:
QpiAI-Indus is the India's first full stack quantum computer. It is a 25 superconducting qubits quantum computer developed by the Banglore based startup company QpiAI. It was launched on the occasion of the World Quantum Day in the year 2025. The quantum computer QpiAI-Indus was developed under the leadership of the CEO Nagendra Nagaraja of the company. The development program of the quantum computer was assisted and supported by the National Quantum Mission of the Government of India. The success of the development of the QpiAI-Indus quantum computer at the silicon city Bangalore in India is considered as one of major milestone in journey of India's quantum computer. == Etymology == QpiAI-Indus is the codename of the 25 qubits quantum computer developed by the startup company QpiAI. In the term QpiAI which also signifies for the company name, the letter Q stands for quantum, pi stands for the mathematical symbol π and AI means algorithmic intelligence. The term Indus signifies for the ancient civilization valley in the Indian subcontinent. Thus the etymology of the codename of the quantum computer QpiAI-Indus signifies the legacy of the development of quantum computing in India. == Description == The QpiAI-Indus quantum computer features a


id: quantum-algorithm-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_algorithm-0.md
category: reference
title: Quantum algorithm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_algorithm
date_saved: 2026-05-05T11:08:07.005881+00:00
instance: kb-cron
parent: quantum-algorithm-20260505-0
summary:
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is generally reserved for algorithms that seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement. Problems that are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms because the quantum superposition and quantum entanglement that quantum algorithms exploit generally cannot be efficiently simulated on classical computers (see Quantum supremacy). The best-known algorithms are Shor's algorithm for factoring and Grover's algorithm for searching an unstructured database or an unordered list. Shor's algorithm would, if implemented, run


id: quantum-algorithm-20260505-1
file: data/en.wikipedia.org/wiki/Quantum_algorithm-1.md
category: reference
title: Quantum algorithm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_algorithm
date_saved: 2026-05-05T11:08:07.005881+00:00
instance: kb-cron
parent: quantum-algorithm-20260505-0
summary:
| f ~ ( z i ) | ⩾ 2. {\displaystyle |{\tilde {f}}(z_{i})|\geqslant 2.} This can be done in bounded-error quantum polynomial time (BQP). == Algorithms based on amplitude amplification == Amplitude amplification is a technique that allows the amplification of a chosen subspace of a quantum state. Applications of amplitude amplification usually lead to quadratic speedups over the corresponding classical algorithms. It can be considered as a generalization of Grover's algorithm. === Grover's algorithm === Grover's algorithm searches an unstructured database (or an unordered list) with N entries for a marked entry, using only O ( N ) {\displaystyle O({\sqrt {N}})} queries instead of the O ( N ) {\displaystyle O({N})} queries required classically. Classically, O ( N ) {\displaystyle O({N})} queries are required even allowing bounded-error probabilistic algorithms. Theorists have considered a hypothetical generalization of a standard quantum computer that could access the histories of the hidden variables in Bohmian mechanics. (Such a computer is completely hypothetical and would not be a standard quantum computer, or even possible under the standard theory of quantum mechanics.) Such a hypothetical computer could implement a search of an N-item database in at most O ( N 3 ) {\displaystyle O({\sqrt[{3}]{N}})} steps.


id: quantum-algorithm-20260505-2
file: data/en.wikipedia.org/wiki/Quantum_algorithm-2.md
category: reference
title: Quantum algorithm
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_algorithm
date_saved: 2026-05-05T11:08:07.005881+00:00
instance: kb-cron
parent: quantum-algorithm-20260505-0
summary:
=== Formula evaluation === A formula is a tree with a gate at each internal node and an input bit at each leaf node. The problem is to evaluate the formula, which is the output of the root node, given oracle access to the input. A well studied formula is the balanced binary tree with only NAND gates. This type of formula requires Θ ( N c ) {\displaystyle \Theta (N^{c})} queries using randomness, where c = log 2 ⁡ ( 1 + 33 ) / 4 ≈ 0.754 {\displaystyle c=\log _{2}(1+{\sqrt {33}})/4\approx 0.754} . With a quantum algorithm, however, it can be solved in Θ ( N 1 / 2 ) {\displaystyle \Theta (N^{1/2})} queries. No better quantum algorithm for this case was known until one was found for the unconventional Hamiltonian oracle model. The same result for the standard setting soon followed. Fast quantum algorithms for more complicated formulas are also known. === Group commutativity === The problem is to determine if a black-box group, given by k generators, is commutative. A black-box group is a group with an oracle function, which must be used to perform the group operations (multiplication, inversion, and comparison with identity). The interest


