Single-qubit gates beyond the rotating-wave approximation for strongly anharmonic low-frequency qubits

Abstract

In many quantum platforms, single-qubit gates are 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 consider the contribution from counterrotating terms to the qubit dynamics. The inclusion of counterrotating terms into the theoretical description gives rise to two challenges. First, 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 derive and verify a correction to the drive pulses that minimizes the effect of these counterrotating terms in a two-level system. We then derive a second correction term that arises from noncomputational levels for a strongly anharmonic system. We experimentally implement these correction terms on a fluxonium superconducting qubit, which is an example of a strongly anharmonic, low-frequency qubit for which the RWA may not hold, and demonstrate how fast, high-fidelity single-qubit gates can be achieved without the need for additional hardware and calibration complexities.