Quantum Simulations of Classical Annealing Processes

TL;DR

This paper introduces a quantum algorithm that enhances classical simulated annealing by leveraging quantum walks and the quantum Zeno effect, achieving a quadratic speedup in finding optimal solutions for combinatorial problems.

Contribution

The authors present a novel quantum simulation approach for classical annealing, significantly reducing the number of steps needed to reach optimal solutions compared to traditional methods.

Findings

Achieves quadratic speedup over classical annealing in terms of spectral gap.

Requires order 1/√δ steps to find an optimal solution.

Demonstrates the effectiveness of quantum simulation for combinatorial optimization.

Abstract

We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order $1/\sqrt{\delta}$ steps to find an optimal solution with bounded error probability, where $\delta$ is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order $1/\delta$ steps required by the latter.