Self-consistent quantum tomography for characterizing super-accurate quantum operations

Increasing number of qubits and improving accuracy of quantum operations are indispensable tasks for realizing a practical quantum computer. A reliable method for characterizing quantum operations is a useful tool toward further improvements of the accuracy. Randomized benchmarking protocols are current standard methods, but they can estimate only a few parameters of errors on gates and cannot characterize accuracies of state preparations and measurements. Gate set tomography is an alternative candidate and can fully characterize all of state preparations, gates, and measurements. However the SPAM-error-freeness are not compatible with the physicality of estimates, and it can handle a limited number of gates. Here we propose a new tomographic method. We mathematically prove that our method provides estimates satisfying both of the SPAM-error-freeness and physicality. Additionally the method can handle flexible numbers of quantum operations.