  We present an efficient approach to continuous-time quantum error correction
that extends the low-dimensional quantum filtering methodology developed by van
Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery
operations in the form of real-time quantum feedback. We expect this paradigm
to be useful for systems in which error recovery operations cannot be applied
instantaneously. While we could not find an exact low-dimensional filter that
combined both continuous syndrome measurement and a feedback Hamiltonian
appropriate for error recovery, we developed an approximate reduced-dimensional
model to do so. Simulations of the five-qubit code subjected to the symmetric
depolarizing channel suggests that error correction based on our approximate
filter performs essentially identically to correction based on an exact quantum
dynamical model.
