固定维持奇偶性编译器契约下对易相位项排序的平台约束选择
Plateau-Constrained Selection: Exploiting Degeneracy for Lower-Depth Quantum Compilation
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中文总结 AI 辅助
该研究针对对易相位项排序的多最优解问题，提出两阶段排列搜索方法，在量子电路优化中减少了受控非门数量，降低了量子比特深度，具有编译器自由度的应用价值。
中文摘要 AI 辅助
对易相位项的排序目标存在多个相等的最优解，但现有方法未对这些等价解进行表征或利用。我们在固定布局和维持奇偶性的量子降级条件下采用经典两阶段排列搜索：第一阶段验证主要支撑最优解，第二阶段对等代价巡游进行采样并通过冻结路由得分进行选择。在合成的16量子比特Ising实例分配中，对20个项进行精确计数确立了实例相关的多重性；当达到支撑下界时，约化宽度等于支撑线图的无向哈密顿路径数量。修订后的工程分析发现，与未优化排序相比，路由受控非门减少了9.14%，与现有随机搜索相比减少了11.10%。在36个项的24个采样最小支撑代价排序中，直接深度选择在所有20个聚合中使相反SABRE种子的深度降低了12.83%，而匹配的24次重启对照仅使深度变化了-0.41%（未解决）。候选排名在SABRE路由种子间保持一致，解释了为何选择能在路由重新随机化中存活。深度优势转移到第二个生成器和48个项，但在BasicSwap下反转。在预期的IBM Heron面板上，原始生成器误差变化了-0.0025（-0.59%）；固定面板的 shot 不确定性排除了零，但项种子推断仍未解决。等主代价巡游是一种有用的路由器条件编译器自由度，而非保证的硬件优势。
英文摘要
Minimum-cost orders of commuting phase terms can produce substantially different routed circuits. On the same 36-term instances, three orders with identical support cost 74 yield mean routed depths of 228.6, 233.8, and 256.7. We exploit this degeneracy under fixed placement and maintained-parity lowering: Stage 1 attains the support optimum, and Stage 2 selects minimum routed depth among 24 equal-cost orders. For distinct pair supports, we characterize orders attaining the support lower bound through Hamiltonian paths of the support line graph and count optima exactly through 20 terms. On synthetic 16-qubit assignment-Ising instances, selection reduces depth by 12.83% under a different SABRE routing seed, with lower depth in all 20 instances. The selected orders lie a median 1.57 pool standard deviations below the pool mean, consistent with ordinary best-of-24 selection; the useful feature is that candidate rankings persist across routing seeds. Depth reductions extend to 48 terms and a random-MaxCut generator, whereas evaluation with BasicSwap reverses the gain. A 40-instance IBM Heron study measures a 0.59% error reduction on the executed stabilizer-probe panel, but the primary confidence interval across instances includes zero. Plateau selection therefore improves routed depth in the tested SABRE pipeline while preserving the logical support optimum.
