Single-Qubit Gates Beyond the Rotating-Wave Approximation for Strongly Anharmonic Low-Frequency Qubits

Single qubit gates are in many quantum platforms applied using a linear drive resonant with the qubit transition frequency which is often theoretically described within the rotating-wave approximation (RWA). However, for fast gates on low-frequency qubits, the RWA may not hold and we need to include the counter-rotating terms in the Hamiltonian. This gives rise to two challenges. In this situation, it becomes challenging to analytically calculate the time evolution, as the Hamiltonian is no longer self-commuting. Moreover, the time evolution now depends on the carrier phase such that, in general, every operation in a sequence of gates is different. In this work, we analytically calculate and numerically verify a correction to the drive pulses that minimizes the effect of these counter-rotating terms in a two-level system. We extend this analysis to a superconducting fluxonium qubit, which is an example of a strongly anharmonic, low-frequency qubit for which the RWA may not hold, and demonstrate both numerically and experimentally how fast, high-fidelity single-qubit gates can be achieved.