Reliable characterization of super-accurate quantum operations
Takanori Sugiyama, Shinpei Imori, Fuyuhiko Tanaka · 2018
Improving accuracy of quantum operations is an indispensable task for realizing a practical quantum computer. A reliable method for characterizing quantum operations is a useful tool towards further improvements of the accuracy. Quantum tomography and randomized benchmarking protocols are current standard methods for evaluating accuracies of quantum operations, but their estimates lack reliability because of high sensitivity to state preparation and measurement (SPAM) errors or they use multiple approximations. Here we propose a self-consistent quantum tomographic method. First, we derive a sufficient condition on experiments for characterizing quantum operations except for the gauge degrees of freedom. Second, we propose a new self-consistent estimator. We mathematically prove that, when the sufficient condition is satisfied, the estimator provides estimates that are always physical and converge to the gauge-equivalence class of the quantum operations of interest at the limit of data size going to infinity. We also derive the rate of the asymptotic convergence. These results theoretically guarantee that the method makes it possible to reliably characterize accurate quantum operations.