Characterizing quantum circuits by short-cutting quantum errors and a unitary-dissipative ''polar'' decomposition for quantum channels

The richness of quantum dynamics allows for a plethora of noise models which, given only a partial knowledge of a device's components can result in widely different conclusions regarding the quality of larger circuits. In fact, the sole formulation of an assessment regarding the overall operational performance is demanding in that it typically requires invoking a broad range of quantum dynamical scenarios. In this work, we pave the way between partially characterized elementary operations and circuits thereof. Our paving stone consists of a simplified picture of quantum processes that we refer to as the leading Kraus (LK) approximation. This incomplete dynamical representation closely prescribes the evolution of celebrated characterization figures of merit, namely the average gate fidelity, which captures the overlap between an implemented operations and their targets, and the unitarity, which captures the level of coherence in the noise. Moreover, the transparency in the LK parametrization allows the derivation of a quantum unitary-dissipative (polar) factorization for quantum channels.