Quantum memristor is a quantum device that accounts for the memory, with the decoherence mechanism controlled by a feedback algorithm [1]. Last year, a variety of prototypes for quantum memristors has been proposed: superconducting circuits and platforms, different realizations of Josephson junctions, photonic systems [2]. 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 [3]. 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 [4] to model statistical micro–states and to control over dynamical characteristics (particularly, the reflectivity and the purity) of photonic quantum memristor [2]. We compare the pros and cons of a few alternative control algorithms: Fradkov’s speed gradient [5] and Kolesnikov’s target attractor feedback [6]. We discuss also possible applications of our approach to memristor–based reservoir computing.
Quantum computer technology harnesses the features of quantum physics for revolutionizing information processing and computing. As such, quantum computers use physical quantum gates that process information unitarily, even though the final computing steps might be measurement-based or non-unitary. The applications of quantum computers cover diverse areas, reaching from well-known quantum algorithms to quantum machine learning and quantum neural networks. The last of these is of particular interest by belonging to the promising field of artificial intelligence. However, quantum neural networks are technologically challenging as the underlying computation requires non-unitary operations for mimicking the behavior of neurons. A landmark development for classical neural networks was the realization of memory-resistors, or "memristors". These are passive circuit elements that keep a memory of their past states in the form of a resistive hysteresis and thus provide access to nonlinear gate operations. The quest for realising a quantum memristor led to a few proposals, all of which face limited technological practicality. Here we introduce and experimentally demonstrate a novel quantum-optical memristor that is based on integrated photonics and acts on single photons. We characterize its memristive behavior and underline the practical potential of our device by numerically simulating instances of quantum reservoir computing, where we predict an advantage in the use of our quantum memristor over classical architectures. Given recent progress in the realization of photonic circuits for neural networks applications, our device could become a building block of immediate and near-term quantum neuromorphic architectures.