---
title: "Adiabatic quantum computation"
chunk: 2/2
source: "https://en.wikipedia.org/wiki/Adiabatic_quantum_computation"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T11:06:32.974566+00:00"
instance: "kb-cron"
---

  
    
      
        
          
            
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          H
          
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    {\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
          
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    {\displaystyle H_{B}}
  
 at the beginning, proceed through an adiabatic process, and end in the ground state of problem Hamiltonian 
  
    
      
        
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    {\displaystyle H_{P}}
  
.
Then measure the z-component of each of the n spins in the final state. This will produce a string 
  
    
      
        
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    {\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 
  
    
      
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    {\displaystyle \varepsilon /g_{\mathrm {min} }^{2}}
  
, where

  
    
      
        
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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 ==