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Journal of Modern Physics

Role of Entanglement in Quantum Neural Networks (QNN)

Manu Pratap Singh, B. S. Rajput

Published Jan 1, 2015• 8 citations
Publisher

Abstract

Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. Carrying out the correct computation of XOR function in neural network, it has been shown that QNN requires the proper correlation between the input and output qubits and the presence of appropriate entanglement in the system guarantees this correlation.

DOI
10.4236/jmp.2015.613196

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Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. Carrying out the correct computation of XOR function in neural network, it has been shown that QNN requires the proper correlation between the input and output qubits and the presence of appropriate entanglement in the system guarantees this correlation.
This paper investigates the feasibility of leveraging quantum entanglement to facilitate self-organizing feature discovery within neural networks. Traditional neural networks rely on gradient-based optimization to learn feature representations, often requiring substantial computational resources and careful hyperparameter tuning. We propose a novel quantum neural network (QNN) architecture designed to exploit the inherent correlations provided by quantum entanglement. The core idea is that dynamic entanglement between qubits will intrinsically adapt the network's weights, leading to the emergence of richer, more relevant feature representations directly from the data. Specifically, we outline a network structure incorporating controlled quantum gates and measurement operations to induce entanglement. The theoretical framework demonstrates how this entanglement can evolve to capture underlying data correlations, effectively performing unsupervised feature learning. We detail the mathematical formulation of the network's dynamics, emphasizing the role of entanglement entropy as a key indicator of feature discovery. While experimental validation is not included in this theoretical exploration, this work lays the groundwork for future investigations into the potential of quantum neural networks for efficient and adaptive feature extraction. The key concepts involve the construction of a QNN with entangled qubits, the evolution of entanglement under data input, and the quantification of feature discovery through entanglement entropy.
Quantum neural networks (QNNs) have been explored as one of the best approach for improving the computational efficiency of neural networks. Because of the powerful and fantastic performance of quantum computation, some researchers have begun considering the implications of quantum computation on the field of artificial neural networks (ANNs).The purpose of this paper is to introduce an application of QNNs in construction of cryptography system in which two networks exchange their outputs (in qubits) and the key to be synchronized between two communicating parties. This system is based on multilayer qubit QNNs trained with back-propagation algorithm.
Based on the theoretical basis of quantum computation, entanglement has been further explored as one of the key resources. An outstanding problem in quantum computation is the detecting of entanglement, but no closed-form algorithm exists. According to an advanced matrix rearrangement approach for detecting multipartite quantum states, we give some examples to verify the effectiveness and practicability of this new criterion. Meanwhile, this paper shows how techniques from the quantum neural network can be utilized to detect entanglement. Two models, known as the discrete-variable and the continuous-variable quantum neural network, are applied to solve the separability problem. We demonstrate the utility that such a discrete-variable quantum neural network can be trained to detect the entanglement with great exactness. And the complexity of network and computation is greatly reduced. Besides, the continuous-variable quantum neural network is applied for detecting two-qumode Gaussian state. Compared with the results of the traditional neural network, this deep quantum neural network demonstrates its capability and adaptability as well.
Most proposals for quantum neural networks have skipped over the implementation of the Qubit, superposition, entanglement and measurement in order to be used in MATLAB environment. Quantum computing uses unitary operators acting on discrete state vectors. Matlab is a well-known (classical) matrix computing environment, which makes it well suited for simulating quantum algorithms. The Quantum Computing Function (QCF) library extends Matlab by adding functions to represent and visualize common quantum operations. On the other hand a new mathematical model of computation called Quantum Neural Networks (QNNs) is defined, building on Deutsch's model of quantum computational network. The Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. In this paper the use and importance of those functions is illustrated with the help of few examples. This paper presents a brief overview of QCF that how it can be useful in Quantum Neural Network simulation.
One of the most promising new directions in quantum computing and artificial intelligence convergence is the Quantum Neural Networks (QNNs) that can potentially revolutionize the manner in which intelligent systems are designed, trained, and implemented. Although traditional deep learning models have proven to be incredibly successful in fields like computer vision, natural language processing and autonomous systems, they are becoming limited by computational bottlenecks, energy use, and scalability constraints when operating on large high-dimensional data. The distinctive principles of quantum mechanics (superposition, entanglement, and quantum parallelism) may be applied to the QNNs to provide a distinct computational paradigm with the ability to execute exponentially complicated computations more effectively than his classical counterparts. This article gives an in-depth analysis of QNNs as the new frontier of artificial intelligence. We start with the description of the theoretical foundations of quantum computation and their realization in the form of neural networks. We then examine state-of-the-art QNN architectures, such as hybrid quantum-classical models that help overcome present quantum hardware limitations in relation to the capabilities of classical machine learning. Some of the upcoming applications are showcased including molecular simulation and drug discovery and financial modeling, optimization, cryptography and intelligent automation. Such applications reveal the revolutionary power of QNNs to tackle the issues that cannot be tackled by traditional systems. Nonetheless, there are also major obstacles on the way to a practical implementation of QNN. Problems that still remain a barrier to widespread adoption include quantum decoherence, noise in near-term quantum devices, and the inability to scale qubit architectures or to train large-scale quantum models. In order to overcome these obstacles, we speak about the current research work on the topic of error correction, variational algorithms, and hybrid system designs. Also we examine the ethical and societal ramifications of quantum-accelerated AI, such as security, data sovereignty, and technological equity globally.
The goal of the artificial neural network is to create powerful artificial problem solving systems. The field of quantum computation applies ideas from quantum mechanics to the study of computation and has made interesting progress. Quantum Neural Network (QNN) is one of the new paradigms built upon the combination of classical neural computation and quantum computation. It is argued that the study of QNN may explain the brain functionality in a better way and create new systems for information processing including solving some classically intractable problems. In this paper we have given an introductory representation of quantum artificial neural network to show how it can be modelled on the basis of double-slit experiment. Also an attempt is made to show the quantum mechanical representation of a classical neuron to implement Hadamard transformation.