Hybrid control of uncertain quantum systems via fuzzy estimation and quantum reinforcement learning

A hybrid control approach for uncertain quantum systems is proposed using probabilistic fuzzy estimators (PFE) and quantum reinforcement learning (QRL). This hybrid control design involves coherent control with PFE and learning control via QRL. The problems of controlling a quantum system from an initial state to a pointed target state are studied in this paper, where we assume that the initial quantum state is a mixed state and the target quantum state is a controllable pure state within a wavefunction controllable subspace. First, the initial quantum system is controlled coherently with the help of a PFE. When the controlled system is estimated to be likely to collapse to an expected eigen state, trigger the measurement and the quantum system collapses to an eigen state in the wavefuntion controllable subspace with a high probability. Then the quantum system is driven to the target state with admissible controls, where the control sequence is learned and optimized with QRL. An example is presented and analyzed to demonstrate the control process.