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Optimal error tracking via quantum coding and continuous syndrome measurement

Ramon van Handel·Hideo Mabuchi
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Abstract

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.

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Ramon van Handel, Hideo Mabuchi. 2005-11-22. Optimal error tracking via quantum coding and continuous syndrome measurement. https://arxiv.org/abs/quant-ph/0511221

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