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

Presenting Author: Arnaud Carignan-Dugas, University of Waterloo
Contributing Author(s): Matthew Alexander, Joseph Emerson

When characterizing a quantum computer, the jump from a characterization of elementary operations to a quantified assertion on the overall device performance is quite involved; errors can coherently interfere and propagate through the entire device via multi-qubit operations. The richness of quantum dynamics allows for a plethora of noise models which, given only a partial knowledge of the device's components, can result in widely different conclusions regarding the quality of larger circuits. In fact, the sole formulation of a conclusion 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. The simplicity of the LK approximation clarifies the path that follows those quantities as elementary components aggregate into larger circuits. Moreover, the same transparency in the LK parametrization allows the derivation of a quantum unitary-incoherent (polar) factorization for quantum channels.

(Session 5 : Sunday from 5:00pm - 7:00pm)


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