Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing

TL;DR

This paper introduces a novel interpolation method combining quantum and classical dynamics to study thermal effects in quantum systems, demonstrating improved quantum annealing performance in spin glasses.

Contribution

The authors develop a new interpolation approach that maintains pure states and captures thermal effects, applicable to quantum annealing and other quantum dynamics.

Findings

Supports thermal relaxation in quantum dynamics

Reveals performance improvements in quantum annealing

Provides a unified framework for quantum-classical interpolation

Abstract

We propose a method to interpolate dynamics of von Neumann and classical master equations with an arbitrary mixing parameter to investigate the thermal effects in quantum dynamics. The two dynamics are mixed by intervening to continuously modify their solutions, thus coupling them indirectly instead of directly introducing a coupling term. This maintains the quantum system in a pure state even after the introduction of thermal effects and obtains not only a density matrix but also a state vector representation. Further, we demonstrate that the dynamics of a two-level system can be rewritten as a set of standard differential equations, resulting in quantum dynamics that includes thermal relaxation. These equations are equivalent to the optical Bloch equations at the weak coupling and asymptotic limits, implying that the dynamics cause thermal effects naturally. Numerical simulations of ferromagnetic and frustrated systems support this idea. Finally, we use this method to study thermal effects in quantum annealing, revealing nontrivial performance improvements for a spin glass model over a certain range of annealing time. This result may enable us to optimize the annealing time of real annealing machines.