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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Adiabatic quantum computation | 2/2 | https://en.wikipedia.org/wiki/Adiabatic_quantum_computation | reference | science, encyclopedia | 2026-05-05T11:06:32.974566+00:00 | kb-cron |
H
~
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s
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=
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1
−
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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
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E
1
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−
E
0
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)
{\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 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.
== D-Wave quantum processors == 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. 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.
== Notes ==