基于稀疏量子松弛的车辆路径聚类
Vehicle-Routing Clustering by Sparse Quantum Relaxation
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中文总结 AI 辅助
针对带时间窗的容量约束取送货问题，提出基于稀疏量子松弛的聚类方法，通过非对角编码和修复策略，在经典强修复下接近最优，并绘制了硬件评估状态图。
中文摘要 AI 辅助
本文研究的是带时间窗的容量约束取送货问题（CPDPTW）的“先聚类后路径”分解中的聚类分配层，而非直接进行路径排序的二次无约束二元优化（QUBO）。基于样本的子空间对角化（SQD）对于任何对角优化哈密顿量都会退化为“最佳样本”方法，因此，要有效地迁移到路径规划问题，需要非对角松弛。量子随机访问优化（QRAO）通过使用非对易的量子随机访问码（QRAC）可观测量对二元变量进行编码，提供了这种非对角性。由CPDPTW衍生的冲突图暴露了路径规划特有的障碍，因为密集的目标函数和惩罚编码的约束破坏了QRAO的压缩效果。我们通过仅编码稀疏化的目标函数，并在舍入后通过修复来强制满足独热、容量和聚类时间预算的可行性，从而保持哈密顿量的稀疏性。我们不声称具有量子优势。在强修复下，仅经典处理即可在测试规模下达到接近最优的成本。结果是一个状态图，将稀疏化、实现的压缩、线性组合酉算子（LCU）1-范数、重六边形双量子比特深度、采样漂移以及最终在Qiskit Aer、校准的FakeTorino和IBM Heron ibm_quebec上的路径规划质量联系起来。在一个跨越四到十二个取送货请求对的108行理想-校准-硬件评估网格中，硬件部分的平均差距为0.0016，设备与理想的平均总变差距离（TVD）为0.279；在规模六到十二的解码器消融实验隔离了非对角信号。
英文摘要
This paper studies the cluster-assignment layer of a cluster-first-route-second decomposition for the capacitated pickup-and-delivery problem with time windows (CPDPTW), instead of a direct route-ordering quadratic unconstrained binary optimization (QUBO). Sample-based subspace diagonalization (SQD) degenerates to best-of-shots for any diagonal optimization Hamiltonian, so a useful transfer to routing requires non-diagonal relaxation. Quantum random access optimization (QRAO) provides this non-diagonality by encoding binary variables through non-commuting quantum random access code (QRAC) observables. CPDPTW-derived conflict graphs expose a routing-specific obstruction because dense objectives and penalty-encoded constraints destroy QRAO compression. We keep the Hamiltonian sparse by encoding only the sparsified objective and enforcing one-hot, capacity, and cluster time-budget feasibility by repair after rounding. We make no quantum-advantage claim. Under strong repair the classical pass alone reaches near-optimal cost at the tested sizes. The result is a regime map linking sparsification, achieved compression, linear-combination-of-unitaries (LCU) 1-norm, heavy-hex two-qubit depth, sampling drift, and final routing quality on Qiskit Aer, calibrated FakeTorino, and IBM Heron ibm_quebec. Across a 108-row ideal-calibrated-hardware evaluation grid spanning four to twelve pickup-delivery request pairs, the hardware slice has mean gap 0.0016 and mean device-vs-ideal total variation distance (TVD) 0.279; a decoder ablation at sizes six through twelve isolates the non-diagonal signal.
发表机构
- Laboratory of Innovations in Transportation (LiTrans) Toronto Metropolitan University（多伦多都会大学交通创新实验室）
机构由 AI 辅助整理，请以论文原文为准。
