Robust Lindbladian Tomography for Cyclic Quantum Gates

Abstract: Precise characterization of noisy quantum operations plays an important role for realizing further accurate operations. Quantum tomography is a popular class of characterization methods, and several advanced methods in the class use error amplification circuit (EAC), a repetition of a sequence of quantum gates, for increasing their estimation precision. Here, we develop new theoretical tools for analyzing effects of an EAC on Lindbladian error of cyclic gates in the EAC for arbitrary finite-dimensional system, which takes non-commutativity between different gates or between ideal and error parts of a gate, periodic properties of ideal gates, and repetition of gate sequence into consideration within a linear approximation. We also propose a tomographic protocol for the Lindbladian errors of cyclic gates based on the linear approximation, named Robust Lindbladian Tomography (RLT). The numerical optimization at data-processing of the proposed method reduces from nonlinear to linear (positive semi-definite) programming. Therefore, compared to the original optimization problem, the reduced one is solvable more efficiently and stably, although its numerical cost grows exponentially with respect to the number of qubits, which is the same as other tomographic methods.