[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119903-en":3,"doc-seo-119903-105":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},119903,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Decohering Tensor Network Quantum Machine Learning Models - Paper Study","Tensor network quantum machine learning (QML) models offer promising capabilities for near-term quantum hardware, but qubit decoherence can reduce classification performance. It remains unclear how much performance loss can be offset by adding ancillas, which increases the virtual bond dimension of the models. The study analyzes the trade-off between decoherence and ancilla augmentation for two tensor-network QML architectures using a regression-based view of the decoherence effect. Numerical results show that a fully-decohered unitary TTN with two ancillas matches or exceeds the non-decohered unitary TTN, indicating that adding at least two ancillas is beneficial across decoherence strengths.","arXiv :2209 .01195v1 [ quant-ph] 2 Sep 2022  \nDecohering Tensor Network Quantum Machine Learning Models  \nHaoran Liao, 1, 2, 􀀃 Ian Convy,3, 2 Zhibo Yang,3, 2 and K. Birgitta Whaley3, 2  \n1 Department of Physics, University of California, Berkeley, CA 94720, USA  \n2 Berkeley Quantum Information and Computation Center,  \nUniversity of California, Berkeley, CA 94720, USA  \n3 Department of Chemistry, University of California, Berkeley, CA 94720, USA  \n(Dated: September 5, 2022)  \nTensor network quantum machine learning (QML) models are promising applications on nearterm quantum hardware. While decoherence of qubits is expected to decrease the performance of QML models, it is unclear to what extent the diminished performance can be compensated for by adding ancillas to the models and accordingly increasing the virtual bond dimension of the models. We investigate here the competition between decoherence and adding ancillas on the classification performance of two models, with an analysis of the decoherence effect from the perspective of regression. We present numerical evidence that the fully-decohered unitary tree tensor network (TTN) with two ancillas performs at least as well as the non-decohered unitary TTN, suggesting that it is beneficial to add at least two ancillas to the unitary TTN regardless of the amount of decoherence may be consequently introduced.  \nI. INTRODUCTION  \nTensor networks (TNs) are compact data structures engineered to efficiently approximate certain classes of quantum states used in the study of quantum many-body systems. Many tensor network topologies are designed to represent the low-energy states of physically realistic systems by capturing certain entanglement entropy and correlation scalings of the state generated by the network [1–4] . Some tensor networks allow for interpretations of coarse-grained states at increasing levels of the network as a renormalization group or scale transformation that retains information necessary to understand the physics on longer length scales [5, 6] . This motivates the usage of such networks to perform discriminative tasks, in a manner similar to classical machine learning (ML) using neural networks with layers like convolution and pooling that perform sequential feature abstraction to reduce the dimension and to obtain a hierarchical representation of the data [7, 8] . In addition to applying TNs such as the tree tensor network (TTN) [9] and the multiscale entanglement renormalization ansatz (MERA)  \n[10] for quantum-inspired tensor network ML algorithms [11–13], there have been efforts to variationally train the generic unitary nodes in TNs to perform quantum machine learning (QML) on data-encoded qubits. The unitary TTN [14, 15] and MERA [14] have been explored for this purpose mindful of feasible implementations, such as normalized input states, on a quantum computer.  \nTensor network QML models are linear classifiers on a feature space whose dimension grows exponentially in the number of data qubits and where the feature map is nonlinear. Such models employ fully-parametrized unitary tensor nodes that form a rich subset of larger unitaries with respect to all input and output qubits upon tensor contractions. They provide circuit variational ansatze more general than those with common parametrized gate  \nsets [16–18], although their compilations into hardwaredependent native gates are more costly because of the need to compile generic unitaries.  \nIn this work, we focus on discriminative QML. We investigate and numerically quantify the competing effect between decoherence and increasing bond dimension of two common tensor network QML models, namely the unitary TTN and the MERA. By removing the offdiagonal elements, i.e., the coherence, from the density matrix of a quantum state, we reduce its representation down to a classical probability distribution over a given basis. The evolution through the unitary matrices at every layer of the model, together with the full dephas","cbCaiqMkgsmtkgFf","https://ap.wps.com/l/cbCaiqMkgsmtkgFf","pdf",2063872,1,15,"English","en",105,"# Introduction\n## Tensor networks and quantum machine learning\n## Discriminative QML and model expressiveness\n# Decoherence and regression perspective\n## Dephasing leading to Bayesian updates\n# Ancilla addition and virtual bond dimension\n## Trade-off between noise and expressiveness\n# Related probabilistic graphical models\n## Fully-dephased tensor networks","[{\"question\":\"Why can decoherence harm tensor network quantum machine learning performance?\",\"answer\":\"Decoherence reduces the quantum information carried by the model, limiting the effectiveness of the classification task. In the dephased limit, the model’s quantumness is removed, which can reduce representative flexibility.\"},{\"question\":\"How does adding ancillas affect the models when decoherence is present?\",\"answer\":\"Adding ancillas increases the virtual bond dimension, enlarging the dimension of the classical probability distributions and their conditionals. This can partially or fully compensate for the lost expressiveness due to decoherence.\"},{\"question\":\"What do the numerical results conclude about unitary TTN with ancillas under full decoherence?\",\"answer\":\"A fully-decohered unitary tree tensor network with two ancillas performs at least as well as the non-decohered unitary TTN, suggesting at least two ancillas are beneficial regardless of the decoherence level.\"}]","Decohering Tensor Network Quantum Machine Learning Models - Paper Study | PDF",1785726918,38,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"decohering-tensor-network-quantum-machine-learning-models-paper-study","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/decohering-tensor-network-quantum-machine-learning-models-paper-study/119903/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why can decoherence harm tensor network quantum machine learning performance?","Question",{"text":75,"@type":76},"Decoherence reduces the quantum information carried by the model, limiting the effectiveness of the classification task. In the dephased limit, the model’s quantumness is removed, which can reduce representative flexibility.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does adding ancillas affect the models when decoherence is present?",{"text":80,"@type":76},"Adding ancillas increases the virtual bond dimension, enlarging the dimension of the classical probability distributions and their conditionals. This can partially or fully compensate for the lost expressiveness due to decoherence.",{"name":82,"@type":73,"acceptedAnswer":83},"What do the numerical results conclude about unitary TTN with ancillas under full decoherence?",{"text":84,"@type":76},"A fully-decohered unitary tree tensor network with two ancillas performs at least as well as the non-decohered unitary TTN, suggesting at least two ancillas are beneficial regardless of the decoherence level.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]