Abstract: Quantum memristor is a quantum device that accounts for the memory, with the decoherence mechanism controlled by a feedback algorithm . Last year, a variety of prototypes for quantum memristors has been proposed: superconducting circuits and platforms, different realizations of Josephson junctions, photonic systems . Nevertheless, still there is a lack of theoretical methods modeling efficient exploitation of such devices. A new statistical physics technique based on Artificial Neural Networks (ANNs) has been developed recently in . Such ANNs are well–trained with the data collected from the ’Ab Initio’ experiment or numerical simulations to mimic the microscopic statistical states, and then to extrapolate the results for evaluation macroscopic states of the quantum system, its phase structures, and thermodynamic characteristics. Here we study a novel procedure based on the small–scale networks of Hodgkin-Huxley neurons  to model statistical micro-states and to control over dynamical characteristics (particularly, the reflectivity and the purity) of photonic quantum memristor . We compare the pros and cons of a few alternative control algorithms: Fradkov’s speed gradient  and Kolesnikov’s target attractor feedback . We discuss also possible applications of our approach to memristor-based reservoir computing.
Keywords: Artificial Neural Networks, Quantum Dynamical Systems, Feedback Control.