Characterization of Control in a Superconducting Qutrit Using Randomized Benchmarking

We characterize control of a qutrit implemented in the lowest three energy levels of a capacitively-shunted flux-biased superconducting circuit. Randomized benchmarking over the qutrit Clifford group yields an average fidelity of 98.89 $\pm$ 0.05%. For a selected subset of the Clifford group, we perform quantum process tomography and observe the behaviour of repeated gate sequences. Each qutrit gate is generated using only two-state rotations via a method applicable to any unitary. We find that errors are due to decoherence primarily and have a significant contribution from level shifts. This work demonstrates high-fidelity qutrit control and outlines avenues for future work on optimal control of superconducting qudits.
Comment: 5 + 7 pages, 4 + 3 figures; v2 has an improved gate decomposition and experimentally measured population data