Robust hardware-efficient implementation of a continuous two-qubit gate set for transmon qubits

Hardware-efficient implementations of continuous gate sets, such as the set of two-qubit controlled-phase gates parameterized by the conditional phase, can improve the performance of noisy intermediate-scale quantum computing by reducing the circuit depth, for example in variational quantum algorithms and quantum machine learning. In a previous experimental demonstration [1], such a continuous gate set was implemented on superconducting transmon qubits, but relied on pulse shapes that are sensitive to distortions and required adjusting multiple control pulse parameters simultaneously. Here, we present an alternative implementation by extending the controlled-phase gate from [2], which is based on the resonant interaction between two flux-tunable transmons. In this implementation, an arbitrary conditional phase can be achieved by tuning a single pulse parameter, and the vanishing time integral of the employed net-zero control pulses [2] provides robustness against memory effects. Furthermore, by activating the gate via flux control of both qubits, we demonstrate that the gate can be performed between far-detuned qubits, strongly suppressing residual interactions. We characterize the continuous gate set with cross-entropy benchmarking for fixed values of the conditional phase and for phases randomly drawn from a uniform distribution, confirming a consistently high gate fidelity over the full range of phases.

[1] Lacroix et al., PRX Quantum 2020

[2] Negirneac et al., PRL 2021