QAOA pseudo-Boltzmann sampling beyond the rapid-mixing regime on superconducting quantum computers

Abstract

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm developed for solving combinatorial optimization problems. It has also been shown to generate pseudo-Boltzmann distributions, with potential applications in various fields of computer science and computational physics. In this work, we build upon previous theoretical results and demonstrate pseudo-Boltzmann sampling with single-layer QAOA on real superconducting quantum computers. We show that the pseudo-Boltzmann distribution and the ability to adjust its effective temperature survive the accumulated errors of a real, noisy superconducting quantum processor. On an IBM processor, we are able to reach temperatures below a classical minimum-temperature boundary that guarantees the rapid mixing of single-site Glauber dynamics. We also run controlled simulations of QAOA with various noise models to characterize how increasing error rates raises the effective temperature of the distribution and limits the lowest accessible temperature.