  Spectator qubits (SQs) are a tool to mitigate noise in hard-to-access data
qubits. The SQ, designed to be much more sensitive to the noise, is measured
frequently, and the accumulated results used rarely to correct the data qubits.
For the hardware-relevant example of dephasing from random telegraph noise, we
introduce a Bayesian method employing complex linear maps which leads to a
plausibly optimal adaptive measurement and control protocol. The suppression of
the decoherence rate is quadratic in the SQ sensitivity, establishing that the
SQ paradigm works arbitrarily well in the right regime.
