Quantum Optimisation of Complex Systems with a Quantum Annealer

TL;DR

This paper compares quantum annealing with classical optimization methods, demonstrating that quantum annealers outperform classical techniques in minimizing complex 2D potentials, with better avoidance of false minima.

Contribution

It provides an in-depth comparison of quantum annealing and classical methods on 2D Ising models and complex potentials, highlighting quantum annealer's superior performance.

Findings

Quantum annealer outperforms classical methods in complex potential minimization.

Classical methods often get trapped in false minima, unlike quantum annealing.

Quantum annealing effectively avoids false minima and rapidly finds true minima.

Abstract

We perform an in-depth comparison of quantum annealing with several classical optimisation techniques, namely thermal annealing, Nelder-Mead, and gradient descent. We begin with a direct study of the 2D Ising model on a quantum annealer, and compare its properties directly with those of the thermal 2D Ising model. These properties include an Ising-like phase transition that can be induced by either a change in 'quantum-ness' of the theory, or by a scaling the Ising couplings up or down. This behaviour is in accord with what is expected from the physical understanding of the quantum system. We then go on to demonstrate the efficacy of the quantum annealer at minimising several increasingly hard two dimensional potentials. For all the potentials we find the general behaviour that Nelder-Mead and gradient descent methods are very susceptible to becoming trapped in false minima, while the thermal anneal method is somewhat better at discovering the true minimum. However, and despite current limitations on its size, the quantum annealer performs a minimisation very markedly better than any of these classical techniques. A quantum anneal can be designed so that the system almost never gets trapped in a false minimum, and rapidly and successfully minimises the potentials.