A parametric analysis of a quantum neuron node dynamics is proposed using an output qubit extraction protocol employed in previous works. The proposed classification method is composed of 5 different types of dynamics which explain the parameter changing behavior. The initial conditions analysis for each dynamics type is investigated. This parametric analysis gives a better understanding of the dynamics suggesting how fine-tune the system parameters can influence the system expected behaviour allowing e.g. For applications in patten recognition and information retrieval.
A parametric analysis of a quantum neuron node dynamics is proposed using an output qubit extraction protocol employed in previous works. The proposed classification method is composed of 5 different types of dynamics which explain the parameter changing behavior. The initial conditions analysis for each dynamics type is investigated. This parametric analysis gives a better understanding of the dynamics suggesting how fine-tune the system parameters can influence the system expected behaviour allowing e.g. For applications in patten recognition and information retrieval.
A wide spectrum of social, biological, physical, chemical and computational systems have been investigated by the tools and techniques from the field of Dynamical Systems Theory to formalize the behaviour in time and quantify and qualify the parametric variations of those systems. In Biology in particular, studies have shown that learning neuron maximization can occur in specific dynamics conditions where information processing is optimized. This it may be expected that some of those conditions can be recognized and used in artificial models. This work studies the quantum artificial neuron weightless qRAM behavior, from the design iteration models - taking into account the physical and mathematical conditions of quantum computing that restricts the extraction of information at every time step - to its parametric analysis where converging behaviors, damped or oscillatory, are detailed. Tools of dynamical systems like orbits diagram and time series qualitatively illustrate its temporal variability. The main contribution of this work is to detail the neuron qRAM behavior so that the results can be used within the machine learning area, coupled with larger systems to achieve maximum learning tasks. As result, we propose a novel dynamical neuron model, named Quadratic Extraction Model (QEM), we perfom parametric studies of the existing models where underdamped, overdamped and undamped behaviour are encountered, and we present apresentation of a neuron configuration inside a quantum architecture with chaos behaviour. A quantitative measure model to compare dynamics orbits was also proposed.
Quantum computing has been revolutionizing the development of algorithms, which in- cludes remarkable advances in artificial neural networks. The exploration of inherently quantum phenomena holds the promise of transcending classical computing. However, only noisy intermediate-scale quantum devices are available currently. To demonstrate advantages in this quantum era, the development of quantum algorithms needs to satisfy several software requirements due to the insufficiency of quantum computing resources. In this research, we propose a kernel-based framework of quantum neurons that not only contemplates existing quantum neurons but also makes room to define countless others, including quantum neurons that comply with the present hardware restrictions. For exam- ple, we propose here a quantum neuron that is implemented by a circuit of constant depth with a linear number of elementary single-qubit gates. Existing quantum neurons are im- plemented by exponentially expensive circuits, even using complex multi-qubit gates. We improve the proposed quantum neuron through a parametrization that can change its ac- tivation function shape in order to fit underlying patterns that existing quantum neurons cannot fit. As an initial demonstration, we show the proposed quantum neuron producing optimal solutions for six classification problems that an existing quantum neuron can solve only two of them. After, we benchmark classical and quantum neurons in several classifi- cation problems. As a result, in the majority of the cases, the proposed quantum neuron is the best over all neurons, which solidly confirms its superiority. The parametrization offers flexibility to not only fit a wide range of problems but also to optimize the margin between classes, at least better than the classical neurons and existing quantum ones. In light of those advantages, this research paves the way to develop quantum neural networks that can demonstrate a practical quantum advantage in the current quantum era already.
The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate theoretical research into practical solutions. Previous studies have shown the advantages of quantum algorithms on artificially generated datasets, and initial experiments with small binary classification problems have yielded comparable outcomes to classical algorithms. However, it is essential to investigate the potential quantum advantage using real-world data. To the best of our knowledge, this study is the first to propose the utilization of quantum systems to classify neuron morphologies, thereby enhancing our understanding of the performance of automatic multiclass neuron classification using quantum kernel methods. We examined the influence of feature engineering on classification accuracy and found that quantum kernel methods achieved similar performance to classical methods, with certain advantages observed in various configurations.
A novel neural networks model with quantum weights is present.Firstly, based on the information processing modes of biology neuron and quantum computing theory, a quantum neuron model is presented, which is composed of weighting, aggregating, activating, and inspiriting.Secondly the quantum neural networks model based on quantum neuron is constructed in which the input and the output are real vectors; the linked weight and the activation value are qubits.On the basic of the gradient descent algorithm, a learning algorithm of this model is proposed.It is shown that this algorithm is super-linearly convergent under certain conditions and can increase the probability of getting the global optimal solution.Finally, the availability of the model is illustrated in both convergence speed and convergence rate by two application examples of pattern recognition and function approximation.
This paper introduces the Quantum Mechanics Simulation of Neurons Model (QMNN), a novel approach to simulating neuronal behavior based on fundamental principles of quantum mechanics. Traditional artificial neural networks (ANNs) often struggle to accurately replicate the complex dynamics observed in biological neurons due to their reliance on classical computational methods. QMNN leverages concepts such as superposition and entanglement, key features of quantum mechanics, to represent neuronal states and interactions. The model employs a discrete quantum system, where neuronal activity is represented by quantum states, allowing for inherent parallelism and potentially capturing phenomena currently inaccessible to classical neural simulations. This work details the core concepts of QMNN, outlining its mathematical formulation, key components, and potential advantages over conventional ANN approaches. We present a simplified model of a single neuron utilizing a quantum bit (qubit) to represent its state. The model's equations reflect the Schrödinger equation and the evolution of quantum states under influence of external stimuli. The simulation explores scenarios demonstrating the potential for increased computational efficiency and the ability to model phenomena like quantum coherence within neuronal networks. Further research will focus on scaling the model to multi-neuron networks and investigating the model's applicability to various neurological conditions.
A quantum neural networks model with learning algorithm is presented. First, based on the information processing modes of biology neuron and quantum computing theory, a quantum neuron model is presented, which is composed of weighting, aggregating, activating, and prompting. Secondly the quantum neural networks model based on quantum neuron is constructed in which the input and the output are real vectors, the linked weight and the activation value are Q-bits. On the basic of gradient descent algorithm, a learning algorithm is proposed. It is shown that this algorithm is super-linearly convergent under certain conditions and can increase the probability of getting optimum solution. Finally, the availability of the approach is illustrated with application of by adjusting PID controller parameters.