Asymptotic error correction in Nature

Quantum error correction is fundamental for realizing a reliable large scale quantum computer. In addition to the quantum computing applications, it has been proven to be insightful for the kinematics of condensed matter and high energy theories, e.g., topological order and holography, respectively. In this talk, I will present recent results about how widespread quantum error correction is in general physical phenomena. We will see that chaotic systems, translation invariant local Hamiltonians, and certain one dimensional critical systems contain error correcting codes with various parameters in their energy spectrum. Furthermore, we will see how to construct error correcting codes out of the low energy subspace of one dimensional local gapped Hamiltonians. I will further mention questions about simulating dynamics of quantum field theories and remark how the techniques that we have developed for the kinematics are also useful for the dynamics. Basics of quantum error correction and various tensor network methods will be reviewed, hence no prior knowledge of these topics is necessary.