Quantum Optimisation of Complex Systems with a Quantum Annealer

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 (by way of the transverse field component on the annealer), 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.

Completely Quantum Neural Networks

“…This has been shown in Ref. [40]. By contrast, classical algorithms must somehow surmount the barriers to find the global minimum.…”

QFitter -- A Quantum Fitting Framework Applied to Effective Field Theories

“…Thus, the problem solved by the transversefield quantum annealers can be viewed equivalently as finding the set of values for the σ i such that H classical is minimized: This problem can be solved both using quantum annealing and classical algorithms, such as simulated annealing. Quantum annealing has been shown to be more consistent in finding the ground state of some non-convex functions [14]. In Section III, we will compare the performance of quantum annealing to several classical methods for EFT fits.…”

“…Quantum annealing provides an optimisation framework with the potential to perform better than classical algorithms in minimising non-convex functions [11][12][13][14][15]. The availability of physical quantum annealing devices with thousands of qubits has made it possible to apply this approach to real-world problems in recent years [16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Qade: Solving Differential Equations on Quantum Annealers

“…Quantum computing provides an immediate solution: the quantum tunnelling mechanism allows to jump between local minima separated by Juan Carlos Criado: juan.c.criado@durham.ac.uk Michael Spannowsky: michael.spannowsky@durham.ac.uk large energy barriers [28]. In this way, the global minimum of non-convex functions can be found reliably [29,43].…”