Alexander G. Balanov

We present a quantum reservoir computing (QRC) framework based on a small-scale quantum system comprising at most six interacting qubits, designed for nonlinear financial time-series forecasting. We apply the model to predict future daily closing trading prices of 20 quantum-sector publicly traded companies over the period from April 11, 2020, to April 11, 2025 (exclusive), as well as minute-by-minute trading prices during out-of-market hours on July 7, 2025. Our analysis identifies optimal reservoir parameters that yield stock trend (up/down) classification accuracies exceeding 86%. Importantly, the QRC model is platform-agnostic and can be realized across diverse physical implementations of qubits, including superconducting circuits and trapped ions. These results demonstrate the expressive power and robustness of small-scale quantum reservoirs for modeling complex temporal correlations in financial data, highlighting their potential applicability to real-world forecasting tasks on near-term quantum hardware.

Despite the explosive expansion of artificial intelligence based on artificial neural networks (ANNs), these are employed as “black boxes,” since it is unclear how, during learning, they form memories or develop unwanted features, such as spurious memories and catastrophic forgetting. Much research is available on isolated aspects of learning ANNs, but due to their high dimensionality and non-linearity, their comprehensive analysis remains a challenge. Here, we comprehensively analyze mechanisms of memory formation and destruction in an 81-neuron Hopfield network undergoing Hebbian learning. We propose a method to analyze bifurcations in a learning ANN in terms of the stage of learning. We discover that individual memories, represented by attractors and their basins, are formed and destroyed, thanks to bifurcations. We show that the same bifurcations cause both the abrupt memory loss while the ANN is trained on a single task, and the conventional catastrophic forgetting while it switches between training tasks. We point to a possible mechanism of spurious-memory formation. We reveal the structure of attractor basins formed at the end of learning. Our strategy to analyze high-dimensional learning ANNs is principally applicable to recurrent ANNs of any form. The demonstrated mechanisms of memory formation and of catastrophic forgetting shed light on the operation of a wider class of recurrent ANNs and could aid the development of approaches to mitigate their flaws.

Typical mammal brains have some form of random connectivity between neurons. Reservoir computing, a neural network approach, uses random weights within its processing layer along with built‐in recurrent connections and short‐term, fading memory, and is shown to be time and training efficient in processing spatiotemporal signals. Here we prepared a niobium oxide‐based thin film memristor device with intrinsic structural inhomogeneity in the form of random nanopores and performed computational tasks of XOR operations, image recognition, and time series prediction and reconstruction. For the latter task we chose a complex three‐dimensional chaotic Lorenz‐63 time series. By applying three temporal voltage waveforms individually across the device and training the readout layer with electrical current signals from a three‐output physical reservoir, we achieved satisfactory prediction and reconstruction accuracy in comparison to the case of no reservoir. This work highlights the potential for scalable, on‐chip devices using all‐oxide reservoir systems, paving the way for energy‐efficient neuromorphic electronics dealing with time signals.

Diffusive memristors show great promise as fundamental components for brain-inspired neuromorphic computing. By relying on the drift and diffusion of charge carriers, which form conductive filaments for charge transport, these devices offer high nonlinearity, tunability, fast switching between resistive states, and low power consumption. Their ability to generate a wide range of nonlinear dynamics, driven by the complex interplay of thermal, electrical, and mechanical effects, mimics the behavior of biological neurons. In this paper, we simulate spiking dynamics in an artificial neuron based on diffusive memristors with two independent conducting filaments. We uncover instabilities that lead to self-sustained spike generation and show that external voltage bias allows the coexistence of two characteristic spiking modes. Noise, either inherent or externally added, facilitates switching between these spiking regimes. The model predictions align well with our experimental measurements, offering the way for the development of neuromorphic devices for parallel signal processing.

We investigate a minimal architecture for quantum reservoir computing based on Hamiltonian encoding, in which input data are injected via modulation of system parameters rather than state preparation. This approach circumvents many of the experimental overheads typically associated with quantum machine learning, enabling computation without feedback, memory, or state tomography. We demonstrate that such a minimal quantum reservoir, despite lacking intrinsic memory, can perform nonlinear regression and prediction tasks when augmented with post-processing delay embeddings. Our results provide a conceptually and practically streamlined framework for quantum information processing, offering a clear baseline for future implementations on near-term quantum hardware.

Rapid development of memristive elements emulating biological neurons creates new opportunities for brain-like computation at low energy consumption. A first step toward mimicking complex neural computations is the analysis of single neurons and their characteristics. Here we measure and model spiking activity in artificial neurons built using diffusive memristors. We compare activity of these artificial neurons with the spiking activity of biological neurons measured in sensory, pre-motor, and motor cortical areas of the monkey (male) brain. We find that artificial neurons can operate in diverse self-sustained and noise-induced spiking regimes that correspond to the activity of different types of cortical neurons with distinct functions. We demonstrate that artificial neurons can function as trans-functional devices (transneurons) that reconfigure their behaviour to attain instantaneous computational needs, each capable of emulating several biological neurons.

We investigate a minimal architecture for quantum reservoir computing based on Hamiltonian encoding, in which input data is injected via modulation of system parameters rather than state preparation. This approach circumvents many of the experimental overheads typically associated with quantum machine learning, enabling computation without feedback, memory, or state tomography. We demonstrate that such a minimal quantum reservoir, despite lacking intrinsic memory, can perform nonlinear regression and prediction tasks when augmented with post-processing delay embeddings. Our results provide a conceptually and practically streamlined framework for quantum information processing, offering a clear baseline for future implementations on near-term quantum hardware.

Diffusive memristors owing to their ability to produce current spiking when a constant or slowly changing voltage is applied are competitive candidates for development of artificial electronic neurons. These artificial neurons can be integrated into various prospective autonomous and robotic systems as sensors, e.g. ones implementing object grasping and classification. We report here Ag nanoparticle-based diffusive memristor prepared on a flexible polyethylene terephthalate substrate in which the electric spiking behaviour was induced by the electric voltage under an additional stimulus of external mechanical impact. By changing the magnitude and frequency of the mechanical impact, we are able to manipulate the spiking response of our artificial neuron. This functionality to control the spiking characteristics paves a pathway for the development of touch-perception sensors that can convert local pressure into electrical spikes for further processing in neural networks. We have proposed a mathematical model which captures the operation principle of the fabricated memristive sensors and qualitatively describes the measured spiking behaviour. Employing such flexible diffusive memristors that can directly translate tactile information into spikes, similar to force and pressure sensors, could offer substantial benefits for various applications in robotics.

We theoretically study an artificial neuron circuit containing a quantum memristor in the presence of relaxation and dephasing. The charge transport in the quantum element is realized via tunneling of a charge through a quantum particle which shuttles between two terminals—a functionality reminiscent of classical diffusive memristors. We demonstrate that this physical principle enables hysteretic behavior in the current-voltage characteristics of the quantum device. In addition, being used in an artificial neural circuit, the quantum switcher is able to generate self-sustained current oscillations. Our analysis reveals that these self-oscillations are triggered only in quantum regimes with a moderate rate of relaxation, and cannot exist either in a purely coherent regime or at a very high decoherence. We investigate the hysteresis and instability leading to the onset of current self-oscillations and analyze their properties depending on the circuit parameters. Our results provide a generic approach to the use of quantum regimes for controlling hysteresis and generating self-oscillations. Published by the American Physical Society 2024