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

TL;DR

This paper addresses scalable, high-fidelity single-qubit control for fluxonium qubits using SFQ pulses. The authors develop a gradient-based ramp-optimized pulse-schedule method, combining on-ramp/off-ramp timing with a relaxed-clock optimization and BFGS, followed by clock snapping, and apply it to both inductive and capacitive couplings. They demonstrate gate fidelities of approximately 99.99% (inductive) and 99.9% (capacitive) with a 128× SFQ clock, with leakage as the main coherent error and ramps significantly reducing both coherent and incoherent errors. The results suggest SFQ-based control as a scalable alternative to traditional microwave control for fault-tolerant quantum computing, and point to future work on stability analyses and two-qubit extensions.

Abstract

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.

Figures (5)

• Figure 1: Circuit diagram of a fluxonium (shown in green) either inductively coupled to the SFQ generator (orange) or capacitively coupled to the SFQ generator (grey).
• Figure 2: Schematic representation of an SFQ pulse schedule with a ramp length of three qubit periods, two pulses within each ramp, and a pulse train comprising 10 pulses.
• Figure 3: Best infidelity obtained as a function of the kick angle with a relaxed SFQ clock constraint (i.e., optimized with respect to continuous variables for SFQ kick arrival times) and for different SFQ clock frequencies in the case of (a) inductive coupling and (b) capacitive coupling. For each kick angle, the pulse schedule is optimized for ramps of $R=1,2, \ldots, 5$ qubit periods in length, for $N=1, 2, \ldots, 6$ pulses, and for a target rotation angle of $\theta_\mathrm{targ}=\pi$.
• Figure 4: Best infidelity obtained as a function of the target rotation angle with a relaxed SFQ clock constraint (i.e., optimized with respect to continuous variables for SFQ kick arrival times) and for different SFQ clock frequencies in the case of (a) inductive coupling with a kick angle of $\theta_\mathrm{L} = 0.15$ radians per kick and (b) capacitive coupling with a kick angle of $\theta_\mathrm{C} = 0.03$ radians per kick. For each target angle, the SFQ ramp is optimized for ramps of $R=1, 2, \ldots, 5$ qubit periods in length, for $N=1, 2, \ldots, 6$ pulses.
• Figure 5: Error budget as a function of the target rotation angle $\theta_\mathrm{targ}$ for an SFQ clock at 128$\times$ the qubit frequency. (a)--(c) Results in the case of inductive coupling with a kick angle of $\theta_\mathrm{L} = 0.15$ radians per kick and (d)--(f) in the case of capacitive coupling with a kick angle of $\theta_\mathrm{C} = 0.03$ radians per kick. The left column ((a) and (d)) shows the error budget for a pulse train without ramps, the middle column ((b) and (e)) for a fixed ramp length of $R=1$, and the right column ((c) and (f)) for a fixed ramp length of $R=5$. The open-system infidelity (show in black) for the implementation without ramps cannot be seen because it falls under the closed-system infidelity (blue).