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

Yuefeng Lin; Chao Zheng; Cong Guo

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arXiv · 2605.00739

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

Yuefeng Lin·Chao Zheng·Cong Guo

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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.

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Yuefeng Lin, Chao Zheng, Cong Guo. 2026-05-01. A Resource-Efficient Variational Quantum Framework for the Traveling Salesman Problem. https://arxiv.org/abs/2605.00739

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