Uniform, rapidly convergent algorithm for quantum optimal control of objectives with a positive semidefinite Hessian matrix

Abstract

A uniform iteration method is presented for achieving quantum optimal control over any real objective with a positive semidefinite Hessian matrix. Theoretical analysis shows that this uniform algorithm exhibits quadratic and monotonic convergence. Numerical calculations verify that for this uniform algorithm, within a few steps, the optimized objective functional comes close to its converged limit. For some optimal control purposes, the objective itself is not required to be directly a physical observable, but it is only necessary that the objective have a suitable association with some desired physical observables. As an illustration of the algorithm, the control objective is chosen to achieve maximum population in a target state as well as minimum phase mismatch with the target state.