A Resource-Efficient Variational Quantum Framework for the Traveling Salesman Problem

TL;DR

This paper introduces a resource-efficient variational quantum approach for solving the Traveling Salesman Problem, reducing qubit requirements and enabling implementation on small quantum hardware.

Contribution

It proposes a compact binary-register encoding and a divide-and-conquer strategy, significantly lowering qubit needs for TSP quantum solutions.

Findings

Achieved 100% success rate on 4- and 5-city TSP instances.

Reduced data qubits to O(n log n) with compact encoding.

Demonstrated implementation on small quantum computers.

Abstract

The Traveling Salesman Problem (TSP) is a prototypical combinatorial optimization problem, but its quantum implementation is limited by the O(n^2)-qubit overhead of standard one-hot encodings. Here, we propose a resource-efficient variational quantum framework based on compact binary-register encoding, a permutation-preserving problem-inspired ansatz, and a complementary divide-and-conquer execution strategy. The compact encoding reduces the data-qubit requirement to O(n log n), while the divide-and-conquer formulation lowers the number of qubits required in each local hardware execution to the size of the largest subsystem. Numerical simulations on TSP instances with 4, 5, and 6 cities achieve best average success rates of 100%, 100%, and 95.5%, respectively. A local two-qubit implementation of the divide-and-conquer approximation is further evaluated for a 5-city TSP instance on SpinQ Gemini Pro and SpinQ Triangulum II NMR quantum computers. Taken together, the results indicate how compact encoding and divide-and-conquer execution with classical post-processing can be used to study small combinatorial optimization instances on resource-constrained quantum hardware.