id: quantum-artificial-intelligence-lab-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_Artificial_Intelligence_Lab-0.md
category: reference
title: Quantum Artificial Intelligence Lab
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_Artificial_Intelligence_Lab
date_saved: 2026-05-05T11:08:08.332857+00:00
instance: kb-cron
parent: quantum-artificial-intelligence-lab-20260505-0
summary:
The Quantum Artificial Intelligence Lab (also called the Quantum AI Lab or QuAIL) is a joint initiative of NASA, Universities Space Research Association, and Google (specifically, Google Research) whose goal is to pioneer research on how quantum computing might help with machine learning and other difficult computer science problems. The lab is hosted at NASA's Ames Research Center. == History == The Quantum AI Lab was announced by Google Research in a blog post on May 16, 2013. At the time of launch, the Lab was using the most advanced commercially available quantum computer, D-Wave Two from D-Wave Systems. On October 10, 2013, Google released a short film describing the current state of the Quantum AI Lab. On October 18, 2013, Google announced that it had incorporated quantum physics into Minecraft. In January 2014, Google reported results comparing the performance of the D-Wave Two in the lab with that of classical computers. The results were ambiguous and provoked heated discussion on the Internet. On 2 September 2014, it was announced that the Google Quantum AI Lab, in partnership with UC Santa Barbara, would be launching an initiative to create quantum information processors based on superconducting electronics. On the 23rd of


id: quantum-computation-and-quantum-information-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_Computation_and_Quantum_Information-0.md
category: reference
title: Quantum Computation and Quantum Information
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_Computation_and_Quantum_Information
date_saved: 2026-05-05T11:08:09.577704+00:00
instance: kb-cron
parent: quantum-computation-and-quantum-information-20260505-0
summary:
Quantum Computation and Quantum Information is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang, regarded as a standard text on the subject. It is informally known as "Mike and Ike", after the candies of that name. The book assumes minimal prior experience with quantum mechanics and with computer science, aiming instead to be a self-contained introduction to the relevant features of both. (Lov Grover recalls a postdoc disparaging it with the remark, "The book is too elementary – it starts off with the assumption that the reader does not even know quantum mechanics.") The focus of the text is on theory, rather than the experimental implementations of quantum computers, which are discussed more briefly. As of December 2024, the book has been cited over 58,000 times on Google Scholar. In 2019, Nielsen adapted parts of the book for his Quantum Country project. == Table of Contents (Tenth Anniversary Edition) == Chapter 1: Introduction and Overview Chapter 2: Introduction to Quantum Mechanics Chapter 3: Introduction to Computer Science Chapter 4: Quantum Circuits Chapter 5: The Quantum Fourier Transform and its Applications Chapter 6: Quantum Search Algorithms Chapter 7: Quantum Computers: Physical Realization Chapter 8: Quantum Noise


id: quantum-computing-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_computing-0.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
A quantum computer is a real or theoretical computer that exploits quantum phenomena like superposition and entanglement in an essential way. It is widely believed that a quantum computer could perform some calculations exponentially faster than any classical computer. For example, a large-scale quantum computer could break some widely used encryption schemes and aid physicists in performing physical simulations. However, current hardware implementations of quantum computation are largely experimental and only suitable for specialized tasks. The basic unit of information in quantum computing, the qubit (or "quantum bit"), serves the same function as the bit in ordinary or "classical" computing. However, unlike a classical bit, which can be in one of two states (a binary), a qubit can exist in a linear combination of two states known as a quantum superposition. The result of measuring a qubit is one of the two states given by a probabilistic rule. If a quantum computer manipulates the qubit in a particular way, wave interference effects amplify the probability of the desired measurement result. The design of quantum algorithms involves creating procedures that allow a quantum computer to perform this amplification. Quantum computers are not yet practical for real-world applications. Physically engineering high-quality qubits


id: quantum-computing-20260505-1
file: data/en.wikipedia.org/wiki/Quantum_computing-1.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
A classical computer is a quantum computer ... so we shouldn't be asking about "where do quantum speedups come from?" We should say, "Well, all computers are quantum. ... Where do classical slowdowns come from?" === Quantum information === Just as the bit is the basic concept of classical information theory, the qubit is the fundamental unit of quantum information. The same term qubit is used to refer to an abstract mathematical model and to any physical system that is represented by that model. A classical bit, by definition, exists in either of two physical states, which can be denoted 0 and 1. A qubit is also described by a state, and two states, often written | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } , serve as the quantum counterparts of the classical states 0 and 1. However, the quantum states | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } belong to a vector space, meaning that they can be multiplied by constants and added together, and the result is again a valid quantum state. Such a combination is known as a superposition of | 0 ⟩ {\displaystyle |0\rangle } and


id: quantum-computing-20260505-2
file: data/en.wikipedia.org/wiki/Quantum_computing-2.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
CNOT := ( 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ) . {\displaystyle \operatorname {CNOT} :={\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{pmatrix}}.} As a mathematical consequence of this definition, CNOT ⁡ | 00 ⟩ = | 00 ⟩ {\textstyle \operatorname {CNOT} |00\rangle =|00\rangle } , CNOT ⁡ | 01 ⟩ = | 01 ⟩ {\textstyle \operatorname {CNOT} |01\rangle =|01\rangle } , CNOT ⁡ | 10 ⟩ = | 11 ⟩ {\textstyle \operatorname {CNOT} |10\rangle =|11\rangle } , and CNOT ⁡ | 11 ⟩ = | 10 ⟩ {\textstyle \operatorname {CNOT} |11\rangle =|10\rangle } . In other words, the CNOT applies a NOT gate ( X {\textstyle X} from before) to the second qubit if and only if the first qubit is in the state | 1 ⟩ {\textstyle |1\rangle } . If the first qubit is | 0 ⟩ {\textstyle |0\rangle } , nothing is done to either qubit. In summary, quantum computation can be described as a network of quantum logic gates and measurements. However, any measurement can be deferred to the end of quantum computation, though this deferment may come at a computational cost, so most quantum circuits depict a network consisting only of quantum


