最优双量子比特门切割成本与非局域性度量
Optimal Two-Qubit Gate-Cutting Cost and Measures of Nonlocality
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中文总结 AI 辅助
本研究从最优双量子比特门切割公式出发，推导出拟概率范围与五个非局域性描述符的尖锐上下界，揭示门切割成本在相似非局域门间的显著差异。
中文摘要 AI 辅助
电路切割使得量子计算能够被分解为更小的子电路，但代价是额外的采样开销。门切割提供了这样一种方法，通过将非局域门替换为局域操作的拟概率分解来实现。从已知的最优双量子比特门切割公式出发，我们推导出完整的尖锐下包络和上包络，将拟概率范围 $\gamma$ 与五个已建立的描述符联系起来：纠缠能力、门典型性、算子纠缠、Schmidt强度和最大乘积输入并发度。我们将 $\gamma$ 重新表述为算子-Schmidt谱的Rényi-$1/2$泛函，并展示了双量子比特谱的物理约束如何锐化通用熵界，并选择一组重复出现的极值Cartan族。五个描述符中的任何一个都不能单独决定 $\gamma$，但每个都施加了精确的约束，揭示了具有相似非局域特性的门之间最优门切割成本可能如何显著变化。
英文摘要
Circuit cutting enables quantum computations to be decomposed into smaller subcircuits at the cost of additional sampling overhead. Gate-cutting provides one such approach by replacing nonlocal gates with quasiprobability decompositions of local operations. Starting from the known optimal two-qubit gate-cutting formula, we derive complete sharp lower and upper envelopes relating the quasiprobability extent $γ$ to five established descriptors: entangling power, gate typicality, operator entanglement, Schmidt strength, and maximum product-input concurrence. We recast $γ$ as a Rényi-$1/2$ functional of the operator-Schmidt spectrum and show how the physical constraints on two-qubit spectra sharpen generic entropy bounds and select a small set of recurring extremal Cartan families. None of the five descriptors generically determines $γ$ alone, but each imposes exact constraints, revealing how substantially the optimal gate-cutting cost can vary between gates with similar nonlocal characteristics.
