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Learn about a novel framework for fault-tolerant quantum error correction through this conference talk that introduces spacetime concatenation for compiling syndrome extraction circuits of stabilizer codes. Discover how this framework enables efficient compilation of syndrome extraction circuits into dynamical codes using structured gadget layouts and encoding matrices, while facilitating low-weight measurements and preserving logical quantum information. Explore the sufficient conditions for fault-tolerance in dynamical codes, including the critical requirements of not measuring logical operators and maintaining spacetime distance. Examine explicit constructions of dynamical codes within this framework, including detailed analysis of the dynamical bivariate bicycle code and dynamical Haah code, with demonstrations of their fault-tolerant properties. Investigate the classification and resource trade-offs inherent in dynamical codes, and understand their practical adaptability to real-world hardware constraints such as fabrication defects and qubit dropout scenarios, making this approach particularly relevant for near-term quantum computing implementations.
