Optimization of High-Fidelity Single-Qubit Gates for Fluxoniums Using Single-Flux Quantum Control

We present a gradient-based method to construct memory-efficient, high-fidelity, single-qubit gates for fluxonium qubits. These gates are constructed using a sequence of single-flux quantum (SFQ) pulses that are sent to the qubit through either capacitive or inductive coupling. The schedule of SFQ pulses is constructed with an on-ramp and an off-ramp applied prior to and after a pulse train, where the pulses are spaced at intervals equal to the qubit period. We reduce the optimization problem to the scheduling of a fixed number of SFQ pulses in the on-ramp and solve it by relaxing the discretization constraint of the SFQ clock as an intermediate step, allowing the use of the Broyden-Fletcher-Goldfarb-Shanno optimizer. Using this approach, gate fidelities of 99.99 % can be achieved for inductive coupling and 99.9 % for capacitive coupling, with leakage being the main source of coherent errors for both approaches.