A sequential quadratic Hamiltonian scheme for solving non-smooth quantum control problems with sparsity

Abstract

A sequential quadratic Hamiltonian (SQH) scheme is investigated for solving non-smooth quantum optimal control problems with control costs that promote sparsity. Quantum control problems are a representative class of bilinear control problems that are central in application in nanosciences, and in this context the use of sparsity promoting functionals are desirable to facilitate the implementation of optimal controls in the laboratory.In this framework, it is shown that the SQH scheme provides many advantages with respect to other state-of-the-art methods, since it allows to also consider non-convex and discontinuous costs, without the need of regularization techniques. A theoretical discussion and results of numerical experiments are presented that demonstrate the effectiveness of the SQH scheme in solving control problems governed by a quantum spin system.