Decoherence and Efficiency of Quantum Error Correction

Quantum error correction is discussed for a quantum computer in contact with a decohering environment. It is argued that ancilla-based correction can be accomplished wholly by unitary operations. Under rather general assumptions upon the form of the computer-environment interaction, the encoded qubit state is shown to be stabilized against the decoherence for short times, the distortion terms of the computer density matrix being proportional to the fourth power of time