Noise-induced leakage and counting errors in the electron pump

Computer simulations reveal that the lowest rates of leakage and counting errors observed in the electron pump can be explained by photon-assisted tunneling driven by $1/f$ noise. The noise power at microwave frequencies required to account for the observed errors is consistent with extrapolation of the low-frequency noise spectrum commonly recorded in single-electron transistors. Pump simulations, based on the ground-capacitance model, include cotunneling as well as single-junction photon-assisted tunneling. Quantitative agreement between theory and experiment is obtained for leakage and counting errors in pumps with four, five, six, and seven junctions in the limit of low temperatures and low counting rates. The effect of self-heating is explored.