We introduce a machine learning model, the q-CNN model, sharing key features with convolutional neural networks and admitting a tensor network description. As examples, we apply q-CNN to the MNIST and Fashion MNIST classification tasks. We explain how the network associates a quantum state to each classification label, and study the entanglement structure of these network states. In both our experiments on the MNIST and Fashion-MNIST datasets, we observe a distinct increase in both the left/right as well as the up/down bipartition entanglement entropy during training as the network learns the fine features of the data. More generally, we observe a universal negative correlation between the value of the entanglement entropy and the value of the cost function, suggesting that the network needs to learn the entanglement structure in order the perform the task accurately. This supports the possibility of exploiting the entanglement structure as a guide to design the machine learning algorithm suitable for given tasks.
We introduce a machine learning model, the q-CNN model, sharing key features with convolutional neural networks and admitting a tensor network description. As examples, we apply q-CNN to the MNIST and Fashion MNIST classification tasks. We explain how the network associates a quantum state to each classification label, and study the entanglement structure of these network states. In both our experiments on the MNIST and Fashion-MNIST datasets, we observe a distinct increase in both the left/right as well as the up/down bipartition entanglement entropy during training as the network learns the fine features of the data. More generally, we observe a universal negative correlation between the value of the entanglement entropy and the value of the cost function, suggesting that the network needs to learn the entanglement structure in order the perform the task accurately. This supports the possibility of exploiting the entanglement structure as a guide to design the machine learning algorithm suitable for given tasks.
From self-driving cars to medical diagnoses, machine learning (ML) has revolutionized our world in the last few decades. Additionally, Quantum Computing has considerable promise for the future, with superposition and entanglement making quantum algorithms much more efficient and effective than their classical counterparts. Quantum ML aims to apply these quantum principles to the groundbreaking field of ML, such as for image classification. Convolutional Neural Networks (CNNs) are very effective for classification, so we study a Quantum Convolutional Neural Network (QCNN) that is trained to distinguish between handwritten numbers in the MNIST dataset and compared to a similar-sized classical network. After tuning the QCNN and quantum encoding, the QCNN achieved comparable accuracy to the classical network.
Convolutional Neural Network (CNN) is a popular model in computer vision and has the advantage of making good use of the correlation information of data. However, CNN is challenging to learn efficiently if the given dimension of data or model becomes too large. Quantum Convolutional Neural Network (QCNN) provides a new solution to a problem to solve with CNN using a quantum computing environment, or a direction to improve the performance of an existing learning model. The first study to be introduced proposes a model to effectively solve the classification problem in quantum physics and chemistry by applying the structure of CNN to the quantum computing environment. The research also proposes the model that can be calculated with O(log(n)) depth using Multi-scale Entanglement Renormalization Ansatz (MERA). The second study introduces a method to improve the model's performance by adding a layer using quantum computing to the CNN learning model used in the existing computer vision. This model can also be used in small quantum computers, and a hybrid learning model can be designed by adding a quantum convolution layer to the CNN model or replacing it with a convolution layer. This paper also verifies whether the QCNN model is capable of efficient learning compared to CNN through training using the MNIST dataset through the TensorFlow Quantum platform.
Recent advancements in quantum machine learning have spurred the development of hybrid quantum-classical convolutional neural networks (HQCCNNs), which have demonstrated promising potential for image classification tasks. Building on the operational principles of classical transposed convolutional neural networks (CNNs), we introduce a novel quantum variant: the Quantum Pseudo-Transposed Convolutional Neural Network (QPTCNN). The QPTCNN adapts the concept of classical transposed CNNs to the quantum domain, leveraging a hybrid quantum-classical framework that combines a quantum convolutional layer with a classical fully connected layer. In the QPTCNN, the quantum convolutional layer emulates a transposed convolution operation, ensuring that the output feature map retains the same dimensions as the input image. This is accomplished using rotational angle encoding and a ring-structured quantum circuit, interconnected by two-qubit control gates such as CNOT and CRY gates, facilitating efficient quantum convolution. We evaluated the performance of the QPTCNN on the MNIST and Fashion-MNIST datasets, with two distinct versions of the model: Model A, which utilizes a CNOT-gate entanglement circuit, and Model B, which employs a CRY-gate entanglement circuit. The results demonstrate that both Model A and Model B achieve strong performance across the datasets. However, Model A outperforms Model B, achieving higher classification accuracy and lower loss compared to earlier models. These findings suggest that the QPTCNN is highly capable of learning and extracting relevant feature information from input images, making it well-suited for high-performance image classification tasks. This work represents a significant advancement in quantum-enhanced image classification.
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.
In recent years, with rapid progress in the development of quantum technologies, quantum machine learning has attracted a lot of interest. In particular, a family of hybrid quantum-classical neural networks, consisting of classical and quantum elements, has been massively explored for the purpose of improving the performance of classical neural networks. In this paper, we propose a novel hybrid quantum-classical algorithm called quantum dilated convolutional neural networks (QDCNNs). Our method extends the concept of dilated convolution, which has been widely applied in modern deep learning algorithms, to the context of hybrid neural networks. The proposed QDCNNs are able to capture larger context during the quantum convolution process while reducing the computational cost. We perform empirical experiments on MNIST and Fashion-MNIST datasets for the task of image recognition and demonstrate that QDCNN models generally enjoy better performances in terms of both accuracy and computation efficiency compared to existing quantum convolutional neural networks (QCNNs).
Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor network approaches over the last 30 years is well understood, very little is yet known about why these techniques work for machine learning. The goal of this paper is to investigate entanglement properties of tensor network models in a current machine learning application, in order to uncover general principles that may guide future developments. We revisit the use of tensor networks for supervised image classification using the MNIST data set of handwritten digits, as pioneered by Stoudenmire and Schwab [Adv. in Neur. Inform. Proc. Sys. 29, 4799 (2016)]. Firstly we hypothesize about which state the tensor network might be learning during training. For that purpose, we propose a plausible candidate state ∣Σℓ⟩ (built as a superposition of product states corresponding to images in the training set) and investigate its entanglement properties. We conclude that ∣Σℓ⟩ is so robustly entangled that it cannot be approximated by the tensor network used in that work, which must therefore be representing a very different state. Secondly, we use tensor networks with a block product structure, in which entanglement is restricted within small blocks of n×n pixels/qubits. We find that these states are extremely expressive (e.g. training accuracy of 99.97% already for n=2), suggesting that long-range entanglement may not be essential for image classification. However, in our current implementation, optimization leads to over-fitting, resulting in test accuracies that are not competitive with other current approaches.