[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119739-en":3,"doc-seo-119739-105":30,"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119739,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Dequantizing quantum machine learning models using tensor networks","Assessing whether a classical model can efficiently replace a quantum model—dequantization—is essential for judging the real potential of quantum algorithms. This work defines the dequantizability of the function class of variational quantum machine learning (VQML) models via a tensor-network formulation, showing that each VQML model can be treated as a matrix product state (MPS) model with constrained coefficient structure and tensor-product feature maps. It derives conditions for (non-)dequantizability and proposes an efficient classical kernel induced by a quantum kernel, unifying classical and quantum learning in one framework.","Dequantizing quantum machine learning models using tensor networks  \narXiv :2307 .06937v2 [ quant-ph] 21 Dec 2023  \nSeongwook Shin, Yong Siah Teo,∗ and Hyunseok Jeong† Department of Physics and Astronomy, Seoul National University, 08826 Seoul, South Korea  \n(Dated: December 22, 2023)  \nAscertaining whether a classical model can e􀀎ciently replace a given quantum model—dequantization—is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function class of variational quantum-machine-learning (VQML) models by employing the tensor network formalism, e􀀋ectively identifying every VQML model asa subclass of matrix product state (MPS) model characterized by constrained coe􀀎cient MPS and tensor product-based feature maps. From this formalism, we identify the conditions for which a VQML model’s function class is dequantizable or not. Furthermore, we introduce an e􀀎cient quantum kernel-induced classical kernel which is as expressive as given any quantum kernel, hinting at a possible way to dequantize quantum kernel methods. This presents a thorough analysis of VQML models and demonstrates the versatility of our tensor-network formalism to properly distinguish VQML models according to their genuine quantum characteristics, thereby unifying classical and quantum machine-learning models within a single framework.  \nI. INTRODUCTION  \nQuantum machine learning (QML) garners a huge interest among various communities and industries in recent years as a prominent candidate for practical applications on quantum devices [1, 2] . Variational QML (VQML) uses a variational quantum circuit as a data processor, and the variational parameters in the quantum circuit are optimized with the help of classical optimization algorithms in order to learn and predict data outputs. VQML aims to achieve a more powerful ML model by exploiting possible quantum advantage of quantum circuits in noisy intermediate scale quantum (NISQ) era.  \nWhile there exist theoretical proofs that demonstrate the possibility of achieving a quantum advantage in ML tasks in fully quantum settings [3, 4], more e􀀋ort is required to understanding whether ML from classical data can also achieve such a quantum advantage [5–9] .  \nFor this purpose, a fair assessment of VQML and classical ML models is in order, both of which possess inherently di􀀋erent structures. Moreover, the pre-processing of classical data always precedes VQML when they are encoded on NISQ machines. This additional computation might lead to the “dequantization” argument when comparing a classical and quantum model [10, 11] . Moreover, if one does not have access to a coherent quantum memory and quantum channel, then even if the QML uses a ‘quantum state’ as its input, one cannot avoid using classical data to ‘upload’ the quantum state onto the quantum circuit. In this study, we propose a uni􀀌ed tensor-network (TN) formalism to systematically analyze VQML models, which permits us to classify all classicaldata-encoded VQML models into a subclass of matrix product state (MPS) ML models [12] . We introduce the concept of dequantization of the function class of VQML  \n∗ [yong.siah.teo@gmail.com](yong.siah.teo@gmail.com)[ ](yong.siah.teo@gmail.com)† [h.jeong37@gmail.com](h.jeong37@gmail.com)  \nmodels—the e􀀎cient approximation of all function-class outputs of a VQML model using a classical model—and 􀀌nd necessary conditions for (non-)dequantizable VQML models by classical MPS models.  \nMore speci􀀌cally, the TN formalism describes the function output of a VQML model as a linear MPS model form, subsequently separating it into two components: the coe􀀎cient part of the linear model which is in the form of MPS containing all quantum-circuit training parameters and the basis part (or a feature map in the ML lingo), which formulates the basis for the linear model. The number of linearly independent basis functions can scale exponentially with the number of encoding gate","cbCaitc16fa9x9Zc","https://ap.wps.com/l/cbCaitc16fa9x9Zc","pdf",3912537,1,29,"English","en",105,"# Introduction\n# Tensor-network formalism for VQML\n## Function-class decomposition into coefficient MPS and feature map\n# Conditions for dequantization vs non-dequantization\n## Classical MPS comparison and non-dequantizable cases\n# Efficient classical kernel induced by quantum kernels","[{\"question\":\"What does dequantization mean in variational quantum machine learning (VQML)?\",\"answer\":\"Dequantization refers to the efficient classical approximation of all function-class outputs of a VQML model using a classical model.\"},{\"question\":\"How does the tensor-network formalism relate VQML models to matrix product states?\",\"answer\":\"The formalism expresses the VQML function output as a linear MPS form, separating it into a coefficient part captured by an MPS (containing circuit training parameters) and a basis/feature-map part given by a tensor-product structure.\"},{\"question\":\"What determines whether a VQML model is dequantizable or not?\",\"answer\":\"The paper derives necessary conditions for non-dequantizable models, including cases where dimensions scale exponentially with the number of qubits and coefficient MPSs are highly entangled.\"}]","Dequantizing quantum machine learning models using tensor networks | 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does dequantization mean in variational quantum machine learning (VQML)?","Question",{"text":75,"@type":76},"Dequantization refers to the efficient classical approximation of all function-class outputs of a VQML model using a classical model.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the tensor-network formalism relate VQML models to matrix product states?",{"text":80,"@type":76},"The formalism expresses the VQML function output as a linear MPS form, separating it into a coefficient part captured by an MPS (containing circuit training parameters) and a basis/feature-map part given by a tensor-product structure.",{"name":82,"@type":73,"acceptedAnswer":83},"What determines whether a VQML model is dequantizable or not?",{"text":84,"@type":76},"The paper derives necessary conditions for non-dequantizable models, including cases where dimensions scale exponentially with the number of qubits and coefficient MPSs are highly 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