Realizing a Continuous Set of Two-Qubit Gates Parameterized by an Idle Time

Continuous gate sets are a key ingredient for near-term quantum algorithms. Here, we demonstrate a hardware-efficient, continuous set of controlled arbitrary-phase ($\mathrm{C}Z_θ$) gates acting on flux-tunable transmon qubits. This implementation is robust to control pulse distortions on time scales longer than the duration of the gate, making it suitable for deep quantum circuits. Our calibration procedure makes it possible to parameterize the continuous gate set with a single control parameter, the idle time between the two rectangular halves of the net-zero control pulse. For calibration and characterization, we develop a leakage measurement based on coherent amplification, and a new cycle design for cross-entropy benchmarking. We demonstrate gate errors of $0.7 \%$ and leakage of $4\times 10^{-4}$ across the entire gate set. This native gate set has the potential to reduce the depth and improve the performance of near-term quantum algorithms compared to decompositions into $\mathrm{C}Z_π$ gates and single-qubit gates. Moreover, we expect the calibration and benchmarking methods to find further possible applications.