id: quantum-computing-20260505-3
file: data/en.wikipedia.org/wiki/Quantum_computing-3.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
Digital cryptography enables communications to remain private, preventing unauthorized parties from accessing them. Conventional encryption, the obscuring of a message with a key through an algorithm, relies on the algorithm being difficult to reverse. Encryption is also the basis for digital signatures and authentication mechanisms. Quantum computing may be sufficiently more powerful that difficult reversals are feasible, allowing messages relying on conventional encryption to be read. Quantum cryptography replaces conventional algorithms with computations based on quantum computing. In principle, quantum encryption would be impossible to decode even with a quantum computer. This advantage comes at a significant cost in terms of elaborate infrastructure, while effectively preventing legitimate decoding of messages by governmental security officials. Ongoing research in quantum and post-quantum cryptography has led to new algorithms for quantum key distribution, initial work on quantum random number generation and to some early technology demonstrations. == Communication == Quantum cryptography enables new ways to transmit data securely; for example, quantum key distribution uses entangled quantum states to establish secure cryptographic keys. When a sender and receiver exchange quantum states, they can guarantee that an adversary does not intercept the message, as any unauthorized eavesdropper would disturb the delicate quantum system and introduce


id: quantum-computing-20260505-4
file: data/en.wikipedia.org/wiki/Quantum_computing-4.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
A notable application of quantum computing is in attacking cryptographic systems that are currently in use. Integer factorization, which underpins the security of public key cryptographic systems, is believed to be computationally infeasible on a classical computer for large integers if they are the product of a few prime numbers (e.g., the product of two 300-digit primes). By contrast, a quantum computer could solve this problem exponentially faster using Shor's algorithm to factor the integer. This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time (in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular public key ciphers are based on the difficulty of factoring integers or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman algorithms could be broken. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security. Identifying cryptographic systems that may be secure against quantum algorithms is an actively researched


id: quantum-computing-20260505-5
file: data/en.wikipedia.org/wiki/Quantum_computing-5.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
Deep generative chemistry models have been explored for potential applications in drug discovery. Early experimental work has explored the use of near-term quantum hardware in molecular generative modeling for drug discovery. In 2023, researchers at Gero reported a hybrid quantum–classical generative model based on a restricted Boltzmann machine, implemented on a commercially available quantum annealing device, to generate novel drug-like small molecules with physicochemical properties comparable to known medicinal compounds. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome in the future by quantum computers. Quantum computers are naturally good for solving complex quantum many-body problems and thus may be instrumental in applications involving quantum chemistry. Therefore, one can expect that quantum-enhanced generative models including quantum GANs may eventually be developed into ultimate generative chemistry algorithms. == Engineering == As of 2023, classical computers outperform quantum computers for all real-world applications. While current quantum computers may speed up solutions to particular mathematical problems, they give no computational advantage for practical tasks. Scientists and engineers are exploring multiple technologies for quantum computing hardware and hope to develop scalable quantum architectures, but serious obstacles remain. In practice, improvements in


id: quantum-computing-20260505-6
file: data/en.wikipedia.org/wiki/Quantum_computing-6.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
==== Decoherence ==== One of the greatest challenges involved in constructing quantum computers is controlling or removing quantum decoherence. This usually means isolating the system from its environment, as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, the lattice vibrations, and the background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time T2 (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperatures. Currently, some quantum computers require their qubits to be cooled to 20 millikelvin (usually using a dilution refrigerator) in order to prevent significant decoherence. A 2020 study argues that ionizing radiation such as cosmic rays can nevertheless cause certain systems to decohere within milliseconds. As a result, time-consuming tasks may render some quantum algorithms inoperable, as attempting to maintain the state of qubits for a long enough duration will eventually corrupt the superpositions. These issues are more difficult for optical approaches


id: quantum-computing-20260505-7
file: data/en.wikipedia.org/wiki/Quantum_computing-7.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
=== Skepticism === Despite high hopes for quantum computing, significant progress in hardware, and optimism about future applications, a 2023 Nature spotlight article summarized current quantum computers as being "For now, [good for] absolutely nothing". The article elaborated that quantum computers are yet to be more useful or efficient than conventional computers in any case, though it also argued that, in the long term, such computers are likely to be useful. A 2023 Communications of the ACM article found that current quantum computing algorithms are "insufficient for practical quantum advantage without significant improvements across the software/hardware stack". It argues that the most promising candidates for achieving speedup with quantum computers are "small-data problems", for example, in chemistry and materials science. However, the article also concludes that a large range of the potential applications it considered, such as machine learning, "will not achieve quantum advantage with current quantum algorithms in the foreseeable future", and it identified I/O constraints that make speedup unlikely for "big data problems, unstructured linear systems, and database search based on Grover's algorithm". This state of affairs can be traced to several current and long-term considerations. Conventional computer hardware and algorithms are not only optimized for practical tasks,


