共享端优先控制排序在清洁辅助V链合成嵌套多控制级联中的应用：量子二进制加法树案例研究
Shared-End-First Control Ordering in Clean-Ancilla V-Chain Synthesis of Nested Multi-Controlled Cascades: A Quantum Binary-Addition-Tree Case Study
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中文总结 AI 辅助
本研究提出共享端优先排序规则，在清洁辅助V链合成中暴露嵌套多控制级联的CX抵消，使QBAT电路成本从1,025降至209，比率接近12/11，为现有优化器提供新的优化机会。
中文摘要 AI 辅助
对于多控制X门，控制顺序在逻辑上无关紧要，但在有序辅助链合成后可能产生物理影响。本研究以可逆二进制加法树（BAT）后继电路为主要案例，推导并验证了嵌套控制级联的共享端优先排序规则。在Maslov清洁辅助V链合成下，预优化CX成本与顺序无关，而共享端优先排序在阶段边界暴露了P(m)=(m-4)(m-3)/2个逆相对相位CCX对；标准优化移除6P(m)个CX，在独立推导的两CX终端恒等式后，对于QBAT得到12m-31。当m=20时，镜像BAT方向后保留升序控制列表产生1,025个CX，而镜像链方向则恢复为209个。不相交目标嵌套级联重现了相同的抵消计数，表明BAT目标几何并非必需；有序脏辅助V链控制显示零方向优势，将机制限定在测试的合成族内。独立行波进位基线在全连接性下给出11m-28个CX，因此QBAT/RC比率接近12/11，在测试的QBAT-A1和INC_RC实现中具有相等的自然宽度2m-3。贡献在于一种合成排序规则，将抵消暴露给现有优化器，而非新的优化器通道或通用MCX规则。
英文摘要
Control order is logically irrelevant for a multi-controlled-X gate but can become physically consequential after ordered ancilla-chain synthesis. This work derives and validates a shared-end-first ordering rule for nested-control cascades, using reversible Binary-Addition-Tree (BAT) successor circuits as the primary case. Under Maslov clean-v-chain synthesis, pre-optimization CX cost is order-invariant, whereas shared-end-first ordering exposes P(m)=(m-4)(m-3)/2 inverse relative-phase-CCX pairs across stage boundaries; standard optimization removes 6P(m) CX, giving 12m-31 for QBAT after an independently derived two-CX terminal identity. At m=20, retaining an ascending control list after mirroring the BAT direction yields 1,025 CX, while mirroring the chain orientation restores 209. A disjoint-target nested cascade reproduces the same cancellation count for count, showing that BAT target geometry is not required; an ordered dirty-v-chain control shows zero orientation advantage, delimiting the mechanism within the tested synthesis families. Independent ripple-carry baselines give 11m-28 CX on FULL connectivity, so the QBAT/RC ratio approaches 12/11, with equal natural width 2m-3 in the tested QBAT-A1 and INC_RC implementations. The contribution is a synthesis-ordering rule that exposes cancellation to an existing optimizer, not a new optimizer pass or a universal MCX rule.
发表机构
- National Tsing Hua University（国立清华大学）
机构由 AI 辅助整理，请以论文原文为准。
