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Brazilian Symposium on Neural Networks (SBRN)

Quantum Logical Neural Networks

Wilson Rosa de Oliveira, Adenilton José da Silva, Teresa B. Ludermir, Amanda Leonel, Wilson R. Galindo, Jefferson C.C. Pereira

Published Oct 1, 2008• 32 citations
Publisher

Abstract

Quantum analogues of the (classical) Logical Neural Networks (LNN) models are proposed in (q-LNN for short). We shall here further develop and investigate the q-LNN composed of the quantum analogue of the Probabilistic Logic Node (PLN) and the multiple-valued PLN (MPLN) variations, dubbed q-PLN and q-MPLN respectively. Besides a clearer mathematical description, we present a computationally efficient and simply described quantum learning algorithm in contrast to what has been proposed to the quantum weighted version.

DOI
10.1109/sbrn.2008.9

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Quantum analogues of the (classical) Logical Neural Networks (LNN) models are proposed in (q-LNN for short). We shall here further develop and investigate the q-LNN composed of the quantum analogue of the Probabilistic Logic Node (PLN) and the multiple-valued PLN (MPLN) variations, dubbed q-PLN and q-MPLN respectively. Besides a clearer mathematical description, we present a computationally efficient and simply described quantum learning algorithm in contrast to what has been proposed to the quantum weighted version.
In this paper we investigate the computational power of the quantum weightless neural networks (q-WNN) and propose a novel quantum weightless neural node. The new quantum neuron is derived from the quantum probabilistic logic node (qPLN), which is a mathematical quantisation of the weightless neural node PLN. By a slight modification on the input lines of the qPLN node it is possible to define the quantum psi-neuron. We show in this paper that psi-neurons can be used to approximate any quantum circuit.
Despite rapid theoretical and practical progress, machine learning algorithms require large computational resources. However, new opportunities are opening up due to the advent of quantum computing devices that directly use the laws of quantum mechanics to bypass the technological and thermodynamic limitations of classical computing. Taking into account that artificial neural networks are actively used in solving a number of practical problems, with the advent of quantum computing technologies, the development of quantum neural networks for the implementation of quantum machine learning is very relevant. The article considers a quantum analogue of classical neurons that form quantum neural networks capable of performing universal quantum computations.
Quantum Machine Learning is gaining prominence with the advent of real quantum processors. The quantum analogue of one of the most important and popular model of machine learning, namely Artificial Neural Network is studied and reviewed here in this paper. Various approaches to design and implement a quantum neural network has been studied. Most of the works done in this field involved a translation of classical neural network components into the language of quantum physics. But direct translation cannot be a solution as not every classical component has a quantum analogue. Non-linear activation functions are good examples of it. Quantum operators need to be linear and therefore finding alternate solutions to activation functions is an active area of research. Nevertheless, its advantages over the classical models are profound. Quantum superposition gives exponential storage capacity to a quantum network. Quantum parallelism can be put to use and to train the network with multiple inputs in one go. Despite being a new field, many real world applications of a quantum neural network has also been theorised. These models, their advantages, applications and limitations has been discussed in this paper.
Quantum Machine Learning refers to the interdisciplinary area of research, blending principles from quantum physics and machine learning that can process information on quantum computers. Quantum machine learning (QML) intentions to exploit the superposition (qubit can exist in multiple states) property and other effects of quantum mechanics for enhanced efficiency and speed in specific machine learning computations, promising exponential-power superiority in particular computations. This paper focusses on Quantum Machine Learning Models to develop the framework to learn complicated associations within the data through the adjustment of the variational parameters during training. This framework serves as a foundational structure for implementing quantum neural networks, allowing for further experimentation and growth in quantum machine learning applications. It highlights the quantum circuits to process and learn from data in a mode distinct from classical neural networks. As the retrieve of quantum computing grows, such frameworks can be adapted and expanded to explore more sophisticated quantum algorithms and architectures. In the circumstances of Quantum Neural Networks, gradient descents is used in minimizing cost or loss function by iteratively adjusting the variational parameters based onto the gradient of the loss with admire to those parameters. The output that indicates the process of installing the Quantum information science Kit (Qiskit) library in Python specifically version 3.7 along with its dependencies.
This paper proposes a novel neural network architecture, termed Entanglement-Based Neural Networks (EBNNs), inspired by the principles of quantum entanglement. Conventional classical neural networks often face challenges in effectively capturing and representing intricate correlations within data, particularly when dealing with high-dimensional or complex datasets. The core idea behind EBNNs is to construct networks where nodes are interconnected in a manner that mirrors the correlated states observed in quantum entanglement, even across spatial separation. This is achieved through a specifically designed network topology that introduces dependencies between nodes, allowing for a more efficient representation of complex relationships. The network's structure is defined by a set of interconnected nodes, each possessing a state (s_i) represented by a real number. The connections between nodes are characterized by a correlation function (C_{ij}), which dictates the degree to which the state of node *j* is influenced by the state of node *i*. The architecture utilizes a layered approach, where layers are composed of interconnected nodes. The propagation of information through the network is governed by a modified version of the Hebbian learning rule, adapted to incorporate the entanglement-like correlation functions. This approach aims to improve the network's ability to learn and represent complex patterns by leveraging inherent correlations rather than relying solely on independent node activations. The key contributions of this work are the conceptual design of EBNNs and the formulation of the core mathematical framework for their implementation. We present a detailed description of the network architecture, the correlation function definition, and the learning rule, offering a foundation for further research and development in this area. Finally, we demonstrate the potential advantages of EBNNs in terms of improved learning efficiency and representation capacity.