发表机构
Qoro Quantum Ltd.; Qoro Quantum GmbH; National Quantum Computing Centre; Quantum Software Lab, The University of Edinburgh; Hartree Centre, STFC; E.ON Digital Technology GmbH（Qoro Quantum有限公司; Qoro Quantum有限责任公司; 国家量子计算中心; 爱丁堡大学量子软件实验室; STFC哈特里中心; E.ON数字技术有限责任公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对最小伯克霍夫分解问题，结合QAOA采样、E-FCFW优化等技术，在千变量输电网络优化任务中实现了量子采样的分布式执行，提升了分解性能并缩短了硬件执行时间。
AI 中文摘要
最小伯克霍夫分解（MBD）旨在求匹配的稀疏加权和，是一个具有网络调度和能源交易应用的挑战性优化问题。我们结合单层QAOA采样、扩展全校正弗兰克-沃尔夫（E-FCFW）优化、谱图划分及贪心可行性修复，扩展了一种量子辅助分解方法。我们在1354节点的PEGASE母线测试案例（代表含1710条传输线的1354母线输电网络）上演示该流程，其1710条边定义了一个原生1710变量的匹配优化问题，未划分编码需1710个量子比特。划分可在IBM超导量子处理器上实现分布式执行。已报道的最佳硬件结果使用50量子比特的划分边界，而将划分减少至20量子比特会在划分规模对比中降低收敛性。更大的划分对矩阵积态（MPS）模拟要求更高，键维测试表明截断量子关联会降低候选质量。因此，结果表明在整体问题扩展时，需在每个划分中保留实质性量子采样任务。在PEGASE-1354基准上，修复后的QAOA采样比模拟退火和均匀随机采样基线实现更低的剩余分解误差，而空间电路打包将硬件执行时间减少约三分之一。这些结果证明，结合谱划分、空间电路打包和经典可行性修复，为在当前硬件上部署基于门的量子采样解决千变量约束优化问题提供了可行路径。
英文摘要
The Minimum Birkhoff Decomposition (MBD) seeks a sparse weighted sum of matchings and is a challenging optimization problem with applications in network scheduling and energy trading. We scale a quantum-assisted decomposition method by combining single-layer QAOA sampling with Extended Fully-Corrective Frank-Wolfe (E-FCFW) optimization, spectral graph partitioning, and greedy feasibility repair. We demonstrate the pipeline on the 1,354-node PEGASE bus test case (representing a 1,354-bus transmission grid with 1,710 transmission lines), whose 1,710 edges define a native 1,710-variable matching optimization problem requiring 1,710 qubits in the unpartitioned encoding. Partitioning enables distributed execution on IBM superconducting quantum processors. The best reported hardware result uses a 50-qubit partition bound, while reducing partitions to 20 qubits degrades convergence in the partition-size comparison. Larger partitions are more demanding for matrix product state (MPS) simulation, and bond-dimension tests show that truncating quantum correlations reduces candidate quality. The results therefore motivate retaining a substantive quantum sampling task within each partition as the overall problem scales. On the PEGASE-1354 benchmark, repaired QAOA samples achieve lower residual decomposition error than both simulated annealing and uniform random sampling baselines, while spatial circuit packing reduces hardware execution time by approximately a factor of three. These results demonstrate that combining spectral partitioning, spatial circuit packing, and classical feasibility repair provides an executable path for deploying gate-based quantum sampling on thousand-variable constrained optimization problems on current hardware.
