Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow calculations of the transform by matrix diagonalization. A particular set of such kernels, namely the wavelets, is tested in a model study.
Optimal control techniques provide a means to tailor the control pulse sequence necessary for the generation of customized quantum gates, which help enhancing the resilience of quantum simulations to gate errors and device noise. However, the substantial amount of (classical) computing required for the generation of customized gates can quickly spoil the effectiveness of such an approach, especially when the pulse optimization needs to be iterated. We report the results of device-level quantum simulations of the unitary (real) time evolution of the hydrogen atom, based on superconducting qubit, and propose a method to reduce the computing time required for the generation of the control pulses. We use a simple interpolation scheme to accurately reconstruct the real time-propagator for a given time step starting from pulses obtained for a discrete set of pre-determined time intervals. We also explore an analogous treatment for the case in which the hydrogen atom Hamiltonian is parameterized by the mass of the electron. In both cases we obtain a reconstruction with very high fidelity and a substantial reduction of the computational effort.
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