Successive quantum feedback control with non-adaptive bare measurements collapses to the ten AZ† symmetry classes that dictate topology of CPTP maps, demonstrated via quantized winding numbers in a chiral demon and an explicit protocol outside the classes.
Optimal error tracking via quantum coding and continuous syndrome measurement
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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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Symmetry and Topology of Successive Quantum Feedback Control
Successive quantum feedback control with non-adaptive bare measurements collapses to the ten AZ† symmetry classes that dictate topology of CPTP maps, demonstrated via quantized winding numbers in a chiral demon and an explicit protocol outside the classes.