Characterizing quantum circuits by short-cutting quantum errors

Just like evaluating a piano doesn't involve playing all possible pieces of music, characterizing a computer doesn't involve running all possible circuits. Instead, people focus on benchmarking a restricted number of... [ view full abstract ]

Just like evaluating a piano doesn't involve playing all possible pieces of music, characterizing a computer doesn't involve running all possible circuits. Instead, people focus on benchmarking a restricted number of components and based on that information they attempt to make conclusions on the quality of more involved circuits. While such extrapolation step is trivial in the piano analogy, the complexity of quantum dynamics obfuscates the relationship between the quality of elementary components and the quality of larger circuits.

I will demonstrate how to drastically simplify the leap from component quality to circuit quality, which would presumptively necessitate the full generality of quantum dynamics. Of course, such a short-cut doesn't apply for tracking any operational characterization parameter, but will apply for important ones such as the so-called average gate fidelity and unitarity (I will provide a family of such easily-tractable figures of merit). 

The proposed dynamical simplification proves itself useful in many ways. Firstly, it enables a more accurate extrapolation of characterization parameters as circuits grow in depth and width, based on benchmarking results. Secondly, the same dynamical simplification allows to go in the opposite direction: the characterization of a circuit allows to infer some information about the quality of its individual components. Thirdly, short-cutting the inner-workings of quantum errors provides important insight on upcoming characterization protocols.