Quantum error correction for continuously detected errors with any number of error channels per qubit

Abstract

It was shown by Ahn, Wiseman, and Milburn [PRA {\bf 67}, 052310 (2003)] that feedback control could be used as a quantum error correction process for errors induced by weak continuous measurement, given one perfectly measured error channel per qubit. Here we point out that this method can be easily extended to an arbitrary number of error channels per qubit. We show that the feedback protocols generated by our method encode $n-2$ logical qubits in $n$ physical qubits, thus requiring just one more physical qubit than in the previous case.