Quon Classical Simulation: Unifying Clifford, Matchgates and Entanglement
演讲者
时间
2025年05月23日 16:00 至 17:30
地点
Shuangqing-B627
线上
Zoom 230 432 7880
(BIMSA)
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.
演讲者介绍
研究领域：数学，数学物理和量子信息，特别是子因子理论和量子傅立叶分析，及其与算子代数、纽结理论、低维拓扑、量子群表示论、傅里叶分析、范畴学、量子信息、量子场论等领域的联系。