Quantum error correction: a window to complex quantum states and dynamics

Quantum error correction was invented as a graceful answer to how quantum computing would be feasible despite continuous noises from environment. It was soon realized that gauge theories had been a quantum error correcting code in disguise. This perspective has influenced designs of quantum fault-tolerant protocols. On the other hand, the language of quantum error correction has transformed how we learn many-body physics, especially in the subject of topological phases. In this talk, I will review elements of this ongoing cross-fertilization, including emergence of topological field theories in 2+1d, fracton physics in 3+1d, and Floquet dynamics and codes.