First order phase transition in the Quantum Adiabatic Algorithm
Statistical Mechanics
2010-01-19 v2 Disordered Systems and Neural Networks
Quantum Physics
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.
Cite
@article{arxiv.0910.1378,
title = {First order phase transition in the Quantum Adiabatic Algorithm},
author = {A. P. Young and S. Knysh and V. N. Smelyanskiy},
journal= {arXiv preprint arXiv:0910.1378},
year = {2010}
}
Comments
5 pages, 3 figures. Replaced with published version; two figures slightly changed and some small changes to the text