标题： Quon经典模拟：统一 Clifford、匹配门和纠缠 显示英文标题

标题： Quon Classical Simulation: Unifying Clifford, Matchgates and Entanglement

摘要： 我们提出了一种统一的经典模拟量子电路的框架，称为Quon经典模拟（QCS），该框架基于Quon语言的图形式主义。 这一框架的核心是引入了魔法孔，这是一种拓扑特征，捕捉了模拟量子系统时计算难度的全局来源。 与传统度量不同，QCS的复杂性由这些魔法孔相关的拓扑纠缠熵所控制。 我们证明了Clifford电路和Matchgate电路没有魔法孔，因此在我们的模型中可以有效地模拟。 为了捕捉魔法孔的相互作用结构，我们定义了一种拓扑张量网络表示，并开发了新的纽结关系和约简算法来简化电路表示。 这种方法显著提高了经典模拟的效率，并为各种已知量子电路类的可处理性提供了统一的解释。 我们的工作为量子系统的经典可模拟性和拓扑复杂性提供了新的拓扑视角。 显示英文摘要

摘要： We propose a unified classical simulation framework for quantum circuits, termed Quon Classical Simulation (QCS), built upon the diagrammatic formalism of the Quon language. Central to this framework is the introduction of magic holes, a topological feature that captures the global source of computational hardness in simulating quantum systems. Unlike conventional measures, the complexity of QCS is governed by the topological entanglement entropy associated with these magic holes. We show that Clifford circuits and Matchgate circuits are free of magic holes and thus efficiently simulable within our model. To capture the interaction structure of magic holes, we define a topological tensor network representation and develop novel skein relations and reduction algorithms to simplify circuit representations. This approach significantly improves the efficiency of classical simulations and provides a unified explanation for the tractability of various known quantum circuit classes. Our work offers a new topological perspective on the classical simulability of quantum systems and topological complexity.