AI 中文总结
本研究提出基于MCMS本德尔斯分解的混合量子-经典端到端优化框架，以VRP为案例验证，发现该规模下框架难获量子优势，需开展更多大规模基准测试研究。
AI 中文摘要
我们展示了一种基于本德尔斯分解（Benders decomposition）的混合量子-经典端到端优化框架，该框架可求解混合整数线性规划（MILP）问题。该框架基于此前提出的、通过多解生成多割（MCMS）本德尔斯分解构建的混合量子-经典端到端管线，此前的割选择步骤在量子退火硬件上执行。我们为张量网络模拟器和超导量子硬件扩展了基于门的量子近似优化算法（QAOA）实现。以车辆路径问题（VRP）作为代表性案例研究，我们在QOptLib的标准化基准实例的10种排列（含20个客户和4辆车）上运行了该端到端管线，其中割选择步骤由经典求解器执行。我们发现，对于我们的实例，经典MCMS本德尔斯分解中只有一小部分计算资源用于割选择步骤。为进行完整的混合端到端评估，我们使用强大的张量网络模拟器MPS-JuliQAOA在一个玩具问题上运行该管线以执行QAOA，此时大部分时间花费在割选择步骤上，这表明在该规模的问题上该框架不太可能取得量子优势。这凸显了当获得更强大的量子处理单元（QPU）二次无约束二元优化（QUBO）求解器时，需要开展更多大规模基准测试研究。
英文摘要
We demonstrate an end-to-end hybrid quantum-classical optimisation framework based on Benders decomposition, capable of solving mixed-integer linear programming (MILP) problems. The framework builds on a previously presented hybrid quantum-classical end-to-end pipeline based on Multiple Cuts via Multiple Solutions (MCMS) Benders decomposition where the cut selection step was performed on quantum annealing hardware. We extend this with gate-based QAOA implementations for both tensor network emulators and superconducting quantum hardware. The Vehicle Routing Problem (VRP) is used as a representative case study and we run the pipeline end-to-end on 10 permutations of a standardised benchmarking instance (20 customers and 4 vehicles from QOptLib) with a classical solver performing the cut selection step. We find that for our instances, only a small fraction of the compute in classical MCMS Benders decomposition is spent on the cut selection step. For a full hybrid end-to-end assessment, we run the pipeline for a toy problem with MPS-JuliQAOA, a powerful tensor network emulator, to execute QAOA. Here, the majority of the time is spent on the cut selection step, deeming quantum advantage of this framework unlikely at problems of this size. This highlights the need for more large-scale benchmarking research when more powerful (QPU) QUBO solvers are available.
