[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-327131-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-327131-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","spectral-geometry-and-bosonicbloch-probes-explorations-in-quantum-learning","Spectral Geometry and Bosonic–Bloch Probes - Explorations in Quantum Learning","","This paper investigates how spectral geometry emerges in quantum learning models and how it can be diagnosed using physically grounded probes. In graph-regularized quantum networks, training reshapes the output similarity graph, altering the Laplacian spectrum and increasing effective spectral dimension. Edge-resolved two-boson interference directly probes this restructuring, linking bosonic enhancement to the Fiedler edge split. A phase diagram shows nonmonotonic dependence on coupling and noise, with hardware confirming shot-noise-limited interference behavior. A hybrid quantum autoencoder further uses Bloch-space drift as a geometric diagnostic of latent representations.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/spectral-geometry-and-bosonicbloch-probes-explorations-in-quantum-learning/327131/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/spectral-geometry-and-bosonicbloch-probes-explorations-in-quantum-learning/327131.png","ImageObject",300,407,{"name":42,"@type":43},"Logic","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-21",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How does spectral geometry emerge in the proposed quantum learning models?","Question",{"text":63,"@type":64},"The paper shows that in graph-regularized quantum networks, training reorganizes the output similarity graph, which increases the effective spectral dimension and reshapes the Laplacian spectrum, reflecting geometric structure in learning.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What role do bosonic–Bloch probes play in diagnosing learned structure?",{"text":68,"@type":64},"Edge-resolved two-boson interference acts as a physically grounded probe, with bosonic enhancement correlating to the Fiedler edge split. In a complementary setup, Bloch-space drift provides a geometric diagnostic for the latent representation of a hybrid quantum autoencoder.",{"name":70,"@type":61,"acceptedAnswer":71},"How does performance depend on coupling strength and noise?",{"text":72,"@type":64},"The paper reports a nonmonotonic dependence of performance on coupling strength and noise, where graph regularization improves fidelity only within a restricted regime; hardware experiments confirm the predicted interference behavior within shot-noise uncertainty.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},327131,1790716558,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":145,"read_time":146,"preview_page_count":4},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","Spectral Geometry and Bosonic–Bloch Probes: Explorations in Quantum Learning  \nSantanu Ganguly†, Xing Liang* and Dimitrios Makris  \nQuantum AIResearch Group,  \nSchool of Computer Science and Mathematics,  \nKingston University London,  \nPenrhyn Road, Kingston upon Thames, KT1 2EE, United Kingdom  \n†[e-mail address:](e-mail address: ganguly.santanu@kingston.ac.uk)[ ](e-mail address: ganguly.santanu@kingston.ac.uk)[ganguly.santanu@kingston.ac.uk](e-mail address: ganguly.santanu@kingston.ac.uk)  \n*[e-mail address:](e-mail address: x.liang@kingston.ac.uk)[ ](e-mail address: x.liang@kingston.ac.uk)[x.liang@kingston.ac.uk](e-mail address: x.liang@kingston.ac.uk)  \nThis paper investigates how spectral geometry emerges in quantum learning models and how it can be diagnosed through physically grounded probes. In graph-regularized quantum networks, training reorganizesthe output similarity graph, increasing its effective spectral dimension ( 􀀧S =+0.23) and reshaping the Laplacian spectrum. Edge-resolved two-boson interference provides a direct probe of this restructuring: the bosonic enhancement 􀀧Puv correlates with the Fiedler edge split 􀀧v2  (r = −0.50 ) , establishing a quantitative link between learned spectral partitions and interference signatures. A phase diagram reveals a nonmonotonic dependence of performance on coupling strength 􀁊 and noise 􀁇 , with graph regularization improving fidelity only within a restricted regime; hardware experiments confirm the predicted interference behavior within shot-noise uncertainty. In a complementary setting, we analyze a hybrid quantum autoencoder and introduce Bloch-space drift as a geometric diagnostic of its latent representation. Using an unsupervised threshold derived from benign data, the model achieves high ranking performance ( ROC − AUC 􀁼 0.99 ) with negligible false-negative rates. Absolute Bloch drift yields strong discrimination ( ROC − AUC 0.9 ), whereas consecutive drift produces near-random classification ( ROC − AUC 􀁼 0.5 ), indicating that detection arises from persistent state-space displacement rather than local fluctuations. Interpreted through the geometry of reduced single-qubit states and their associated quantum Fisher information, these results demonstrate that learning-induced spectral organization manifests as measurable structure in quantum state space. Together, these findings establish a unified spectral–geometric framework for diagnosing quantum learning systems using bosonic and Bloch probes.  \nKeywords: graph neural networks, boson sampling, quantum autoencoder, Bloch drift, security, spectral geometry, quantum learning.  \nI. INTRODUCTION  \nA quantum network connected via suitable nodes can be represented by graphs and be used to implement quantum computations, quantum-to-classical interfaces for measurements, quantum-to-quantum interfaces for different quantum physical systems, and quantum sensors [1, 2], just to name a few. The cost vectors associated with links could include measures that are uniquely quantum, such as fidelity, purity or entanglement measures, none of which are applicable to classical digital data [3] . In the quantum context costs is defined and optimised (minimised) via an entirely different approach leveraging in quantum machine learning (QML) fundamentals owing to the quantum nature of the information being handled [2, 4] . Graph-structured data is one of the commonest in the field of quantum networking and data communication [2, 5, 8, 15, 21] . Graphs consist of sets that are in some way connected or related  \nobjects [2, 3] . We develop a hybrid quantum–classical framework in which bosonic sampling [8, 28] devices generate nonclassical graph features that are processed by a graph neural network for scalable inference. Rather than treating boson sampling as a complexity-theoretic primitive, we use multiphoton interference [5, 43, 55, 93] as a physically grounded probe of relational structure. In addition, we show that the geometry and s","cbCaimOdF5aCwP99","https://ap.wps.com/l/cbCaimOdF5aCwP99","pdf",2860213,37,"English","# Introduction\n## Spectral structure in graph learning\n## Bosonic probes as structural diagnostics\n# Quantum learning with geometric diagnostics","[{\"question\":\"How does spectral geometry emerge in the proposed quantum learning models?\",\"answer\":\"The paper shows that in graph-regularized quantum networks, training reorganizes the output similarity graph, which increases the effective spectral dimension and reshapes the Laplacian spectrum, reflecting geometric structure in learning.\"},{\"question\":\"What role do bosonic–Bloch probes play in diagnosing learned structure?\",\"answer\":\"Edge-resolved two-boson interference acts as a physically grounded probe, with bosonic enhancement correlating to the Fiedler edge split. In a complementary setup, Bloch-space drift provides a geometric diagnostic for the latent representation of a hybrid quantum autoencoder.\"},{\"question\":\"How does performance depend on coupling strength and noise?\",\"answer\":\"The paper reports a nonmonotonic dependence of performance on coupling strength and noise, where graph regularization improves fidelity only within a restricted regime; hardware experiments confirm the predicted interference behavior within shot-noise uncertainty.\"}]","Spectral Geometry and Bosonic–Bloch Probes - Explorations in Quantum Learning | PDF",1789976496,93]