Characterization of Control in a Superconducting Qutrit Using Randomized Benchmarking

We present experimental results on the characterization of control fidelity for a qutrit implemented in the lowest three levels of a capacitively shunted flux-biased superconducting circuit. Using randomized benchmarking, we measure an average fidelity over the elements of the qutrit Clifford group of 99.0 $\pm$ 0.2%. In addition, for a selected subset of the Clifford group, we characterize the fidelity using quantum process tomography, and by observing the periodic behaviour of repeated gate sequences. We use a general method for implementation of qutrit gates, that can be used to generate any unitaries based on two-state rotations. The detailed analysis of the results indicates that errors are dominated by ac-Stark and Bloch-Siegert shifts. This work demonstrates the ability for high-fidelity control of qutrits and outlines interesting avenues for future work on optimal control of single and multiple superconducting qudits.