标题： 量子经典模拟：统一克利福德、匹配门和纠缠 显示英文标题

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

摘要： 我们提出了一种新的拓扑复杂性框架，用于研究量子电路和张量网络的计算复杂性。 在此框架中，我们建立了混合Clifford-Matchgate电路的Quon经典模拟（QCS），这对于Clifford电路和Matchgate电路都是高效的，因此回答了一个长期存在的关于统一高效经典模拟的开放问题。 该框架建立在Quon语言之上，这是一种具有时空边界和缺陷的2+1D拓扑量子场论。 其指数级计算复杂性由Magic holes捕捉，Magic holes是一种捕捉全局长程纠缠的拓扑特征。 Clifford电路和Matchgate电路都没有Magic holes。 Cliffords和Matchgates的高效经典模拟通过两种并行操作实现，分别是3-流形的广义手术理论和二维边界上的Yang-Baxter关系，同时还具有额外的二进制算术性质。 显示英文摘要

摘要： We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate circuits, which is efficient for both Clifford circuits and Matchgate circuits, therefore answering a long standing open question on unifying efficient classical simulations. This framework is built upon the Quon language, a 2+1D topological quantum field theory with space-time boundary and defects. Its exponential computation complexity is captured by Magic holes, a topological feature capturing the global long-range entanglement. Both Clifford circuits and Matchgate circuits are free of Magic holes. Efficient classical simulations of Cliffords and Matchgates are implemented by two parallel operations, generalized surgery theory of 3-manifolds and Yang-Baxter relations on the 2D boundary respectively, with additional binary arithmetic properties.