id: quantum-computing-20260505-8
file: data/en.wikipedia.org/wiki/Quantum_computing-8.md
category: reference
title: Quantum computing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing
date_saved: 2026-05-05T11:08:10.743299+00:00
instance: kb-cron
parent: quantum-computing-20260505-0
summary:
While quantum computers cannot solve any problems that classical computers cannot already solve, it is suspected that they can solve certain problems faster than classical computers. For instance, it is known that quantum computers can efficiently factor integers, while this is not believed to be the case for classical computers. The class of problems that can be efficiently solved by a quantum computer with bounded error is called BQP, for "bounded error, quantum, polynomial time". More formally, BQP is the class of problems that can be solved by a polynomial-time quantum Turing machine with an error probability of at most 1/3. As a class of probabilistic problems, BQP is the quantum counterpart to BPP ("bounded error, probabilistic, polynomial time"), the class of problems that can be solved by polynomial-time probabilistic Turing machines with bounded error. It is known that B P P ⊆ B Q P {\displaystyle {\mathsf {BPP\subseteq BQP}}} but there is no proof B Q P ≠ B P P {\displaystyle {\mathsf {BQP\neq BPP}}} , which intuitively would mean that quantum computers are more powerful than classical computers in terms of time complexity. The exact relationship of BQP to P, NP, and PSPACE is not known. However, it


id: quantum-volume-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_volume-0.md
category: reference
title: Quantum volume
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_volume
date_saved: 2026-05-05T11:08:11.904022+00:00
instance: kb-cron
parent: quantum-volume-20260505-0
summary:
Quantum volume is a metric that measures the capabilities and error rates of a quantum computer. It expresses the maximum size of square quantum circuits that can be implemented successfully by the computer. The form of the circuits is independent from the quantum computer architecture, but compiler can transform and optimize it to take advantage of the computer's features. Thus, quantum volumes for different architectures can be compared. == Introduction == Quantum computers are difficult to compare. Quantum volume is a single number designed to show all around performance. It is a measurement and not a calculation, and takes into account several features of a quantum computer, starting with its number of qubits—other measures used are gate and measurement errors, crosstalk and connectivity. IBM defined its Quantum Volume metric because a classical computer's transistor count and a quantum computer's quantum bit count aren't the same. Qubits decohere with a resulting loss of performance so a few fault tolerant bits are more valuable as a performance measure than a larger number of noisy, error-prone qubits. Generally, the larger the quantum volume, the more complex the problems a quantum computer can solve. Alternative benchmarks include Cross-entropy benchmarking, reliable Quantum Operations per Second


id: quantum-computing-scaling-laws-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_computing_scaling_laws-0.md
category: reference
title: Quantum computing scaling laws
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_computing_scaling_laws
date_saved: 2026-05-05T11:08:13.112711+00:00
instance: kb-cron
parent: quantum-computing-scaling-laws-20260505-0
summary:
Quantum computing scaling laws (sometimes abbreviated as QC scaling laws) are a set of observations describing the exponential growth of various aspects of quantum computer development. The most important scaling laws in quantum computing are Rose's law, Neven's law, and Schoelkopf's law. These laws are named after prominent quantum computing researchers and predict continued improvement in quantum computer performance in the coming years. However, it is important to note that these laws are more empirical rules of thumb and predictions based on observations rather than immutable truths, and technological development may bring unexpected challenges and breakthroughs. == Rose's law == Rose's law observes that the number of qubits on chips doubles roughly every 18 months. The law is often described as the quantum-computing equivalent of Moore's law. The term was coined by Steve Jurvetson after meeting D-Wave founder Geordie Rose. This law attempts to measure rapid processor scaling, though different quantum computing technologies may follow different trajectories depending on their design constraints. == Neven's law == Neven's law states that the computational power of quantum computers appears to be growing at a doubly exponential rate. In other words, not only is computational power increasing exponentially—that exponential growth is itself accelerating


id: quantum-computing-since-democritus-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_Computing_Since_Democritus-0.md
category: reference
title: Quantum Computing Since Democritus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_Computing_Since_Democritus
date_saved: 2026-05-05T11:08:14.294374+00:00
instance: kb-cron
parent: quantum-computing-since-democritus-20260505-0
summary:
Quantum Computing Since Democritus is a 2013 book on quantum information science written by Scott Aaronson. It is loosely based on a course Aaronson taught at the University of Waterloo, Canada, the lecture notes for which are available online. == Contents == Aaronson has stated that he intends the book to be at the same level as Leonard Susskind's The Theoretical Minimum or Roger Penrose's The Road to Reality; Physics Today compared it to George Gamow's One Two Three... Infinity. The book covers everything from computer science to mathematics to quantum mechanics and quantum computing, starting, as the title indicates, with Democritus. === Front cover === The front cover image is an oil canvas painting of Democritus by Hendrik ter Brugghen dated 1628. It depicts Democritus as a young, laughing hedonist who points in the distance, as to where the folly of mankind is found. The image invokes Aaronson's discussions on Democritus' concept of atoms and the void, which forms the foundational understanding of matter at the atomic level, is relevant to quantum computing, where manipulating and controlling individual quantum objects for calculations echoes the early atomic theory's significance. == Author == Scott Aaronson is a professor of theoretical computer


