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Learn about operator algebra and computational algorithms for analyzing topological Pauli stabilizer codes in a 55-minute lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar. Explore how these codes form the foundation for studying topological phases of matter and designing quantum codes for fault-tolerant quantum computation. Discover algorithms for extracting topological data including anyon types, fusion rules, topological spins, and braiding statistics. Master methods for constructing gapped boundaries and defects through boundary anyon condensation, utilizing matrix operations like Hermite and Smith normal forms for efficient analysis of surface codes. Examine practical examples including toric codes, color codes, and bivariate bicycle codes to understand bulk and boundary topological properties of quantum codes. Delivered by Yu-An Chen, Assistant Professor at Peking University's Quantum Materials Science Center, this talk draws from his extensive research experience at MIT, Caltech, Google's Quantum AI team, and the University of Maryland.
