Analysis of Randomized Benchmarking with Realistic Noise

Recently, a leakage-detecting (“blind”) randomized benchmarking (RB) technique has been employed to characterize overall error and, via interleaving, errors for specific gates, in 6-dot arrays of silicon quantum dots operated as exchange-only qubits [Andrews et al., Nature Nano. 14, 747 (2019)].  Here, we analytically compute functional forms for these RB decays using the group Fourier transform convolutional analysis described in Merkel et al., arXiv:1804.05951. Our analysis includes gate-dependent errors caused by composite pulses and control and environmental noise, as well as leakage. The effects of both Markovian and non-Markovian noise are analyzed, with excellent agreement found between simulations and group Fourier transform theory. We find that, for exchange-only qubits at least, Markovian and non-Markovian noise-induced RB decays are qualitatively similar.