Semi-Analytic Method for Rapid Simulation and Optimization of Driven Quantum Systems

The controls that are used to enact logical operations on qubits and cavities in circuit QED are described by time-dependent Hamiltonians that often include rapid oscillations. In order to fully capture these fast time dynamics in numerical calculations, a very small integration time step is required. In practice, this can be performance intensive impacting the simulation time and memory requirements. In this work, we present a semi-analytic method based on a Dyson expansion for arbitrary time-dependent quantum systems with a diagonal circuit Hamiltonian. This method captures the entire dynamics of the highly oscillatory terms of the Hamiltonian, reducing sensitivity to the chosen step size and providing significant performance improvements over current numerical integrators. This approach also returns the analytic derivative with respect to the drive strength amplitudes, which allows for rapid optimization with routines such as GRAPE to return high fidelity gates.