title: First-order phase transition in the quantum adiabatic algorithm.
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.
authors.affiliation: Department of Physics, University of California, Santa Cruz, California 95064, USA.
authors.forename: A P
authors.initials: AP
authors.lastname: Young
authors.forename: S
authors.initials: S
authors.lastname: Knysh
authors.forename: V N
authors.initials: VN
authors.lastname: Smelyanskiy