Reliable characterization for improving and validating accurate elementary quantum operations*

A reliable method for characterizing elementary quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Current standard methods, e.g., randomized benchmarking, quantum tomography, and gate-set tomography, are not sufficient because they lack reliability or are not suitable for the improvement and validation. A new characterization method, called regularized self-consistent quantum tomography (RSCQT), is an attractive alternative and has superior properties such as (i) the high reliability guaranteed by the asymptotic convergence of predicted probability distributions to the true probability distributions, (ii) applicability of the estimates to conventional validation protocols, and (iii) availability of detailed information of errors on the operations. Here we derive the asymptotic convergence rate, which would be optimal, and show numerical results on 1-qubit system, which confirm the theoretical results and prove that RSCQT is useful in practice.