We revisit a scenario of continuous quantum error detection proposed by Ahn, Doherty and Landahl [Phys. Rev. A 65, 042301 (2002)] and construct optimal filters for tracking accumulative errors. These filters turn out to be of a canonical form from hybrid control theory; we numerically assess their performance for the bit-flip and five-qubit codes. We show that a tight upper bound on the stochastic decay of encoded fidelity can be computed from the measurement records. Our results provide an informative case study in decoherence suppression with finite-strength measurement.
@article{arxiv.quant-ph/0511221,
title = {Optimal error tracking via quantum coding and continuous syndrome measurement},
author = {Ramon van Handel and Hideo Mabuchi},
journal= {arXiv preprint arXiv:quant-ph/0511221},
year = {2007}
}