First order phase transition in the Quantum Adiabatic Algorithm

A. P. Young; S. Knysh; V. N. Smelyanskiy

First order phase transition in the Quantum Adiabatic Algorithm

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arxiv 0910.1378 v2 pith:7737GTXP submitted 2009-10-07 cond-mat.stat-mech cond-mat.dis-nnquant-ph

First order phase transition in the Quantum Adiabatic Algorithm

A. P. Young , S. Knysh , V. N. Smelyanskiy This is my paper

classification cond-mat.stat-mech cond-mat.dis-nnquant-ph

keywords quantumadiabaticalgorithmfirstorderphasetransitioncarlo

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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.

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