发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出可从ZX图高效估计纠缠与魔力，通过流提取范式得到纠缠熵和对数稳定子范围的界，经基准测试适用于多量子比特等场景，建立了ZX演算与量子多体资源表征的桥梁。
AI 中文摘要
纠缠与非 stabilizerness（非稳定子性）是量子态复杂性的互补资源，但从大量量子电路中提取任一量通常需要指数级扩展的资源。在ZX演算（ZX-calculus）等量子计算的图解方法中，这两个量同样通常需要昂贵的张量收缩，而这并非图形重写的原生特性。本文中，我们证明可直接从ZX图高效估计纠缠与魔力（magic）。流（Flow）可高效提取一种范式，该范式将可能具有大量纠缠的图态主干与非克利福德（non-Clifford）泡利小工具分离。此结构给出了二分纠缠熵的加性上下界，我们通过移除或合并冗余非克利福德贡献的预处理步骤进一步收紧了这些界。同一范式给出了对数稳定子范围（logarithmic stabilizer extent）的上界。我们在随机幺正电路、受监控电路以及结合了Trotter化哈密顿量演化与克利福德层的电路中对这些方法进行了基准测试，发现即使在大量量子比特、电路深度和内部蜘蛛数的情况下，所得界仍具有参考价值。我们的结果为ZX图的纠缠与非稳定子性提供了可扩展的探测手段，并在ZX演算与量子多体资源表征之间建立了桥梁，可应用于量子计算、量子信息和凝聚态物理领域。
英文摘要
Entanglement and non-stabilizerness are complementary resources underlying the complexity of quantum states, yet extracting either quantity from large quantum circuits generally requires exponentially scaling resources. In diagrammatic approaches to quantum computation, such as the ZX-calculus, both quantities likewise typically require expensive tensor contractions that are not native to graphical rewriting. Here we show that both entanglement and magic can be efficiently estimated directly from ZX-diagrams. Flow enables efficient extraction of a normal form separating a potentially extensively entangled graph-state backbone from non-Clifford Pauli gadgets. This structure yields additive upper and lower bounds on bipartite entanglement entropy, which we further tighten through a preprocessing procedure that removes or merges redundant non-Clifford contributions. The same normal form gives an upper bound on logarithmic stabilizer extent. We benchmark these methods in random unitary and monitored circuits, and a circuit combining Trotterized Hamiltonian evolution with Clifford layers, finding that the resulting bounds remain informative even at large qubit numbers, circuit depths, and internal spider counts. Our results provide scalable probes of entanglement and non-stabilizerness of ZX-diagrams and establish a bridge between ZX-calculus and quantum many-body resource characterization, with applications across quantum computing, quantum information, and condensed-matter physics.
Comments6+6 pages, 3+2 figures
