Freeze and Conquer: Reusable Ansatz for Solving the Traveling Salesman Problem

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 ~ 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.