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We present an efficient approach to continuous-time quantum error correctionthat extends the low-dimensional quantum filtering methodology developed by vanHandel and Mabuchi [quant-ph/0511221 (2005)] to include error recoveryoperations in the form of real-time quantum feedback. We expect this paradigmto be useful for systems in which error recovery operations cannot be appliedinstantaneously. While we could not find an exact low-dimensional filter thatcombined both continuous syndrome measurement and a feedback Hamiltonianappropriate for error recovery, we developed an approximate reduced-dimensionalmodel to do so. Simulations of the five-qubit code subjected to the symmetricdepolarizing channel suggests that error correction based on our approximatefilter performs essentially identically to correction based on an exact quantumdynamical model.

Efficient feedback controllers for continuous-time quantum error correction