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Laser Physics Letters

Design of a novel quantum neural network

Xu-Feng Niu, Wenping Ma

Published Sep 9, 2020• 7 citations
Publisher

Abstract

Abstract With the overwhelming success in the field of quantum computing, much attention has been paid to constructing a quantum neural network by combining a classical neural network with quantum computing. In this paper, we propose a novel quantum neural network model based on a quantum version of the sigmoid function, which skillfully combines the non-linear dissipation dynamics of neural computation with the linear unitary dynamics of quantum computation. Moreover, we also add connections from the input layer to the output layer to increase the non-linear expression ability of the network and the similarity to the human brain’s information processing. The specific steps and relevant formulas of the conjugate gradient algorithm in the learning stage of the quantum network parameters are also given in this paper. Finally, the feasibility and properties of the model are demonstrated by MATLAB simulation with a encryption and decryption experiment.

DOI
10.1088/1612-202x/abaf58

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Abstract With the overwhelming success in the field of quantum computing, much attention has been paid to constructing a quantum neural network by combining a classical neural network with quantum computing. In this paper, we propose a novel quantum neural network model based on a quantum version of the sigmoid function, which skillfully combines the non-linear dissipation dynamics of neural computation with the linear unitary dynamics of quantum computation. Moreover, we also add connections from the input layer to the output layer to increase the non-linear expression ability of the network and the similarity to the human brain’s information processing. The specific steps and relevant formulas of the conjugate gradient algorithm in the learning stage of the quantum network parameters are also given in this paper. Finally, the feasibility and properties of the model are demonstrated by MATLAB simulation with a encryption and decryption experiment.
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementations of the quantum perceptron model have failed to fuse the two elegantly. This was due to a slow learning rule and a disregard for the unitary requirement. In this paper, we present a quantum perceptron that can compute functions uncomputable by the classical perceptron while analytically solving for parameters and preserving the unitary and dissipative requirements.
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.
Quantum computing enables quantum neural networks (QNNs) to have great potential to surpass artificial neural networks. The powerful generalization of neural networks is attributed to nonlinear activation functions. Although various models related to QNNs have been developed, they are facing the challenge of merging the nonlinear, dissipative dynamics of neural computing into the linear, unitary quantum system. In this paper, we establish different quantum circuits to approximate nonlinear functions and then propose a generalizable framework to realize any nonlinear quantum neuron. We present two quantum neuron examples based on the proposed framework. The quantum resources required to construct a single quantum neuron are polynomial in function of the input size. Finally, both IBM Quantum Experience results and numerical simulations illustrate the effectiveness of the proposed framework.
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.
Quantum Neural Networks (QNNs) hold immense promise for revolutionizing artificial intelligence, offering the potential to tackle complex problems currently intractable for classical neural networks. A crucial component of QNNs is the network architecture and the activation functions that govern the flow of information. This paper explores the design of a novel non-linear activation function specifically tailored for QNNs, focusing on its ability to promote self-organizing connectivity and enhanced information transfer. We introduce a concept of "self-regulation" within the activation function's design, aiming to enhance the network's expressiveness and robustness. This research employs a rigorous mathematical analysis and demonstrates its potential to significantly improve the performance of QNNs across various tasks. The core mechanism involves manipulating the activation function's output to encourage specific patterns in the network's connectivity.
Artificial neural networks, usually just called neural networks, computing systems indefinitely inspired by the biological neural networks and they are extensive in both research as well as industry. It is critical to design quantum Neural Networks for complete quantum learning tasks. In this project, we suggest a computational neural network model based on principles of quantum mechanics which form a quantum feed-forward neural network proficient in universal quantum computation. This structure takes input from one layer of qubits and drives that input onto another layer of qubits. This layer of qubits evaluates this information and drives on the output to the next layer. Eventually, the path leads to the final layer of qubits. The layers do not have to be of the same breadth, meaning they need not have the same number of qubits as the layer before and/or after it. This assembly is trained on which path to take identical to classical ANN. The intended project can be compiled by the subsequent points provided here: 1. The expert training of the quantum neural network utilizing the fidelity as a cost function, providing both conventional and efficient quantum implementations. 2. Use of methods that enable quick optimization with reduced memory requirements. 3. Benchmarking our proposal for the quantum task of learning an unknown unitary and find extraordinary generality and a remarkable sturdiness to noisy training data.