提出高效训练方法，让量子电路解更大规模旅行商问题。
Understanding the Nature of Depth-1 Equivariant Quantum Circuit
- 用新优化方法实现深度1量子电路的快速训练
- 350节点问题仿真时间减少96.4%，精度接近最优
- 适合研究量子强化学习与大规模问题求解者
针对旅行商问题（TSP），深度1等变量子电路（EQC）仅用两个参数即可在20个节点以下达到近似最优性能。然而，由于量子电路模拟存在指数级时间与内存开销，且实际硬件噪声与退相干问题，扩展至更大规模仍具挑战。本文提出一种名为大小不变网格搜索（SIGS）的高效量子强化学习（QRL）训练优化方法，成功模拟了最多达350节点的TSP实例。在100节点问题上，相比传统基于解析表达式的强化学习模拟，总仿真时间从151分钟降至6分钟，降幅达96.4%，且测试集平均最优差距控制在0.005以内。该方法为QRL社区提供了实用的大规模性能评估工具。我们进一步提出理论解释——大小不变性（Size-Invariant Properties），超越以往关于等变性的讨论。
原文摘要 · Abstract (English)
The Equivariant Quantum Circuit (EQC) for the Travelling Salesman Problem (TSP) has been shown to achieve near-optimal performance in solving small TSP problems (up to 20 nodes) using only two parameters at depth 1. However, extending EQCs to larger TSP problem sizes remains challenging due to the exponential time and memory for quantum circuit simulation, as well as increasing noise and decoherence when running on actual quantum hardware. In this work, we propose the Size-Invariant Grid Search (SIGS), an efficient training optimization for Quantum Reinforcement Learning (QRL), and use it to simulate the outputs of a trained Depth-1 EQC up to 350-node TSP instances - well beyond previously tractable limits. At TSP with 100 nodes, we reduce total simulation times by 96.4%, when comparing to RL simulations with the analytical expression (151 minutes using RL to under 6 minutes using SIGS on TSP-100), while achieving a mean optimality gap within 0.005 of the RL trained model on the test set. SIGS provides a practical benchmarking tool for the QRL community, allowing us to efficiently analyze the performance of QRL algorithms on larger problem sizes. We provide a theoretical explanation for SIGS called the Size-Invariant Properties that goes beyond the concept of equivariance discussed in prior literature.
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