Gaussian Decomposition of Magic States for Matchgate Computation

Watch a 26-minute conference talk from the 19th Theory of Quantum Computation, Communication and Cryptography Conference (TQC 2024) exploring the decomposition of magic states in matchgate computation. Delve into groundbreaking research that extends classical simulation methods to Matchgate circuits (MGCs) through an explicit characterization of Gaussian states. Learn about the novel concept of Gaussian rank and its crucial role in determining simulation runtimes for matchgate circuits with magic state inputs. Discover findings on the Gaussian rank of canonical magic states under symmetry-restricted decompositions, numerical analysis results on multi-copy decompositions, and important theorems regarding Gaussian extent's multiplicative behavior in 4-qubit systems. Presented by researchers Joshua Cudby and Sergii Strelchuk at OIST, Japan, this talk advances theoretical quantum information science by addressing fundamental questions about classical simulation capabilities and resource theories in quantum computation.