Title: Topological Complexity for Quantum Information

Abstract: The distinction between “quantum” and “classical” is a main theme in quantum information. Whether a quantum circuit can be classically simulated in polynomial time, and in general, whether the partition function of a lattice model or a tensor network can be computed efficiently? In this talk, we introduce a topological complexity for quantum information using the quon language. We show that two well-known efficiently classically simulable families, Clifford circuits and matchgate circuits, correspond to two kinds of topological complexities. Beyond the two, we introduce a new method to design efficiently classically simulable families. As an application, we construct new families of exactly solvable modes.

Talk – Video

Talk – Slides