用冻结的量子电路解决旅行商问题，省去反复优化，提升效率。
Freeze and Conquer: Reusable Ansatz for Solving the Traveling Salesman Problem
- 先用模拟退火优化电路结构，再冻结复用，仅重调参数。
- 4-6城问题平均成功率超80%，7城降至20%显出扩展瓶颈。
- 适合想快速部署量子算法的科研或工业用户。
本文提出一种变分量子算法求解旅行商问题（TSP），采用紧凑的排列编码方式，减少所需量子比特数。提出“优化-冻结-复用”策略：先用模拟退火（SA）在训练实例上优化电路结构（Ansatz），随后冻结结构，在新实例上仅快速重调参数。该流程避免了测试阶段的结构搜索成本，可直接应用于当前量子硬件（NISQ）。在40个随机生成的对称实例（4-7个城市）上，该方法在4城、5城、6城问题上平均最优路径采样概率分别为100%、90%和80%；7城时下降至约20%，显示出方法的可扩展性局限。结果表明，冻结电路结构可在不降低解质量的前提下大幅缩短求解时间。论文还讨论了参数热启动的影响及向车辆路径等问题扩展的可能性。
原文摘要 · Abstract (English)
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.
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