Characterization of leakage errors in a transmon qubit due to resonant digital control

We present experimental measurements and analysis of leakage errors occurring during resonant digital control of a superconducting qubit. By increasing the amplitude of the digital pulse trains and therefore decreasing the duration of the control gates, from 100 to 40 ns for a π-gate, the leakage error rate measured per Clifford gate in a randomized benchmarking test increases from 4.3×10−4 to 2.4×10−3 and becomes the dominant source of single-qubit gate errors for our qubit; these error rates are 1–2 orders of magnitude larger than we measure when controlling the same qubit using traditional, shaped-analog signals. Simulations show the dominant leakage mechanism arises from the increased spectral power of the pulse trains at the frequency ω12 corresponding to excitations from the first excited state |1⟩ to the second excited state |2⟩. Our measurements demonstrate the fundamental limits to resonant digital control of low-anharmonicity qubits and outline the trade-off between reducing gate times while preserving gate fidelity. We discuss possible strategies for mitigating this issue in future digital control implementations.