An investigation of IBM quantum computing device performance on combinatorial optimisation problems

Abstract

The intractability of deterministic solutions in solving NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {NP}$$\end{document}-Hard Combinatorial Optimisation Problems (COP) is well reported in the literature. One mechanism for overcoming this difficulty has been the use of efficient COP non-deterministic approaches. However, with the advent of quantum technology, these modern devices’ potential to overcome this tractability limitation requires exploration. This paper juxtaposes classical and quantum optimisation algorithms’ performance to solve two common COP, namely the Travelling Salesman Problem and the Quadratic Assignment Problem. Two accepted classical optimisation methods, Branch and Bound and Simulated Annealing, are compared to two quantum optimisation methods, Variational Quantum Eigensolver (VQE) algorithm and Quantum Approximate Optimisation Algorithm (QAOA). These algorithms are, respectively, executed on both classical devices and IBM’s suite of Noisy Intermediate-Scale Quantum (NISQ) devices. We have encoded the COP problems for the respective technologies and algorithms and provided the computational encodings for the NISQ devices. Our experimental results show that current classical devices significantly outperform the presently available NISQ devices, which both agree with and extend on those findings reported in the literature. Further, we introduce additional performance metrics to better compare the two approaches with respect to computational time, feasibility and solution quality. Our results show that the VQE performs better than QAOA with respect to these metrics, and we infer that this is due to the increased number of operations required. Additionally, we investigate the impact of a new set of basis gates on the quantum optimisation techniques and show they yield no notable improvement on obtained results. Finally, we highlight the present shortcomings of state-of-the-art NISQ IBM quantum devices and argue for continued future work on improving evolving devices.