Abstract
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 time step is required, which can severely impact the simulation run time. Here, we introduce a semianalytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical integrators. This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulation's run time as well as its sensitivity to the time-step size. Furthermore, this solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations. As an illustration of our method, we show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
Highlights
High-fidelity logical gates are paramount to the realization of useful quantum computation
This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulation’s run time as well as its sensitivity to the time-step size. This solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations
We have demonstrated that the Dysolve algorithm provides a means to quickly and accurately simulate driven systems while accounting for all of the effects of the counterrotating and off-resonant terms
Summary
High-fidelity logical gates are paramount to the realization of useful quantum computation. When including the effects of the counter-rotating terms, there exists no simple derivative of time-ordered unitaries with respect to the drive amplitudes, and one must resort to approximating the gradients This approach may not converge to the optimal solution, which is problematic when targeting very high-fidelity gates. In this approach, which we call Dysolve, the time-ordered unitary evolution operator is written as a product of time-independent operators which are weighted by the drive amplitudes and dynamical phases This algorithm captures the full fast-oscillatory dynamics irrespective of the integration step size, thereby decreasing the complexity of the numerical problem. This greatly decreases the simulation time in comparison to traditional integration-based solvers without loss of numerical precision This approach trivializes the derivative with respect to the drive strength, which can be calculated to an accuracy equivalent to the order of the Dyson series. IV, and show as an example optimized two-qubit gates in the circuit QED architecture
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