Solving the Shortest Path Problem with QAOA

Abstract

Graph computation is a core technique for solving realistic problems of graph representations. In solving the shortest path problem (SPP), the current classical methods are encountering a huge performance bottleneck. Attempting to solve this dilemma, we try to solve the SPP with a Quantum Approximate Optimal Algorithm (QAOA)-based quantum method. In this paper, we propose a QAOA-based shortest path algorithm (SPA) by constructing a suitable Hamiltonian quantity and using the idea of variational quantum computing, and verify the algorithm using a quantum simulator and an International Business Machines cloud quantum computer. The proposed algorithm is able to achieve a near-optimal solution with a correct rate that significantly exceeds the invalid solutions, reaching a good preliminary result. Furthermore, the proposed algorithm is expected to achieve a huge advantage over the classical algorithm and the SPA based on Grover’s algorithm with a suitable selection of parameters and number of steps. In addition, the proposed algorithm requires fewer quantum bits than other quantum algorithms, thus promising quantum computing superiority on current noisy intermediate-scale quantum (NISQ) quantum computing devices.