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Quantum weightless neuron dynamics

Paula Neto, Fernando Maciano de

Published Mar 1, 2016• 0 citations

Abstract

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.

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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.

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.

Understanding how biological neural networks process information is one of the biggest open scientific questions of our time. Advances in machine learning and artificial neural networks have enabled the modeling of neuronal behavior, but classical models often require a large number of parameters and highly task-specific architectures, which can complicate model design and scalability. Quantum computing offers an alternative approach through quantum machine learning, which can achieve efficient training with fewer parameters. In this work, we introduce a quantum generative model framework for generating synthetic data that captures the spatial and temporal correlations of biological neuronal activity. Our model demonstrates the ability to achieve reliable outcomes with fewer trainable parameters compared to classical methods. These findings highlight the potential of quantum generative models to provide new tools for modeling and understanding neuronal behavior, offering a promising avenue for future research in neuroscience.

We investigate the dynamics of the quantum weightless neuron (qRAM) regarding entanglement. Previous works used a quantum extractor operator (QEO) to iterate the qRAM. With the QEO the qRAM output channel can be fed back or iterated despite possible entanglement of the overall output quantum state. Two measures are used here for the quantitative analysis: von Neummann entropy and entanglement entropy. We find that entanglement is disturbed and even increased when the QEO is used. In contrast entanglement stays unchanged under coherent feedback. The results indicate that QEO produces a more diverse dynamics and can be viewed as an environment interaction operator but not with decaying properties. A descriptive analyse of the entropy and entanglement dynamics is presented.

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.

Understanding the information processing in neuronal networks relies on the development of computational models that accurately reproduce their activity data. Machine learning techniques have shown promising results in generating synthetic neuronal data, but interpretability remains an issue due to a large number of parameters requiring fitting. Quantum machine learning models, particularly quantum generative learning, are emerging as more compact alternatives that offer similar outcomes. This study presents an efficient framework for generating synthetic neuronal data using a Quantum Generative Adversarial Network (QGAN), with a quantum generator and a classical discriminator. We tested the proposed framework for the minimal case of two neurons, considering the case of single time-steps. Preliminary results demonstrate the QGAN's capability to achieve reliable outcomes with a reduced number of trainable parameters, scaling efficiently for increasing neuronal network sizes. The model effectively captures spiking frequencies of real data, although further refinement is required to incorporate temporal correlations for more extended time-steps. Despite certain limitations, this study lays the foundation for future advancements in using quantum adversarial generative networks to model neuronal activity. The promising potential of QGANs in this domain highlights the possibility of gaining valuable insights into the functioning of complex biological systems through quantum-inspired computational methods.

This paper proposes a novel quantum computing model that leverages the dynamics of neuronal behavior as its foundational building blocks. Unlike conventional quantum computing approaches reliant on purely classical qubits, this model utilizes quantum systems designed to mimic the dynamic changes observed in biological neural networks, specifically at the level of synaptic connections. The core principle involves employing quantum superposition and interference to construct quantum bits (qubits) representing the state of these simulated synapses. Algorithm execution is achieved through precise manipulation, or "quantum tuning," of these qubits. The proposed architecture represents a biologically-inspired paradigm shift in quantum computation, potentially offering advantages in terms of computational efficiency and resilience, particularly for problems exhibiting inherent biological complexity. This work outlines the theoretical framework, key equations, and the fundamental principles driving this new approach to quantum information processing.