nt - p h / 97 07 04 9 v 1 2 5 Ju l 1 99 7 Continuous error correction

We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error correcting code. In the limit of continuous error correction we introduce a Markovian master equation that includes the effects of: a) Hamiltonian evolution, b) errors caused by the interaction with an environment and c) error–correcting operations. The master equation is formally presented for all stabilizer codes and its solution is analyzed for the simplest such code.