Using spectator qubit to Optimally mitigating qubit decoherence

To reduce or mitigate the decoherence caused by environmental noise on quantum systems, one first need to characterize the noise. This is the goal of "quantum noise spectroscopy" (QNS). QNS provide information about correlation functions which are average quantities over many noise realisations. Here we go one step further; equipped with the knowledge from QNS, we would like to track the effect of single noise realization. To do that, we introduce a spectator qubit which senses the same noise and we use it to monitor the noise and predict the evolution of the logical qubit.

In this project, we consider decoherence effect caused by a random telegraph process (RTP). Two question arises; (1) How often and (2) What measurement basis we should use? Note that the second question is not necessary independent of the the first one. Also, a sequence of measurements on the spectator qubit is adaptive, meaning that the basis for later measurements depends on the results of the earlier measurements. Furthermore the quantity to be estimated is the cumulative phase acquired by the target qubit, proportional to the integral of the RTP. Despite these complications, we identify a measurement strategy for the spectator qubit to optimally mitigate the decoherence in the target qubit.