更少量子比特，更好选择：面向量子辅助交通区域划分的耦合感知子QUBO选择
Fewer Qubits, Better Choices: Coupling-Aware Sub-QUBO Selection for Quantum-Assisted Traffic Zone Partitioning
- FAMU-FSU College of Engineering（FAMU-FSU工程学院）
- Rensselaer Polytechnic Institute（伦斯勒理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对量子优化子问题选择，提出耦合感知的二阶选择方法，证明在单变量最优时随机选择远不如基于成对交互的贪心选择，并在交通分区任务中以更少量子比特取得更优效果。
AI中文摘要：
近期量子优化器大约可容纳一百个二进制变量，这要求将大型二次无约束二进制优化问题分解为硬件规模的子问题，同时保持其他变量固定。变量通常通过按单个翻转的目标变化进行排序来选择。我们证明，一旦当前解在单变量翻转下达到最优，该规则便不再具有信息量：每个分数代表一个代价，而剩余改进取决于被忽略的成对交互。二阶展开反而产生一个奖励收集最密子图选择问题，可在变量数量线性时间内贪心求解，并给出两个无求解器的界，包围所选子集内可实现的改进。在芝加哥和费城的交通网络上，我们的规则使用16变量子问题的表现优于使用64变量的随机选择，表明将设备容量翻两番无法弥补较弱的选择。用道路网络连通性替代几何邻接将差距扩大1.6至1.9倍。固定选择轨迹后，在120量子比特设备上解决的子问题比例从零变化到一，最终目标值在六位有效数字内保持不变。因此，在测试的硬件可访问规模下，收益来自选择而非后端。硬件可行性受耦合项限制：120变量问题在7,260项时编译失败，但在5,118项时成功。编译时间几乎随项数二次增长并主导执行成本，达到1,752秒，而量子处理为469秒。
英文摘要：
Near-term quantum optimizers accommodate roughly a hundred binary variables, requiring large Quadratic Unconstrained Binary Optimization problems to be decomposed into hardware-sized subproblems while other variables remain fixed. Variables are typically selected by ranking the objective changes from individual flips. We show that this rule is uninformative once the incumbent is optimal under single-variable flips: every score represents a cost, while remaining improvements depend on overlooked pairwise interactions. A second-order expansion instead yields a prize-collecting densest-subgraph selection problem, solvable greedily in time linear in the number of variables, and two solver-free bounds bracketing the improvement achievable within a selected subset. On transportation networks from Chicago and Philadelphia, our rule with 16-variable subproblems outperforms random selection with 64, demonstrating that quadrupling device capacity cannot compensate for weaker selection. Replacing geometric adjacency with road-network connectivity widens the margin by a factor of 1.6-1.9. With the selection trace fixed, varying the fraction of subproblems solved on a 120-qubit device from zero to one leaves the final objective unchanged to six significant figures. At tested hardware-accessible sizes, gains therefore arise from selection rather than the backend. Hardware feasibility is limited by coupling terms: 120-variable problems fail to compile with 7,260 terms but succeed with 5,118. Compilation scales almost quadratically with term count and dominates execution cost, reaching 1,752 seconds versus 469 seconds of quantum processing.
