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The European Physical Journal Special Topics

, Volume 224, Issue 1, pp 75–88 | Cite as

Quantum annealing: The fastest route to quantum computation?

  • C.R. Laumann
  • R. Moessner
  • A. Scardicchio
  • S.L. Sondhi
Review
Part of the following topical collections:
  1. Quantum Annealing: The Fastest Route to Quantum Computation?

Abstract

In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to avoided crossings inside a phase. We argue that the thermodynamic order of the phase transitions is not predictive of the scaling of the gap with the system size. On the contrary, we also argue that, if the phase surrounding the problem Hamiltonian is a Many-Body Localized (MBL) phase, the gaps are going to be typically exponentially small and that this follows naturally from the existence of local integrals of motion in the MBL phase.

Keywords

Domain Wall European Physical Journal Special Topic Quantum Computation Order Phase Transition Local Integral 
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

  • C.R. Laumann
    • 1
    • 2
  • R. Moessner
    • 3
  • A. Scardicchio
    • 4
    • 5
    • 6
    • 7
    • 8
  • S.L. Sondhi
    • 3
    • 4
  1. 1.Department of PhysicsUniversity of WashingtonSeattleUSA
  2. 2.Perimeter Institute for Theoretical PhysicsWaterloo, OntarioCanada
  3. 3.Max-Planck-Institut fur Physik komplexer SystemDresdenGermany
  4. 4.Physics Department, Princeton UniversityPrincetonUSA
  5. 5.Physics Department, Columbia UniversityNew YorkUSA
  6. 6.ITS, Graduate Center, City University of New YorkNew YorkUSA
  7. 7.INFN, Sezione di TriesteTriesteItaly
  8. 8.On leave from Abdus Salam ICTPTriesteItaly

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