Randomized benchmarking protocols in the all-electrical quantum dot qubit with 1/f noise

Abstract

Randomized benchmarking (RB) protocols represent an efficient tool to compare different qubit technologies and architectures. Despite traditional methods of characterizing gate fidelity that involve quantum process tomography, RB possesses some advantages in terms of the robustness against the state preparation and measurement (SPAM) errors, beyond the fact that it scales efficiently with the system size, requiring fewer resources. RB experiments have been performed in many different physical contexts for quantum technologies, ranging from superconducting qubits, trapped ions or semiconducting qubits, i.e. nitrogen-vacancy centers in diamond, quantum dots and donors (e.g. phosphorous) atoms in silicon. In this study, we simulated randomized benchmarking protocols in a semiconducting all-electrical three-electron double-quantum dot qubit, i.e. hybrid qubit, under different error models, that include quasi-static Gaussian and the more realistic 1/f noise model, for the input controls. The average error of specific quantum computational gates is extracted through interleaved randomized benchmarking obtained including Clifford gates between the gate of interest. Quantitative results are reported that on one hand allow to predict the fidelity when specific error parameters are included, on the other provide a complete picture of the hybrid qubit operations in view of realization of more complex circuits, such as quantum error correction circuits.