id: quantum-computing-a-gentle-introduction-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_Computing:_A_Gentle_Introduction-0.md
category: reference
title: Quantum Computing: A Gentle Introduction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_Computing:_A_Gentle_Introduction
date_saved: 2026-05-05T11:08:15.435261+00:00
instance: kb-cron
parent: quantum-computing-a-gentle-introduction-20260505-0
summary:
Quantum Computing: A Gentle Introduction is a textbook on quantum computing. It was written by Eleanor Rieffel and Wolfgang Polak, and published in 2011 by the MIT Press. == Topics == Although the book approaches quantum computing through the model of quantum circuits, it is focused more on quantum algorithms than on the construction of quantum computers. It has 13 chapters, divided into three parts: "Quantum building blocks" (chapters 1–6), "Quantum algorithms" (chapters 7–9), and "Entangled subsystems and robust quantum computation" (chapters 10–13). After an introductory chapter overviewing related topics including quantum cryptography, quantum information theory, and quantum game theory, chapter 2 introduces quantum mechanics and quantum superposition using polarized light as an example, also discussing qubits, the Bloch sphere representation of the state of a qubit, and quantum key distribution. Chapter 3 introduces direct sums, tensor products, and quantum entanglement, and chapter 4 includes the EPR paradox, Bell's theorem on the impossibility of local hidden variable theories, as quantified by Bell's inequality. Chapter 5 discusses unitary operators, quantum logic gates, quantum circuits, and functional completeness for systems of quantum gates. Chapter 6, the final chapter of the building block section, discusses (classical) reversible computing, and the conversion of arbitrary


id: quantum-error-correction-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_error_correction-0.md
category: reference
title: Quantum error correction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_error_correction
date_saved: 2026-05-05T11:08:16.683136+00:00
instance: kb-cron
parent: quantum-error-correction-20260505-0
summary:
Quantum error correction (QEC) comprises a set of techniques used in quantum memory and quantum computing to protect quantum information from errors arising from decoherence and other sources of quantum noise. QEC schemes that employ codewords stabilized by a set of commuting operators are known as stabilizer codes, and the corresponding codewords are referred to as quantum error-correcting codes (QECCs). Conceptually, to use a quantum error-correcting code, one can append ancilla qubits to qubits that need protection, and apply a unitary encoding circuit to rotate the global state into a subspace of a larger Hilbert space. This highly entangled, encoded state corrects for local noisy errors. A quantum error-correcting code makes quantum computation and quantum communication practical by providing a way for a sender and receiver to simulate a noiseless qubit channel given a noisy qubit channel whose noise conforms to a particular error model. == Overview == Much of the terminology in QEC is derived from its classical counterpart, the classical error-correcting code. In classical coding theory, a code is commonly denoted by the notation [ n , k , d ] {\displaystyle [n,k,d]} , which represents the encoding of k {\displaystyle k} logical bits into n {\displaystyle n}


id: quantum-error-correction-20260505-1
file: data/en.wikipedia.org/wiki/Quantum_error_correction-1.md
category: reference
title: Quantum error correction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_error_correction
date_saved: 2026-05-05T11:08:16.683136+00:00
instance: kb-cron
parent: quantum-error-correction-20260505-0
summary:
=== More general QEC schemes === The [ [ n , k , d ] ] {\displaystyle [[n,k,d]]} QECCs do not encompass all possible quantum codes. These belong to the class of additive codes, defined within the stabilizer formalism. A more general class, known as non-additive codes, extends beyond this framework. For instance, the ( ( 5 , 6 , 2 ) ) {\displaystyle ((5,6,2))} code encodes more than two qubits ( log 2 ⁡ 6 ≈ 2.585 ) {\displaystyle (\log _{2}6\approx 2.585)} into five physical qubits with code distance two. Non-additive codes can, in principle, achieve higher code rates than additive ones, but their construction and analysis are considerably more challenging. As a result, they remain relatively unexplored, with only limited studies to date. Beyond encoding qubits into qubits, quantum information can also be stored in more general physical systems, such as d {\displaystyle d} -level systems (qudits) or infinite-dimensional oscillators. Encoding a smaller logical system into a larger physical Hilbert space is an active area of research. == Important code families == The first QECC, named after Peter Shor, can be generalized as a [ [ d 2 , 1 , d ] ] {\displaystyle [[d^{2},1,d]]} code, which


