First order phase transition in the Quantum Adiabatic Algorithm

TL;DR

This paper investigates the behavior of the quantum adiabatic algorithm on the exact cover problem, revealing that it undergoes a first order quantum phase transition at large problem sizes, which impacts its efficiency.

Contribution

It provides the first large-scale simulation evidence of first order phase transitions in the QAA for the exact cover problem, highlighting potential limitations.

Findings

First order phase transitions occur at large N in QAA.

The fraction of instances with first order transitions increases with N.

Transitions may become universal as N approaches infinity.

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.