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Abstract
Quantum machine learning researchers often rely on incorporating tensor networks (TN) into deep neural networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable weights of each model layer suffer from the correlations and entanglement structure between the model parameters in classical implementations. To address this issue, a multi-layer design of a tensor ring optimized variational quantum learning classifier (Quan-TR) comprising cascading entangling gates replacing the fully connected (dense) layers of a TN is proposed, and it is referred to as tensor ring optimized quantum-enhanced tensor neural networks (TR-QNet). TR-QNet parameters are optimized using the stochastic gradient descent algorithm on qubit measurements. The proposed TR-QNet is evaluated on three distinct datasets, namely Iris, MNIST, and CIFAR-10, to demonstrate the enhanced precision achieved for binary classification. In quantum simulations, the proposed TR-QNet achieves promising precision of 94.5%, 86.16%, and 83.54% on the Iris, MNIST, and CIFAR-10 datasets. Benchmark studies have been conducted on state-of-the-art quantum and classical implementations of TN models to show the efficacy of the proposed TR-QNet. Moreover, the scalability of TR-QNet highlights its potential for exhibiting in deep learning applications on a large scale. The PyTorch implementation of TR-QNet is available on Github https://github.com/konar1987/TR-QNet/.
Highlights
Deep learning is a very effective and widely used machine learning method, which has shown remarkable performance in various tasks, including recognition, classification, regression, and clustering (Lathuiliére et al 2020; Li et al 2019; He et al 2016; Peng et al 2020)
Applying tensor networks (TN) to deep neural networks (DNN) to generate tensor neural networks (TNN) is one of them since TNN retains outstanding potential to approximate original weights with fewer parameters (Panagakis et al 2021), involving reconstruction of convolutional and fully connected layers using a range of tensor decomposition (TD) formats (Hayashi et al 2019)
In line with the impressive advances in quantum machine learning, the proposed tensor ring optimized quantum-enhanced tensor neural networks (TR-QNet) framework improves over fully classical TNN
Summary
Deep learning is a very effective and widely used machine learning method, which has shown remarkable performance in various tasks, including recognition, classification, regression, and clustering (Lathuiliére et al 2020; Li et al 2019; He et al 2016; Peng et al 2020). The scalability of DNN is hindered when a substantial number of neurons are taken into account, thereby restricting the feasible number of layers. This is primarily due to the time-consuming training process and the need for a lot of memory to store the large-weight matrices. The accuracy and effectiveness of the DNN model will suffer with an increase in the hidden layers if the parameters for such large-weight matrices are not optimized. The present hardware used to train neural networks significantly restricts their scale and usefulness These concerns have gained significance due to the imminent approach of physical limitations to impede the progress of performance enhancements in deep classical neural networks
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