  A reliable method for characterizing quantum operations that is suitable for
improving and validating their accuracies is indispensable for realizing a
practical quantum computer. Known methods are still not sufficient because they
lack reliability or are not suitable for use in the improvement and validation
steps. Here we propose a reliable characterization method that is suitable for
the accuracy validation step. First, we introduce a new self-consistent
estimator with regularization and physicality constraints that are designed for
improvement and validation. Second, we mathematically prove that the method
provides estimation results that are stringently physical and converge to the
gauge-equivalence class of the quantum operations of interest at the limit of
data size going to infinity. The asymptotic convergence guarantees the
reliability of the method, and the physical and regularized results ensure the
suitability to the validation task. We also derive the asymptotic convergence
rate, which would be optimal. Finally, we show numerical results on 1-qubit
system, which confirm the theoretical results and prove that the method
proposed is practical.
