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Quantum Engineering

Design of quantum neuron model for quantum neural networks

Yao Zhang, Qiang Ni

Published Aug 25, 2021• 10 citations
Publisher

Abstract

Quantum neural network is a network which is to be composed of several quantum neurons, which is required to have a certain topological structure. In this article, we propose a new method to encode classical input data into quantum states to represent a quantum neuron, which has a low-complexity form and can be easily utilized to construct a quantum neural network. The numerical simulation of two classification tasks with the proposed quantum neuron model is conducted to show its validity.

DOI
10.1002/que2.75

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Quantum neural network is a network which is to be composed of several quantum neurons, which is required to have a certain topological structure. In this article, we propose a new method to encode classical input data into quantum states to represent a quantum neuron, which has a low-complexity form and can be easily utilized to construct a quantum neural network. The numerical simulation of two classification tasks with the proposed quantum neuron model is conducted to show its validity.
Quantum Neural Networks (QNNs) represent a novel approach to artificial neural networks, leveraging the unique properties of quantum mechanics to enhance computation capabilities. This paper investigates the design and implementation of a quantum neural network (QNN) that employs adaptive neuron structures, dynamically adjusting their connections based on input data. We explore the potential of quantum entanglement to facilitate this self-adaptive behavior, aiming to achieve improved efficiency and robustness compared to classical neural networks. The core mechanism centers around utilizing quantum entanglement to enable neurons to subtly influence each other's states, promoting a form of self-organization within the network. This research offers a promising avenue for advancing QNNs and opens up new possibilities for complex computational tasks.
An artificial neural network, consisting of many neurons in different layers, is an important method to simulate the human brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is the inner product and the nonlinear operation is represented by an activation function. In this work, we introduce a kind of quantum neuron whose inputs and outputs are quantum states. The inner product and activation operator of the quantum neurons can be realized by quantum circuits. Based on the quantum neuron, we propose a model of a quantum neural network in which the weights between neurons are all quantum states. We also construct a quantum circuit to realize this quantum neural network model. A learning algorithm is proposed meanwhile. We show the validity of the learning algorithm theoretically and demonstrate the potential of the quantum neural network numerically.
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.
A quantum neural networks model based on quantum neurons and traditional neurons is presented in this paper. The input of quantum neuron is real vector, its weight is quantum bits, its transforming function is an inner product operator and its output is a real number. The network includes three layers. Input layer is composed of traditional neurons that receive input information. Hidden layer is composed of quantum neurons that extract pattern feature of input information and transfer them to output layer. Output layer is composed of traditional neurons that export calculation result. The weightings of output layer are rectified by back propagation algorithm. The weightings of hidden layer are rectified by a group of quantum gates. A detailed learning algorithm is designed. Finally the availability of the model and algorithm is illustrated by two application examples of pattern recognition and functional 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.
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.