Quantum algorithms for simulated annealing

TL;DR

This paper discusses a quantum algorithm that accelerates classical simulated annealing for discrete optimization by achieving a quadratic speedup related to the spectral gap, promising more efficient problem-solving.

Contribution

It introduces a quantum algorithm that simulates classical annealing with a quadratic speedup, improving efficiency in solving discrete optimization problems.

Findings

Quantum algorithm scales with the inverse square root of the spectral gap.

Achieves quadratic speedup over classical simulated annealing.

Potential for more efficient discrete optimization solutions.

Abstract

This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales with the inverse square root of the spectral gap of an associated stochastic matrix. This represents a quadratic quantum speedup, in terms of the gap, with respect to classical simulated annealing.