An investigation of IBM Quantum Computing device performance on Combinatorial Optimisation Problems

Abstract: The intractability of deterministic solutions in solving $\mathcal{NP}$-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, the Travelling Salesman Problem (TSP) and the Quadratic Assignment Problem (QAP). Two accepted classical optimisation methods, Branch and Bound (BNB) and Simulated Annealing (SA), 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 agrees and extends with findings in the literature. Further, we introduce additional performance metrics to better compare the two approaches concerning computational time, feasibility and solution quality. Our results show that the VQE performs better than QAOA for 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 in the results. Finally, we present the shortcomings of state-of-the-art NISQ IBM quantum devices and argue for potential future work and investigation.