Codes and Homology in Topological Quantum Computing - Part 2

Learn about quantum codes and homology in this lecture from Microsoft Research scientist Jeongwan Haah, exploring the mathematical foundations of quantum error correction. Examine the surface code's significance in quantum computing, both for practical applications and its connection to topological phases of matter. Delve into key concepts including the limitations of local codes in one dimension, the relationship between code distance and system size in two dimensions, logical qubit constraints in d-dimensional local codes, and the equivalence of two-dimensional translation invariant codes to surface codes. Access accompanying lecture notes and problem sets to reinforce understanding of codes and homology in quantum error correction. Part of the 2023 IAS/PCMI Graduate Summer School program on Quantum Computation, this lecture contributes to a comprehensive exploration of near-term quantum computing mathematics and applications.