First order phase transition in the Quantum Adiabatic Algorithm

Preprint

8 October 2009

preprint
Published by arXiv in arXiv

Abstract

We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem for sizes up to N=256 using quantum Monte Carlo simulations incorporating parallel tempering. At large N we find that some instances have a discontinuous (first order) quantum phase transition during the evolution of the QAA. This fraction increases with increasing N and may tend to 1 for N -> infinity.

Keywords

QUANTUM ADIABATIC ALGORITHM
QUANTUM PHASE TRANSITION
MONTE CARLO SIMULATIONS
ORDER PHASE
QAA

All Related Versions

Version 1, 2009-10-08, ArXiv
Version 2, 2010-01-19, ArXiv
Published version: Physical Review Letters, 104 (2), 020502.

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