id: quantum-error-correction-20260505-2
file: data/en.wikipedia.org/wiki/Quantum_error_correction-2.md
category: reference
title: Quantum error correction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_error_correction
date_saved: 2026-05-05T11:08:16.683136+00:00
instance: kb-cron
parent: quantum-error-correction-20260505-0
summary:
== Classical codes as bias quantum code == Classical error-correcting codes that employ redundancy can be mapped to biased quantum codes that correct either Pauli X (bit-flip) or Pauli Z (phase-flip) errors. The simplest, though inefficient, example is the repetition code. In a repetition code, the logical information is stored as multiple copies of a bit. If these copies are later found to disagree due to errors, the most likely original value is inferred via majority vote. For example, consider a logical bit in the "1" state copied three times. If noise corrupts one of the three bits, leaving the other two unchanged, the most likely scenario is that a single-bit error occurred, and the original logical value was "1." While it is possible that two bits flip, producing three zeros, this outcome is less probable. In this example, the logical information is the single bit, and the three copies are the physical representation. Repetition codes work in classical channels because classical bits can be freely measured and duplicated. In quantum channels, however, the no-cloning theorem prevents copying an unknown qubit, seemingly posing an obstacle to quantum error correction. This challenge is overcome by encoding the logical information of a


id: quantum-error-correction-20260505-3
file: data/en.wikipedia.org/wiki/Quantum_error_correction-3.md
category: reference
title: Quantum error correction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_error_correction
date_saved: 2026-05-05T11:08:16.683136+00:00
instance: kb-cron
parent: quantum-error-correction-20260505-0
summary:
E corr ( ρ ) = P 0 ρ P 0 + ∑ i = 1 3 X i P i ρ P i X i . {\displaystyle {\mathcal {E}}_{\operatorname {corr} }(\rho )=P_{0}\rho P_{0}+\sum _{i=1}^{3}X_{i}P_{i}\rho \,P_{i}X_{i}.} Note that, while this procedure perfectly corrects the output when zero or one flips are introduced by the channel, if more than one qubit is flipped then the output is not properly corrected. For example, if the first and second qubits are flipped, then the syndrome measurement gives the outcome P 3 {\displaystyle P_{3}} , and the third qubit is flipped, instead of the first two. To assess the performance of this error-correcting scheme for a general input we can study the fidelity F ( ψ ′ ) {\displaystyle F(\psi ')} between the input | ψ ′ ⟩ {\displaystyle \vert \psi '\rangle } and the output ρ out ≡ E corr ( E ( | ψ ′ ⟩ ⟨ ψ ′ | ) ) {\displaystyle \rho _{\operatorname {out} }\equiv {\mathcal {E}}_{\operatorname {corr} }({\mathcal {E}}(\vert \psi '\rangle \langle \psi '\vert ))} . Being the output state ρ out {\displaystyle \rho _{\operatorname {out} }} correct when no more than one qubit is flipped, which happens with


id: quantum-error-correction-20260505-4
file: data/en.wikipedia.org/wiki/Quantum_error_correction-4.md
category: reference
title: Quantum error correction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_error_correction
date_saved: 2026-05-05T11:08:16.683136+00:00
instance: kb-cron
parent: quantum-error-correction-20260505-0
summary:
If a bit flip error happens to a qubit, the syndrome analysis will be performed on each block of qubits (1,2,3), (4,5,6), and (7,8,9) to detect and correct at most one bit flip error in each block. If the three bit flip group (1,2,3), (4,5,6), and (7,8,9) are considered as three inputs, then the Shor code circuit can be reduced as a sign flip code. This means that the Shor code can also repair a sign flip error for a single qubit. The Shor code also can correct for any arbitrary errors (both bit flip and sign flip) to a single qubit. If an error is modeled by a unitary transform U, which will act on a qubit | ψ ⟩ {\displaystyle |\psi \rangle } , then U {\displaystyle U} can be described in the form U = c 0 I + c 1 X + c 2 Y + c 3 Z {\displaystyle U=c_{0}I+c_{1}X+c_{2}Y+c_{3}Z} where c 0 {\displaystyle c_{0}} , c 1 {\displaystyle c_{1}} , c 2 {\displaystyle c_{2}} , and c 3 {\displaystyle c_{3}} are complex constants, I is the identity, and the Pauli matrices are given by X = ( 0 1 1 0 ) ; Y


id: quantum-error-correction-20260505-5
file: data/en.wikipedia.org/wiki/Quantum_error_correction-5.md
category: reference
title: Quantum error correction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_error_correction
date_saved: 2026-05-05T11:08:16.683136+00:00
instance: kb-cron
parent: quantum-error-correction-20260505-0
summary:
and it remains maximal. Thus, even without an error correction step, the metrological properties remain the same. (See the Supplement E in Ref., and Ref.) == Experimental realization == There have been several experimental realizations of CSS-based codes. The first demonstration was with nuclear magnetic resonance qubits. Subsequently, demonstrations have been made with linear optics, trapped ions, and superconducting (transmon) qubits. In 2016 for the first time the lifetime of a quantum bit was prolonged by employing a QEC code. The error-correction demonstration was performed on Schrödinger-cat states encoded in a superconducting resonator, and employed a quantum controller capable of performing real-time feedback operations including read-out of the quantum information, its analysis, and the correction of its detected errors. The work demonstrated how the quantum-error-corrected system reaches the break-even point at which the lifetime of a logical qubit exceeds the lifetime of the underlying constituents of the system (the physical qubits). Other error correcting codes have also been implemented, such as one aimed at correcting for photon loss, the dominant error source in photonic qubit schemes. In 2021, an entangling gate between two logical qubits encoded in topological quantum error-correction codes has first been realized using 10 ions in a


