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Explore the intricate world of topological codes in this comprehensive lecture by Yale University's Meng Cheng, delivered at the Workshop on Quantum Information and Physics. Delve into the fundamental principles and advanced concepts of topological quantum error correction, examining their crucial role in quantum computing. Gain insights into the physical implementations, theoretical foundations, and practical applications of these robust error-correcting codes. Analyze the interplay between quantum information theory and condensed matter physics, and discover how topological codes leverage the unique properties of quantum systems to protect quantum information from decoherence and errors.