# 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.