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New Trends in Mathematical Science

Artificial neural network modeling and control for dynamical and statistical characteristics of photonic quantum memristor

Sergey Borisenok

Published Mar 13, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.20852/ntmsci.2022.457

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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.
Abstract Memristive devices are a class of physical systems with history-dependent dynamics characterized by signature hysteresis loops in their input–output relations. In the past few decades, memristive devices have attracted enormous interest in electronics. This is because memristive dynamics is very pervasive in nanoscale devices, and has potentially groundbreaking applications ranging from energy-efficient memories to physical neural networks and neuromorphic computing platforms. Recently, the concept of a quantum memristor was introduced by a few proposals, all of which face limited technological practicality. Here we propose and experimentally demonstrate a novel quantum-optical memristor (based on integrated photonics) that acts on single-photon states. We fully characterize the memristive dynamics of our device and tomographically reconstruct its quantum output state. Finally, we propose a possible application of our device in the framework of quantum machine learning through a scheme of quantum reservoir computing, which we apply to classical and quantum learning tasks. Our simulations show promising results, and may break new ground towards the use of quantum memristors in quantum neuromorphic architectures.
A quantum memristor is a passive resistive circuit element with memory, engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system–bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work could be a building block for constructing quantum neural networks in quantum photonics, when scaling up.
A quantum memristor is a passive resistive circuit element with memory, engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work could be a building block for constructing quantum neural networks in quantum photonics, when scaling up.
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
A quantum memristor combines the memristive dynamics with the quantum behavior of the system. We analyze the idea of a quantum memristor based on ultracold ions trapped in a Paul trap. Corresponding input and output memristor signals are the ion electronic levels populations. We show that under certain conditions the output/input dependence is a hysteresis curve similar to classical memristive devices. This behavior becomes possible due to the partial decoherence provided by the feedback loop, which action depends on previous state of the system (memory). The feedback loop also introduces nonlinearity in the system. Ion-based quantum memristor possesses several advantages comparing to other platforms-photonic and superconducting circuits-due to the presence of a large number of electronic levels with different lifetimes as well as strong Coulomb coupling between ions in the trap. The implementation of the proposed ion-based quantum memristor will be a significant contribution to the novel direction of "quantum neural networks".