The challenge to all quantum information processing is isolation from the environment and effects of imperfect isolation, i.e. decoherence and errors. Quantum error correction allows a general strategy for overcoming these effects, while also providing rich connections to quantum information science and the many-body physics of open quantum systems. Some topics of interest include noisy, random and monitored quantum circuits, quantum coding theory, theory of fault-tolerance thresholds and protocols, and statistical mechanics mappings for quantum error correction. Research is also done in collaboration with experimental groups at NIST and University of Maryland.