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We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution, or more generally, any unital trace-preserving evolution.
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In full generality, p p corresponds to an eigenvalue of the map resulting from randomizing ℰ {\mathcal{E}} by conjugation with elements of either the full unitary group or the Clifford group King and Ruskai 2001 ; Rahn et al. 2002 ; Emerson et al. 2007 ; Silva et al. 2008 . The eigenvalue interpretation can be used to more clearly see how independence of the estimate from the initial and final states comes about, and it can also be more naturally generalized to cases where the randomizing operations are elements of the Pauli group Silva et al. 2008 . Randomization over more general operations can also be considered Bartlett et al. 2007
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