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arXiv:2412.08207

Measurement-based quantum convolutional neural network for deep learning

Yifan Sun, Xiangdong Zhang

Published Dec 11, 2024• 1 citation
arXivHTMLPDF

Abstract

Recently, quantum convolutional neural networks (QCNNs) are proposed, harnessing the power of quantum computing for faster training compared to the classical counterparts. However, this framework for deep learning also relies on multiple processing layers to capture the representation of data, which necessitates precise dynamical control. Given the current stage of quantum computing, achieving this level of control at a large scale remains challenging. Here, we propose an alternate approach to implementing QCNNs by utilizing cluster states. The training process of the method involves tuning the projection basis of each qubit in cluster states, rather than adjusting the parameters of layers of operators in deep quantum circuits. Hence, the whole system is easier to stabilize by avoiding the complex controls. Leveraging techniques in measurement-based quantum computing, we present an exact cluster state solution to general QCNNs. Followingly, we provide numerical evidence that both quantum and classical data can be learned by measuring cluster states, and a faster convergence of the method is observed. The cluster states we consider in our learning examples are merely square-lattice cluster states, whose implementation at large scale have been reported recently. It indicates that our method has the potential for realizing the advance of quantum deep learning for practical uses.

DOI
10.48550/arxiv.2412.08207

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Abstract Quantum neural networks (QNNs) represent a pioneering intersection of quantum computing and deep learning. In this study, we unveil a fundamental convolution property inherent to QNNs, stemming from the natural parallelism of quantum gate operations on quantum states. Notably, QNNs are capable of performing a convolutional layer using a single quantum gate, whereas classical methods require 2n2^n2n basic operations. This essential property has been largely overlooked in the design of existing quantum convolutional neural networks (QCNNs), limiting their ability to capture key structural features of classical CNNs, including local connectivity, parameter sharing, and multi-channel, multi-layer architectures. To address these limitations, we propose novel QCNN architectures that explicitly harness the convolutional nature of QNNs. We validate the effectiveness of these architectures through extensive numerical experiments focused on multiclass image classification. Our findings provide deep insights into the realization of convolutional mechanisms within QNNs, marking a substantial advancement in the development of QCNNs and broadening their potential for efficient data processing.
Quantum computing is a new computational paradigm that promises applications in several fields, including machine learning. In the last decade, deep learning, and in particular Convolutional neural networks (CNN), have become essential for applications in signal processing and image recognition. Quantum deep learning, however remains a challenging problem, as it is difficult to implement non linearities with quantum unitaries. In this paper we propose a quantum algorithm for applying and training deep convolutional neural networks with a potential speedup. The quantum CNN (QCNN) is a shallow circuit, reproducing completely the classical CNN, by allowing non linearities and pooling operations. The QCNN is particularly interesting for deep networks and could allow new frontiers in image recognition, by using more or larger convolution kernels, larger or deeper inputs. We introduce a new quantum tomography algorithm with ℓ∞\ell_{\infty}ℓ∞​ norm guarantees, and new applications of probabilistic sampling in the context of information processing. We also present numerical simulations for the classification of the MNIST dataset to provide practical evidence for the efficiency of the QCNN.
The convolutional neural network (CNN) is a widely recognized model in computer vision due to its capability to utilize data correlation effectively. However, CNNs often face challenges when training on large datasets or dimensions. To address this, the Quantum Convolutional Neural Network (QCNN) introduces an innovative solution for CNN-based problems, specifically within quantum computing frameworks. By integrating CNN architecture into quantum environments, QCNN enhances the model's overall efficiency and functionality. This approach marks an initial effort to propose a solution for classification challenges in quantum physics and chemistry. Furthermore, the study highlights a computational method utilizing the Multi-scale Entanglement Renormalization Ansatz (MERA) with logarithmic depth O(log(n)). Experiments conducted using the TensorFlow Quantum platform on the MNIST dataset demonstrate that QCNNs can achieve faster learning compared to conventional CNNs.
The convolutional neural network (CNN) has become a general approach for image processing in machine learning tasks. Quantum CNN (QCNN) is an emerging method to implement CNN using quantum computing. Quantum computing utilizes the properties of quantum mechanics to perform efficient computing. However, current quantum machines do not support large-scale QCNNs due to a lack of qubits. As a consequence, QCNNs are limited in scale and cannot directly process high-dimensional images. These shortcomings result in suboptimal QCNN performance. Meanwhile, building quantum machines with enough qubits is technically difficult and costly. These obstacles motivate us to design a quantum edge computing (QEC) system capable of achieving the scalability of QCNNs. Quantum machines are organized hierarchically in the QEC system. The quantum machines closer to the users collaboratively load and extract quantum features from the high-dimensional input data. Subsequently, the quantum machine in the next layer collects the extracted features and performs further operations to produce the final results. Each quantum machine in the QEC system is equipped with a local small-scale QCNN to capture the data pattern of its input. The local QCNNs could be combined to form a large-scale QCNN capable of learning and processing high-dimensional data, overcoming hardware limitations and improving performance.