Real Randomized Benchmarking. (arXiv:1801.06121v1 [quant-ph])

Randomized benchmarking provides a tool for obtaining precise quantitative
estimates of the average error rate of a physical quantum channel. Here we
define real randomized benchmarking, which enables a separate determination of
the average error rate in the real and complex parts of the channel. This
provides more fine-grained information about average error rates with
approximately the same cost as the standard protocol. The protocol requires
only averaging over the real Clifford group, a subgroup of the full Clifford
group, and makes use of the fact that it forms an orthogonal 2-design. Our
results are therefore especially useful when considering quantum computations
on rebits (or real encodings of complex computations), in which case the real
Clifford group now plays the role of the complex Clifford group when studying
stabilizer circuits.

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