Control Design of Uncertain Quantum Systems With Fuzzy Estimators

An approach of control design using fuzzy estimators (FEs) is proposed for quantum systems with uncertainties. Two types of quantum control problems are considered: 1) control of a pure-state quantum system in the presence of uncertainties and 2) control design of quantum systems with initial mixed states and uncertainties. For the first type of tasks, a partial feedback control scheme with an FE is presented to design controllers. In this scheme, an FE is trained to estimate the quantum state for feedback control of a quantum system, and controlled projective measurement is used to assist in controlling the system. For the second type of quantum control tasks, a probabilistic fuzzy estimator (PFE) is trained to estimate the quantum state for control design of a quantum system with an initial mixed state, and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state. Two examples of two-spin-¹/₂ systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach.