Beijing Institute of Mathematical Sciences and Applications

Song Cheng , Da Wei Ding , Jin Peng Liu , Zheng Wei Liu , Ziwen Liu

Zheng Wei Liu

Friday, May 23, 2025 4:00 PM - 5:30 PM

Shuangqing-B627

Zoom 230 432 7880 (BIMSA)

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.

I am currently working on Quantum Fourier Analysis, Quantum Information and Subfactor Theory. I am also interested in category theory, harmonic analysis, knot theory, lower dimensional topology, operator algebras, representation theory in mathematics; and quantum field theory and condensed matter in physics. Website: https://ymsc.tsinghua.edu.cn/info/1031/2299.htm