[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118703-en":3,"doc-seo-118703-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},118703,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Quantum-Classical Machine learning by Hybrid Tensor Networks","Tensor networks are widely used in quantum many-body physics and have also been adopted across multiple machine learning tasks, yet regular tensor networks face clear constraints in representation power and architecture scalability. The work introduces quantum-classical hybrid tensor networks (HTN), combining tensor networks with classical neural networks in a unified deep-learning framework. It analyzes why regular tensor networks are insufficient as foundational components, then shows HTN can be trained with standard deep-learning methods like backpropagation and stochastic gradient descent. Two application cases—quantum state classification and a quantum-classical autoencoder—illustrate practical potential.","Quantum-Classical Machine learning by Hybrid Tensor Networks  \narXiv :2005 .09428v1 [ cs .LG] 15 May 2020  \nDing Liu, 1, 􀀃 Zekun Yao, 1 and Quan Zhang 1  \n1 School of Computer Science and Technology, Tiangong University, Tianjin 300387, China  \nTensor networks (TN) have found a wide use in machine learning, and in particular, TN and deep learning bear striking similarities. In this work, we propose the quantum-classical hybrid tensor networks (HTN) which combine tensor networks with classical neural networks in a uniform deep learning framework to overcome the limitations of regular tensor networks in machine learning. We first analyze the limitations of regular tensor networks in the applications of machine learning involving the representation power and architecture scalability. We conclude that in fact the regular tensor networks are not competent to be the basic building blocks of deep learning. Then, we discuss the performance of HTN which overcome all the deficiency of regular tensor networks for machine learning. In this sense, we are able to train HTN in the deep learning way which is the standard combination of algorithms such as Back Propagation and Stochastic Gradient Descent. We finally provide two applicable cases to show the potential applications of HTN, including quantum states classification and quantum-classical autoencoder. These cases also demonstrate the great potentiality to design various HTN in deep learning way.  \nI. INTRODUCTION.  \nIn recent year, tensor networks (TN) have drawn more attention as one of the most powerful numerical tools for studying quantum many-body systems [1–4] . Furthermore, TN have been recently applied to many research areas of machine learning [5–8], such as image classi􀀌cation [9–11], dimensionality reduction [12, 13], generative model [10 , 14], data compression [15], improving deep neural network [16], probabilistic graph model [17], quantum compressed sensing [18], even the promising way to implement quantum circuit [19–23] . As a consequence, people encounter the serious computing complexity problem and raise the question: Are the tensor networks able to be the universal deep learning architecture? As we know, the theoretical foundation of deep neural networks is the principle of universal approximation which states that a feed-forward network with a single hidden layer is a universal approximator if and only if the activation function is not polynomial [24, 25] . In this context, the key point of the question of tensor network machine learning will be: Are the tensor networks able to be the universal approximator?  \nSome pioneering researches have started to focus on this fundamental problem. Ref. [26] propose the concept of generalized tensor networks to outperform the regular tensor networks particularly in term of the representation power. Speci􀀌cally, if the entanglement entropy of the function violates the area low [27], then the function can not be represented by regular tensor networks e􀀎ciently. Moreover, they try to combine generalized tensor networks with convolution neural networks together and achieve some good results. Note that they take the convolutions as feature map, then place tensor network in the 􀀌nal layer and take it as the classi􀀌er. Ref. [16] propose the tensor regression network which re-  \n􀀃 [liuding@tiangong.edu.cn](liuding@tiangong.edu.cn)  \nplace the full connect layer by tensor regression layer in order to save storage space.This is another feasible way to take advantage of tensor network in deep learning. Ref. [28] provides a mathematic analysis of the representation power of some typical tensor network factorizations of discrete multivariate probability distributions involving matrix product states (MPS), Born machines and locally puri􀀌ed states (LPS) . Ref. [29] discusses the equivalence of restricted boltzmann machines (RBM) and tensor network states. They prove that this kinds of speci􀀌c neural networks can be translated into MPS and devise ","cbCaima0O7dxtSI9","https://ap.wps.com/l/cbCaima0O7dxtSI9","pdf",497637,1,"English","en",105,"# Introduction\n## Limitations of Regular Tensor Networks in Machine Learning\n## Quantum-Classical Hybrid Tensor Networks (HTN) Framework\n## Training HTN with Deep Learning Methods\n## Applications: Quantum State Classification and Quantum-Classical Autoencoder","[{\"question\":\"What limitations of regular tensor networks motivate the proposed HTN framework?\",\"answer\":\"The document identifies restrictions in representation power and architecture scalability, which limit regular tensor networks in machine learning, especially deep learning.\"},{\"question\":\"How does HTN combine tensor networks with classical neural networks?\",\"answer\":\"HTN merges tensor networks with classical neural network components (e.g., fully connected, convolutional, recurrent networks) into a single deep learning architecture, allowing the network to be trained end-to-end.\"},{\"question\":\"Which training methods does the document state can be used to train HTN?\",\"answer\":\"HTN can be trained in a deep-learning manner using standard optimization techniques such as backpropagation and stochastic gradient descent.\"}]","Quantum-Classical Machine learning by Hybrid Tensor Networks | 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limitations of regular tensor networks motivate the proposed HTN framework?","Question",{"text":75,"@type":76},"The document identifies restrictions in representation power and architecture scalability, which limit regular tensor networks in machine learning, especially deep learning.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does HTN combine tensor networks with classical neural networks?",{"text":80,"@type":76},"HTN merges tensor networks with classical neural network components (e.g., fully connected, convolutional, recurrent networks) into a single deep learning architecture, allowing the network to be trained end-to-end.",{"name":82,"@type":73,"acceptedAnswer":83},"Which training methods does the document state can be used to train HTN?",{"text":84,"@type":76},"HTN can be trained in a deep-learning manner using standard optimization techniques such as backpropagation and stochastic gradient 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