A reduced complexity min-plus method for synchronisation of qubits

Abstract

Solutions to optimal control problems can be obtained via grid-based dynamic programming iterations. However, such an approach is prohibitively expensive for problems with higher state dimensions, due to the exponential increase in grid points required in approximating the state space. This issue is especially severe in quantum systems whose dimensions grow exponentially with the number of interacting subsystems therein. In this paper, we study state synchronisation of two coupled qubits as an optimal control problem by tuning the interaction Hamiltonian of the system, whose dynamic programming equation is solved via a min-plus curse-of-dimensionality-free method. An illustration in the cont..