Quantum Approaches to Urban Logistics: From Core QAOA to Clustered Scalability

TL;DR

This paper explores the application of quantum algorithms, specifically QAOA and a clustering extension, to solve large-scale, real-world constrained TSP instances, demonstrating potential and limitations in current quantum hardware.

Contribution

It introduces Cl-QAOA, a hybrid quantum-classical clustering method, to improve scalability of quantum TSP solutions on limited hardware.

Findings

QAOA shows promise for constrained TSP but faces scalability challenges.

Cl-QAOA effectively decomposes large TSPs into manageable sub-problems.

Experimental results highlight strengths and current limitations of quantum approaches.

Abstract

The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.