On the Computational Performance of IBM Quantum Devices Applied to Combinatorial Optimisation Problems

The prevalence of NP-Hard Combinatorial Optimisation Problems (COP) requires a continuous search for powerful heuristic techniques to efficiently solve problems of this nature, due to the exponentially growing CPU times faced by deterministic methods. This paper focuses on two COP, namely the Travelling Salesmen Problem (TSP) and the Quadratic Assignment Problem (QAP). In particular, the computational performance of classical optimisation techniques, Branch and Bound (BNB) and Simulated Annealing (SA), are compared to the Variational Quantum Eigensolver (VQE) algorithm. These algorithms are executed respectively on classical and Noisy Intermediate-Scale Quantum (NISQ) computers, in this case, a host of IBM quantum devices. The experimental results resemble and extend on previously reported results found in the literature. Furthermore, this research critically analyses, compares and comments on the performance of quantum computing techniques to that of classical techniques. The results highlight the current shortcomings of NISQ devices, as classical optimisation techniques significantly outperform the VQE algorithm when run on state of the art IBM Quantum devices.