id: quantum-experiments-using-satellite-technology-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_Experiments_using_Satellite_Technology-0.md
category: reference
title: Quantum Experiments using Satellite Technology
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_Experiments_using_Satellite_Technology
date_saved: 2026-05-05T11:08:17.875461+00:00
instance: kb-cron
parent: quantum-experiments-using-satellite-technology-20260505-0
summary:
Quantum Experiment using Satellite Technology was launched in 2017 by the Raman Research Institute. In February 2021, the project demonstrated quantum communication for 50 m apart, and on 19 March 2021 for 300 m apart inline of sight in the Space Applications Centre, which was done in coordination with the Indian Space Research Organisation, Indian Institute of Science and Tata Institute of Fundamental Research. Quantum Experiment using Satellite Technology is India's first project on satellite based long distance quantum communication. == Technical specifications == Indigenously developed NAVIC receiver for time synchronization Gimbal mechanism system instead of large aperture telescope for optical alignment. Shared quantum secure text. Shared image transmission. Quantum assisted two ways video conferencing at the Space Applications Centre and Physical Research Laboratory It used robust and high brightness entangled photon source, used BBM92 protocol implementation NAVIC enabled synchronization polarization compensation technique. It is hack proof as it uses quantum key distribution. It uses quantum cryptography and carried out by Quantum information and computing (QuIC) lab . == References ==


id: quantum-flagship-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_Flagship-0.md
category: reference
title: Quantum Flagship
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_Flagship
date_saved: 2026-05-05T11:08:35.116311+00:00
instance: kb-cron
parent: quantum-flagship-20260505-0
summary:
The Quantum Technologies Flagship is a European Union scientific research initiative. With a budget of €1 billion, it is one of the large scale initiatives organized by the Future and Emerging Technologies program, along with the Human Brain Project and the Graphene Flagship.The Quantum Flagship funds over 5,000 European researchers over ten years. Its long-term vision is to develop in Europe a quantum web, where quantum computers, simulators and sensors are interconnected via quantum communication networks. The objective being to develop in Europe a competitive quantum industry making research results available as commercial applications and disruptive technologies. == Beginning of the flagship == In 2016, the European Commissioner for digital economy and society Günther Oettinger invited the quantum community to provide a common European strategy on quantum technologies. Endorsed by 3.400 individuals from academia and industry, a “quantum manifesto” was released in May 2016 in the Netherlands The document called for the European Commission to launch an ambitious European initiative in quantum technologies to ensure Europe's leading role in a technological revolution underway. Following this document, the European Commission appointed a High Level Steering Committee, composed of 12 academic members and 12 industry members, to deliver a strategic research agenda,


id: quantum-image-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_image-0.md
category: reference
title: Quantum image
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_image
date_saved: 2026-05-05T11:08:36.236401+00:00
instance: kb-cron
parent: quantum-image-20260505-0
summary:
Quantum computation, which exploits quantum parallelism, is in principle faster than a classical computer for certain problems. Quantum image is encoding the image information in quantum-mechanical systems instead of classical ones and replacing classical with quantum information processing may alleviate some of these challenges. Humans obtain most of their information through their eyes. Accordingly, the analysis of visual data is one of the most important functions of our brain and it has evolved high efficiency in processing visual data. Currently, visual information like images and videos constitutes the largest part of data traffic in the internet. Processing of this information requires ever-larger computational power. The laws of quantum mechanics allow one to reduce the required resources for some tasks by many orders of magnitude if the image data are encoded in the quantum state of a suitable physical system. The researchers discuss a suitable method for encoding image data, and develop a new quantum algorithm that can detect boundaries among parts of an image with a single logical operation. This edge-detection operation is independent of the size of the image. Several other algorithms are also discussed. It is theoretically and experimentally demonstrated that they work in practice. This is the


id: quantum-image-processing-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_image_processing-0.md
category: reference
title: Quantum image processing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_image_processing
date_saved: 2026-05-05T11:08:37.475265+00:00
instance: kb-cron
parent: quantum-image-processing-20260505-0
summary:
Quantum image processing (QIMP) is using quantum computing or quantum information processing to create and work with quantum images. Due to some of the properties inherent to quantum computation, notably entanglement and parallelism, it is hoped that QIMP technologies will offer capabilities and performances that surpass their traditional equivalents, in terms of computing speed, security, and minimum storage requirements. == Background == A. Y. Vlasov's work in 1997 focused on using a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images and detect the posture of certain targets. Notably, more optics-based interpretations for quantum imaging were initially experimentally demonstrated in and formalized in after seven years. In 2003, Salvador Venegas-Andraca and S. Bose presented Qubit Lattice, the first published general model for storing, processing and retrieving images using quantum systems. Later on, in 2005, Latorre proposed another kind of representation, called the Real Ket, whose purpose was to encode quantum images as a basis for further applications in QIMP. Furthermore, in 2010 Venegas-Andraca and Ball presented a method for storing and retrieving binary geometrical shapes in quantum mechanical systems in which it is shown that maximally entangled qubits


