We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances in classical communication. The particular example shown here uses the stabilizer formalism. We provide an explicit encoding circuit and its associated error estimation algorithm. The latter gives the most likely error over any memoryless quantum channel, with a complexity growing only linearly with the number of encoded qubits.

• Received 29 April 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.177902