Greedy versus map-based optimized adaptive algorithms for random-telegraph-noise mitigation by spectator qubits

In a scenario where data-storage qubits are kept in isolation as far possible, with minimal measurements and controls, noise mitigation can still be done using additional probes, corrections applied only when needed. Motivated by the case of solid-state qubits, we consider dephasing arising from two-state fluctuator, described random telegraph process, probe which is also qubit, so-called spectator qubit (SQ). We construct theoretical model assuming projective on SQ, derive performance different measurement control strategies regime works well. start Greedy algorithm; that is, strategy always maximizes data coherence immediate future. show numerically this algorithm very well, find its adaptive well approximated simpler just few parameters. Based this, an analytical construction Bayesian maps, design one-parameter ($\mathrm{\ensuremath{\Theta}}$) family algorithms. asymptotic high sensitivity analytically $\mathrm{\ensuremath{\Theta}}$ algorithms reduces decoherence rate divisor scaling square sensitivity. Setting equal to optimal value, ${\mathrm{\ensuremath{\Theta}}}^{?}$, yields Map-based Optimized Adaptive Algorithm for Asymptotic Regime (MOAAAR). show, numerically, MOAAAR outperforms algorithm, especially SQ.