Quantum Gate Dynamics Beyond the Rotating-Wave Approximation using Multi-Timescale Quantum Averaging Theory

We present a quantum averaging theory (QAT) for analytically modeling unitary gate dynamics in driven quantum systems beyond the rotating-wave approximation. QAT addresses the simultaneous presence of distinct timescales by generating a rotating frame with a dynamical phase operator that toggles with the high-frequency dynamics and yields an effective Hamiltonian for the slow degree of freedom. By accounting for the fast-varying effects, we demonstrate that high-fidelity two-qubit gates in strongly driven systems are achievable by going beyond the validity of first-order approximations. The QAT results rapidly converge with numerical calculations of a fast-entangling M{\o}lmer-S{\o}rensen trapped-ion-qubit gate in the strong coupling regime, illustrating QAT's ability to simultaneously provide both an intuitive, effective-Hamiltonian model and high accuracy.