Optimization of two-qubit gates in tunable-coupler architectures using single-flux-quantum control

We present a gradient-based method to construct high-fidelity, two-qubit quantum gates in a system consisting of two transmon qubits coupled via a tunable coupler. In particular, we focus on single-flux-quantum pulses as a promising and scalable alternative to traditional control schemes that use microwave electronics. We develop a continuous embedding scheme to optimize these discrete pulses, taking advantage of autodifferentiation of our model. This approach allows us to achieve fSim-type gates with average gate fidelities on the order of 99.99% and controlled-$Z$ and controlled-not gates with fidelities above 99.9%. Furthermore, we provide an alternative semianalytical construction of these gates via an exact decomposition using a pair of fSim gates, which leads to the reduction in memory required to store the associated pulse sequences.