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Explore a comprehensive lecture on transversal gates and topological aspects of quantum codes in this advanced graduate-level presentation from the 2023 PCMI Quantum Computation program. Delve into the significance of surface code in quantum computing, examining its practical applications and connections to topological phases of matter. Learn about the limitations of local codes in one dimension, understand how two-dimensional local codes achieve linear code distance, discover the relationship between logical qubits and system dimensions, and explore how two-dimensional translation invariant codes relate to surface codes. Conclude with an examination of triorthogonal codes and their application in magic state distillation. Accompanied by detailed lecture notes and problem sessions, gain hands-on experience through structured exercises designed to reinforce understanding of these complex quantum computing concepts.
