arXiv:2508.21730v1 Announce Type: new Abstract: In this paper we present a variational algorithm for the Traveling Salesman Problem (TSP) that combines (i) a compact encoding of permutations, which reduces the qubit requirement too, (ii) an optimize-freeze-reuse strategy: where the circuit topology (“Ansatz'') is first optimized on a training instance by Simulated Annealing (SA), then “frozen'' and re-used on novel instances, limited to a rapid re-optimization of only the circuit parameters. This pipeline eliminates costly structural research in testing, making the procedure immediately implementable on NISQ hardware. On a set of $40$ randomly generated symmetric instances that span $4 – 7$ cities, the resulting Ansatz achieves an average optimal trip sampling probability of $100%$ for 4 city cases, $90%$ for 5 city cases and $80%$ for 6 city cases. With 7 cities the success rate drops markedly to an average of $sim 20%$, revealing the onset of scalability limitations of the proposed method. The results show robust generalization ability for moderate problem sizes and indicate how freezing the Ansatz can dramatically reduce time-to-solution without degrading solution quality. The paper also discusses scalability limitations, the impact of “warm-start'' initialization of parameters, and prospects for extension to more complex problems, such as Vehicle Routing and Job-Shop Scheduling.
Original: https://arxiv.org/abs/2508.21730