Relation of classical non-equilibrium dynamics and quantum annealing

TL;DR

This paper explores the formal relationship between classical non-equilibrium dynamics and quantum annealing, showing that quantum processes can efficiently simulate classical dynamics, suggesting quantum annealing's potential superiority in optimization tasks.

Contribution

The authors reformulate the relationship between classical stochastic dynamics and quantum mechanics, demonstrating the potential advantages of quantum annealing over simulated annealing in solving optimization problems.

Findings

Classical dynamics can be efficiently simulated by quantum processes.

Quantum annealing may be more powerful than simulated annealing.

The formal relationship helps compare the efficiency of both methods.

Abstract

Non-equilibrium dynamics of the Ising model is a classical stochastic process whereas quantum mechanics has no stochastic elements in the classical sense. Nevertheless, it has been known that there exists a close formal relationship between these two processes. We reformulate this relationship and use it to compare the efficiency of simulated annealing that uses classical stochastic processes and quantum annealing to solve combinatorial optimization problems. It is shown that classical dynamics can be efficiently simulated by quantum-mechanical processes whereas the converse is not necessarily true. This may imply that quantum annealing may be regarded as a more powerful tool than simulated annealing for optimization problems.