Control Optimization for Parametric Hamiltonians by Pulse Reconstruction

The standard quantum computing approach, based on expressing arbitrary unitary operations in terms of a set of universal quantum gates, has been demonstrated to be in principle efficient for the simulation of complex systems on a quantum computer. In practice, the performance and reliability of the generated real-time evolution suffer from gate error rates and quantum device noise. Optimal control techniques provide a means to tailor the control pulse sequence necessary for the generation of customized quantum gates, which help to reduce gate errors and device noise since it eliminates the need to split an arbitrary gate into its primitive constituents, obtaining a shallower quantum circuit. 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.