Fast and differentiable simulation of driven quantum systems

The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very small integration step is required, which can severely impact simulation run time. Here, we introduce semianalytic method based Dyson expansion allows us time-evolve driven much faster than standard integrators. This solver, name Dysolve, efficiently captures effect of highly oscillatory terms system Hamiltonian, significantly reducing simulation's as well its sensitivity time-step size. Furthermore, this solver provides exact derivative time-evolution operator with respect drive amplitudes. key feature for optimal control limit strong drives and goes beyond common pulse-optimization approaches rely rotating-wave approximations. As an illustration our method, show results optimization two-qubit gate using transmon qubits circuit QED architecture.