发表机构
Kvantify（Kvantify）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展LMC框架至Clifford电路，提出可计算下界并证明对量子比特置换紧致，且作为A*启发式可提升最优性证明能力。
AI 中文摘要
最小化合成Clifford算子所需的CNOT门数量是量子电路优化中的一个核心问题。我们将用于线性可逆电路的link-middle-cut（LMC）框架扩展到由二元辛表格表示的Clifford算子。通过引入块支撑连通图和行列式不变量，我们获得了可高效计算的无辅助比特CNOT复杂度的下界。我们证明了这些下界对于量子比特置换是紧的：具有k个循环的n个量子比特的置换恰好需要3(n-k)个CNOT门，即使允许任意单量子比特Clifford门也是如此。我们还推导了在输出量子比特置换（对应于自由量子比特重标记）意义下进行综合的可高效计算的界。最后，我们进一步展示了该界作为A*算法为基础的Clifford综合的可采纳启发式函数的实用性，并表明在基准实例上，由此产生的搜索能够证明最优性，其能力超越了早期基于SAT的方法，并且它可以与早期的A*启发式函数结合使用，以改善通过启发式搜索获得的CNOT门数量。
英文摘要
Minimizing the number of CNOT gates required to synthesize a Clifford operator is a central problem in quantum circuit optimization. We extend the link--middle--cut (LMC) framework for linear reversible circuits to Clifford operators represented by binary symplectic tableaux. By introducing block-support connectivity graphs and determinantal invariants, we obtain efficiently computable lower bounds on ancilla-free CNOT complexity. We prove that these bounds are tight for qubit permutations: a permutation of $n$ qubits with $k$ cycles requires exactly $3(n-k)$ CNOT gates, even when arbitrary one-qubit Clifford gates are available. We also derive efficiently computable bounds for synthesis up to a permutation of the output qubits, corresponding to free qubit relabeling. Finally, we further demonstrate the utility of the bound by using it as an admissible heuristic for $A^*$-based Clifford synthesis and show that, on benchmark instances, the resulting search can prove optimality beyond what was possible with earlier SAT-based methods, and that it may be used in combination with earlier $A^*$ heuristics to improve the CNOT counts obtained through heuristic search.