id: quantum-image-processing-20260505-1
file: data/en.wikipedia.org/wiki/Quantum_image_processing-1.md
category: reference
title: Quantum image processing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_image_processing
date_saved: 2026-05-05T11:08:37.475265+00:00
instance: kb-cron
parent: quantum-image-processing-20260505-0
summary:
== Quantum image manipulations == A lot of the effort in QIMP has been focused on designing algorithms to manipulate the position and color information encoded using flexible representation of quantum images (FRQI) and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations and restricted geometric transformations to constrain these operations to a specified area of an image were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image and quantum image scaling to resize a quantum image were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates. Later, Multi-Channel Quantum Image-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels have been fully discussed. To illustrate the feasibility and capability of QIMP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic


id: quantum-natural-language-processing-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_natural_language_processing-0.md
category: reference
title: Quantum natural language processing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_natural_language_processing
date_saved: 2026-05-05T11:08:38.718259+00:00
instance: kb-cron
parent: quantum-natural-language-processing-20260505-0
summary:
Quantum natural language processing (QNLP) is the application of quantum computing to natural language processing (NLP). It computes word embeddings as parameterised quantum circuits that can solve NLP tasks faster than any classical computer. It is inspired by categorical quantum mechanics and the DisCoCat framework, making use of string diagrams to translate from grammatical structure to quantum processes. == Theory == The first quantum algorithm for natural language processing used the DisCoCat framework and Grover's algorithm to show a quadratic quantum speedup for a text classification task. It was later shown that quantum language processing is BQP-Complete, i.e. quantum language models are more expressive than their classical counterpart, unless quantum mechanics can be efficiently simulated by classical computers. These two theoretical results assume fault-tolerant quantum computation and a QRAM, i.e. an efficient way to load classical data on a quantum computer. Thus, they are not applicable to the noisy intermediate-scale quantum (NISQ) computers available today. == Experiments == The algorithm of Zeng and Coecke was adapted to the constraints of NISQ computers and implemented on IBM quantum computers to solve binary classification tasks. Instead of loading classical word vectors onto a quantum memory, the word vectors are computed directly as


id: quantum-programming-20260505-0
file: data/en.wikipedia.org/wiki/Quantum_programming-0.md
category: reference
title: Quantum programming
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_programming
date_saved: 2026-05-05T11:08:39.917227+00:00
instance: kb-cron
parent: quantum-programming-20260505-0
summary:
Quantum programming refers to the process of designing and implementing algorithms that operate on quantum systems, typically using quantum circuits composed of quantum gates, measurements, and classical control logic. These circuits are developed to manipulate quantum states for specific computational tasks or experimental outcomes. Quantum programs may be executed on quantum processors, simulated on classical hardware, or implemented through laboratory instrumentation for research purposes. When working with quantum processor-based systems, quantum programming languages provide high-level abstractions to express quantum algorithms efficiently. These languages often integrate with classical programming environments and support hybrid quantum-classical workflows. The development of quantum software has been strongly influenced by the open-source community, with many toolkits and frameworks—such as Qrisp, Qiskit, Cirq, PennyLane, and qBraid SDK—available under open licenses. Quantum programming can also be used to model or control experimental systems through quantum instrumentation and sensor-based platforms. While some quantum computing architectures—such as linear optical quantum computing using the KLM protocol—require specialized hardware, others use gate-based quantum processors accessible through software interfaces. In both cases, quantum programming serves as the bridge between theoretical algorithms and physical implementation. == Quantum instruction sets == Quantum instruction sets are used to turn higher level algorithms into physical instructions that


id: quantum-programming-20260505-1
file: data/en.wikipedia.org/wiki/Quantum_programming-1.md
category: reference
title: Quantum programming
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantum_programming
date_saved: 2026-05-05T11:08:39.917227+00:00
instance: kb-cron
parent: quantum-programming-20260505-0
summary:
==== qBraid SDK ==== The qBraid SDK is an open-source platform-agnostic quantum runtime framework developed by qBraid. It enables users to write quantum programs once and execute them across various quantum hardware and simulators without modifying the code. The SDK supports multiple quantum programming libraries, including Qiskit, Cirq, PennyLane, PyQuil, and Braket, among others. It features a graph-based transpiler that facilitates conversion between different quantum program types, allowing seamless interoperability between frameworks. The SDK also provides tools for job submission, result retrieval, and circuit visualization. It is integrated with qBraid Lab, offering access to over 20 quantum devices and simulators from providers such as IonQ, Rigetti, QuEra, and IQM. ==== Qibo ==== An open source full-stack API for quantum simulation, quantum hardware control and calibration developed by multiple research laboratories, including QRC, CQT and INFN. Qibo is a modular framework which includes multiple backends for quantum simulation and hardware control. This project aims at providing a platform agnostic quantum hardware control framework with drivers for multiple instruments and tools for quantum calibration, characterization and validation. This framework focuses on self-hosted quantum devices by simplifying the software development required in labs. ==== Qiskit ==== An open source project developed by IBM.


