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Shared-End-First Control Ordering in Clean-Ancilla V-Chain Synthesis of Nested Multi-Controlled Cascades: A Quantum Binary-Addition-Tree Case Study
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 circu
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