Continuous quantum error correction

Quantum error correction is an essential ingredient for quantum computation. The standard descriptions of how to implement active error correction assume ideal resources such as projective measurements and instantaneous gate operations. Unfortunately in practice such resources are not realizable in most quantum computing architectures and it is not clear how such error correction implementations will perform under more realistic conditions. Motivated by this we examine schemes for implementing active error correction that use a more modest set of resources. This leads to new implementations of error correction that are continuous in time, and thus described by continuous dynamical maps. We evaluate the performance of such schemes using numerical simulations and comment on the applicability and effectiveness of continuous error correction for quantum computing.