Improving Quantum and Classical Decomposition Methods for Vehicle Routing

TL;DR

This paper combines graph shrinking and circuit cutting techniques to improve the scalability of quantum algorithms for vehicle routing problems, successfully solving a 7-city TSP with fewer qubits.

Contribution

It introduces an integrated decomposition approach that enhances quantum algorithm scalability for vehicle routing problems, demonstrating practical application on current quantum hardware.

Findings

Successfully solved a 7-city TSP with fewer qubits

Decomposition methods reduce quantum resource requirements

Insights into quantum algorithm performance on current hardware

Abstract

Quantum computing is a promising technology to address combinatorial optimization problems, for example via the quantum approximate optimization algorithm (QAOA). Its potential, however, hinges on scaling toy problems to sizes relevant for industry. In this study, we address this challenge by an elaborate combination of two decomposition methods, namely graph shrinking and circuit cutting. Graph shrinking reduces the problem size before encoding into QAOA circuits, while circuit cutting decomposes quantum circuits into fragments for execution on medium-scale quantum computers. Our shrinking method adaptively reduces the problem such that the resulting QAOA circuits are particularly well-suited for circuit cutting. Moreover, we integrate two cutting techniques which allows us to run the resulting circuit fragments sequentially on the same device. We demonstrate the utility of our method by successfully applying it to the archetypical traveling salesperson problem (TSP) which often occurs as a sub-problem in practically relevant vehicle routing applications. For a TSP with seven cities, we are able to retrieve an optimum solution by consecutively running two 7-qubit QAOA circuits. Without decomposition methods, we would require five times as many qubits. Our results offer insights into the performance of algorithms for combinatorial optimization problems within the constraints of current quantum technology.