Compiling arbitrary single-qubit gates via the phase shifts of microwave pulses

Abstract

We give an arbitrary single-qubit gate compilation scheme on superconducting processors that takes advantage of tuning the phase shift of microwave pulses to obtain a continuous gate set. This scheme is compatible with any two-qubit gate, and we only need to calibrate the X_{π} and X_{π/2} pulses. We report an experimental implementation on a fluxonium device in [Phys. Rev. Lett. 130, 070601 (2023)10.1103/PhysRevLett.130.070601] and obtain state-of-the-art fidelities. We give two other schemes: the first requires one X_{π} pulse and one pulse with a variable rotation angle, and the second requires four X_{π/2} pulses. We also find that if we can do virtual Z gates, then we can also do virtual gates around any axis. Our results apply to any physical platform that natively supports virtual Z.