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

In this work, we present a gradient-based method for constructing memory-efficient, high-fidelity single-qubit gates for a fluxonium qubit using the single-flux quantum (SFQ) control scheme. This type of control is a promising and scalable alternative to traditional microwave control schemes, with respect to which a number of challenges are foreseen when scaling up the number of physical qubits, such as heat dissipation, connectivity logistics, and physical space for the wires and the control and readout devices.

These SFQ gates are constructed using a sequence of SFQ pulses that are sent to a qubit through either capacitive or inductive coupling. The schedule of SFQ pulses incorporates both an on-ramp and an off-ramp applied prior to and after a pulse train, respectively, where the pulses are spaced at intervals equal to the qubit’s 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 BFGS optimizer. We show that using this approach, gate fidelities of 99.99% are achieved for inductive coupling and 99.9% for capacitive coupling, with leakage being the main source of coherent errors in both approaches.