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Explore the intersection of algebraic topology and quantum error correction in this 36-minute conference talk examining sheaf codes and their applications to quantum LDPC codes. Learn how cup products from algebraic topology provide a framework for constructing quantum error-correcting codes with transversal non-Clifford gates, addressing a fundamental challenge in fault-tolerant quantum computation. Discover the mathematical foundations connecting sheaf theory to coding theory, and understand how these theoretical tools enable the construction of quantum codes that can implement logical operations beyond the Clifford group while maintaining their error-correcting properties. Gain insights into the latest developments in quantum LDPC codes and their potential for scalable quantum computing architectures, presented as part of the ICTS Workshop on High Dimensional Expanders and Codes.
