First-Order Phase Transition in the Quantum Adiabatic Algorithm.

摘要

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.