Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing

TL;DR

This paper introduces a classical, gradient-based algorithm inspired by quantum annealing to efficiently find approximate solutions for large-scale quadratic unconstrained binary optimization problems, matching state-of-the-art performance.

Contribution

It proposes a novel quantum-inspired classical algorithm that replaces quantum dynamics with gradient descent, enabling fast solutions on large problem instances.

Findings

Achieves high-quality solutions quickly for large-scale problems

Performs comparably to current state-of-the-art methods

Can be accelerated using GPU hardware

Abstract

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where the dynamical evolution in quantum annealing is replaced with a gradient-descent based method. This formulation is able to quickly find high-quality solutions to large-scale problem instances, and can naturally be accelerated by dedicated hardware such as graphics processing units. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions. We find that our algorithm offers a similar performance to current state of the art approaches within a comparably simple gradient-based and non-stochastic setting.