Freeze and Conquer: Reusable Ansatz for Solving the Traveling Salesman Problem
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| Format: | Preprint |
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2025
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| author | Fagiolo, Fabrizio Vescera, Nicolò |
| author_facet | Fagiolo, Fabrizio Vescera, Nicolò |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_21730 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Freeze and Conquer: Reusable Ansatz for Solving the Traveling Salesman Problem Fagiolo, Fabrizio Vescera, Nicolò Artificial Intelligence 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. |
| title | Freeze and Conquer: Reusable Ansatz for Solving the Traveling Salesman Problem |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2508.21730 |