Comparative study of variations in quantum approximate optimization algorithms for the Traveling Salesman Problem

TL;DR

This study evaluates different QAOA mixer designs for solving small TSP instances on digital quantum simulators, highlighting a balanced mixer as most promising for future quantum devices.

Contribution

It introduces an improved qubit encoding and layerwise learning protocol for QAOA applied to TSP, analyzing mixer performance and noise resilience.

Findings

Balanced QAOA mixer outperforms others in accuracy and cost

Simulation results support the viability of quantum algorithms for TSP

Noise models indicate robustness of the proposed approach

Abstract

The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this paper, we tackle the TSP using the quantum approximate optimization algorithm (QAOA) approach by formulating it as an optimization problem. By adopting an improved qubit encoding strategy and a layerwise learning optimization protocol, we present numerical results obtained from the gate-based digital quantum simulator, specifically targeting TSP instances with 3, 4, and 5 cities. We focus on the evaluations of three distinctive QAOA mixer designs, considering their performances in terms of numerical accuracy and optimization cost. Notably, we find a well-balanced QAOA mixer design exhibits more promising potential for gate-based simulators and realistic quantum devices in the long run, an observation further supported by our noise model simulations. Furthermore, we investigate the sensitivity of the simulations to the TSP graph. Overall, our simulation results show the digital quantum simulation of problem-inspired ansatz is a successful candidate for finding optimal TSP solutions.