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arXiv:1905.10912

Defining Quantum Neural Networks via Quantum Time Evolution

Aditya Dendukuri, Blake Keeling, Arash Fereidouni, Joshua Burbridge, Khoa Luu, Hugh Churchill

Published May 27, 2019• 4 citations
arXivHTMLPDF

Abstract

This work presents a novel fundamental algorithm for for defining and training Neural Networks in Quantum Information based on time evolution and the Hamiltonian. Classical Neural Network algorithms (ANN) are computationally expensive. For example, in image classification, representing an image pixel by pixel using classical information requires an enormous amount of computational memory resources. Hence, exploring methods to represent images in a different paradigm of information is important. Quantum Neural Networks (QNNs) have been explored for over 20 years. The current forefront work based on Variational Quantum Circuits is specifically defined for the Continuous Variable (CV) Model of quantum computers. In this work, a model is proposed which is defined at a more fundamental level and hence can be inherited by any variants of quantum computing models. This work also presents a quantum backpropagation algorithm to train our QNN model and validate this algorithm on the MNIST dataset on a quantum computer simulation.

DOI
10.48550/arxiv.1905.10912

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This work presents a novel fundamental algorithm for for defining and training Neural Networks in Quantum Information based on time evolution and the Hamiltonian. Classical Neural Network algorithms (ANN) are computationally expensive. For example, in image classification, representing an image pixel by pixel using classical information requires an enormous amount of computational memory resources. Hence, exploring methods to represent images in a different paradigm of information is important. Quantum Neural Networks (QNNs) have been explored for over 20 years. The current forefront work based on Variational Quantum Circuits is specifically defined for the Continuous Variable (CV) Model of quantum computers. In this work, a model is proposed which is defined at a more fundamental level and hence can be inherited by any variants of quantum computing models. This work also presents a quantum backpropagation algorithm to train our QNN model and validate this algorithm on the MNIST dataset on a quantum computer simulation.
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Artificial neural networks have achieved great success in many fields ranging from image recognition to video understanding. However, its high requirements for computing and memory resources have limited further development on processing big data with high dimensions. In recent years, advances in quantum computing show that building neural networks on quantum processors is a potential solution to this problem. In this paper, we propose a novel neural network model named Quantum Convolutional Neural Network (QCNN), aiming at utilizing the computing power of quantum systems to accelerate classical machine learning tasks. The designed QCNN is based on implementable quantum circuits and has a similar structure as classical convolutional neural networks. Numerical simulation results on the MNIST dataset demonstrate the effectiveness of our model.
Image classification is a fundamental task in computer vision that involves assigning labels to images based on their content. In recent years, deep learning techniques based on classical neural networks (CNN) have achieved modern performance on many image classification tasks. However, there is growing interest in using quantum neural networks (QNNs) for image classification, as quantum computing has the potential to improve the accuracy and speed of computation. We demonstrate the potential of our QNN model and QCNN model by applying it to the fashion MNIST dataset. The results indicate that the QNN model exhibits faster training speed and higher testing set accuracy compared to a QCNN with a similar architecture.
We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized models such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the strawberry fields software library. These experiments, including a classifier for fraud detection, a network which generates tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks.
Abstract Quantum neural networks (QNNs) are emerging as a promising paradigm at the intersection of quantum computing and artificial intelligence. However, their conceptual abstraction and physical implementation remain challenging in educational contexts. In this work, we present a didactic framework to teach the fundamentals of QNNs by leveraging classical artificial neural networks (ANNs), Python simulation with Qiskit, and analysis of training dynamics using the Iris dataset. The paper begins with a theoretical comparison between classical and quantum neurons, followed by the design of a full QNN training algorithm implemented in Python. Through simulated results and pedagogical discussion, we show how learners can explore key aspects of quantum learning—including superposition, variational circuits, probabilistic measurement, and optimization—without access to quantum hardware. The use of graphical outputs and code-structure correspondence enhances student engagement and promotes algorithmic thinking. This approach supports quantum science education by offering a reproducible, interactive, and conceptually aligned method for introducing QNNs in undergraduate and graduate classrooms.
Image classification is a fundamental task in deep learning, and recent advances in quantum computing have generated significant interest in quantum neural networks. Traditionally, Convolutional Neural Networks (CNNs) are employed to extract image features, while Multilayer Perceptrons (MLPs) handle decision making. However, parameterized quantum circuits offer the potential to capture complex image features and define sophisticated decision boundaries. In this paper, we present a novel Hybrid Quantum–Classical Neural Network (H-QNN) for image classification, and demonstrate its effectiveness using the MNIST dataset. Our model combines quantum computing with classical supervised learning to enhance classification accuracy and computational efficiency. In this study, we detail the architecture of the H-QNN, emphasizing its capability in feature learning and image classification. Experimental results demonstrate that the proposed H-QNN model outperforms conventional deep learning methods in various training scenarios, showcasing its effectiveness in high-dimensional image classification tasks. Additionally, we explore the broader applicability of hybrid quantum–classical approaches in other domains. Our findings contribute to the growing body of work in quantum machine learning, and underscore the potential of quantum-enhanced models for image recognition and classification.