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The European Physical Journal Special Topics

, Volume 224, Issue 1, pp 63–73 | Cite as

Performance of the quantum adiabatic algorithm on constraint satisfaction and spin glass problems

  • I. Hen
  • A.P. Young
Review
Part of the following topical collections:
  1. Quantum Annealing: The Fastest Route to Quantum Computation?

Abstract

One of the major ongoing debates on the future of quantum annealers pertains to their robustness against the decohering effects of finite temperature and interactions with the environment. We argue that even in an ideal setting of very low temperatures and in the absence of a decohering environment, quantum annealers may find it challenging to solve optimization problems significantly faster than state-of-the-art heuristic classical algorithms. Here, we study the performance of the quantum adiabatic algorithm (QAA) on a variety of constraint satisfaction problems by examining the size dependence of the minimum energy gap during the evolution of the QAA. We do so by employing Quantum Monte Carlo schemes as these allow us to study these problems at much larger scales than exact methods would allow. We find that in all cases a quantum phase transition occurs and the minimum gap decreases exponentially with system size, leading to an exponentially large running time for the QAA. Based on these and other results, we discuss potential modifications to the QAA that may improve the scaling of the minimum gap, leading to faster quantum adiabatic algorithms.

Keywords

European Physical Journal Special Topic Spin Glass Spin Glass Phase Quantum Annealing Quantum Monte Carlo Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  • I. Hen
    • 1
  • A.P. Young
    • 2
  1. 1.Information Sciences Institute, University of Southern California, Marina del ReyMarina del ReyUSA
  2. 2.Department of PhysicsUniversity of CaliforniaSanta CruzUSA

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