Classical simulation and theory of quantum annealing in a thermal environment

TL;DR

This paper investigates the behavior of quantum annealing in a thermal environment, developing a phenomenological theory for excess energy scaling and confirming it with a novel non-Markovian numerical method, with implications for quantum annealer experiments.

Contribution

It introduces a phenomenological theory for quantum annealing in thermal environments and validates it with a new non-Markovian numerical approach.

Findings

Excess energy scales predictably after annealing.

Quasistatic evolution fails near the end due to relaxation time divergence.

Crossovers between different coupling and regime regimes are characterized.

Abstract

We study quantum annealing in the quantum Ising model coupled to a thermal environment. When the speed of quantum annealing is sufficiently slow, the system evolves following the instantaneous thermal equilibrium. This quasistatic and isothermal evolution, however, fails near the end of annealing because the relaxation time grows infinitely, therefore yielding excess energy from the thermal equilibrium. We develop a phenomenological theory based on this picture and derive a scaling relation of the excess energy after annealing. The theoretical results are numerically confirmed using a novel non-Markovian method that we recently proposed based on a path-integral representation of the reduced density matrix and the infinite time evolving block decimation. In addition, we discuss crossovers from weak to strong coupling as well as from the adiabatic to quasistatic regime, and propose experiments on the D-Wave quantum annealer.