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Explore the evolution of quantum information under Pauli measurement circuits in this comprehensive lecture. Delve into the concept of "local reversibility" in measurement circuits and its implications for preserving and localizing quantum information. Discover how measurement circuits can exhibit more diverse behaviors compared to unitary counterparts, including the ability of finite depth circuits to implement one-dimensional translation. Examine the introduction of "measurement quantum cellular automata" and its unifying role in these concepts. Investigate the Z_2 bulk invariant for two-dimensional Floquet topological codes and its significance in indicating obstructions to trivial boundaries. Learn about the Hastings-Haah honeycomb code and its classification within a group exhibiting such obstructions, leading to implications for boundary dynamics, period doubling, or anomalous quantum information flow.
