194 lines
3.6 KiB
Markdown
194 lines
3.6 KiB
Markdown
---
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title: "Adiabatic quantum computation"
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chunk: 2/2
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source: "https://en.wikipedia.org/wiki/Adiabatic_quantum_computation"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T11:06:32.974566+00:00"
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instance: "kb-cron"
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---
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H
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~
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(
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s
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)
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=
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(
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1
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−
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s
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)
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H
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B
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+
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s
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H
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P
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{\displaystyle {\tilde {H}}(s)=(1-s)H_{B}+sH_{P}}
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, which is the adiabatic evolution Hamiltonian of the algorithm.
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In accordance with the adiabatic theorem, start from the ground state of Hamiltonian
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H
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B
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{\displaystyle H_{B}}
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at the beginning, proceed through an adiabatic process, and end in the ground state of problem Hamiltonian
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H
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P
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{\displaystyle H_{P}}
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.
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Then measure the z-component of each of the n spins in the final state. This will produce a string
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z
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1
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,
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z
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2
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,
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…
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,
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z
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n
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{\displaystyle z_{1},z_{2},\dots ,z_{n}}
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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
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ε
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/
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g
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m
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2
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{\displaystyle \varepsilon /g_{\mathrm {min} }^{2}}
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, where
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g
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=
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min
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0
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≤
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s
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≤
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1
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E
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1
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0
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{\displaystyle g_{\mathrm {min} }=\min _{0\leq s\leq 1}(E_{1}(s)-E_{0}(s))}
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is the minimum energy gap between ground state and first excited state.
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== Comparison to gate-based quantum computing ==
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Adiabatic quantum computing is equivalent in power to standard gate-based quantum computing that implements arbitrary unitary operations. However, the mapping challenge on gate-based quantum devices differs substantially from quantum annealers as logical variables are mapped only to single qubits and not to chains.
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== D-Wave quantum processors ==
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The D-Wave One is a device made by Canadian company D-Wave Systems, which claims that it uses quantum annealing to solve optimization problems. On 25 May 2011, Lockheed-Martin purchased a D-Wave One for about US$10 million. In May 2013, Google purchased a 512 qubit D-Wave Two.
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The question of whether the D-Wave processors offer a speedup over a classical processor is still unanswered. Tests performed by researchers at Quantum Artificial Intelligence Lab (NASA), USC, ETH Zurich, and Google show that as of 2015, there is no evidence of a quantum advantage.
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== Notes == |