[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85480-en":3,"doc-seo-85480-105":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":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85480,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","Graph-Based Bayesian Optimization for Quantum Circuit Architecture Search with Uncertainty Calibrated Surrogates","Quantum circuit design becomes a key bottleneck for practical quantum machine learning on complex, real-world data. The framework introduces automated variational quantum circuit (VQC) discovery and refinement using graph-based Bayesian optimization with a graph neural network surrogate. Circuits are encoded as graphs and selected through an expected-improvement acquisition function driven by surrogate uncertainty calibrated via Monte Carlo dropout. A hybrid quantum–classical variational classifier evaluates candidates on the NF-ToN-IoT-V2 cybersecurity dataset, with noise-robust benchmarks across multiple quantum noise channels, using reproducible, scalable implementation.","Graph-Based Bayesian Optimization for Quantum Circuit Architecture Search with Uncertainty Calibrated Surrogates  \nPrashant Kumar Choudhary 1 , Nouhaila Innan2,3 , Muhammad Shafique2,3  and Rajeev Singh 1   \n1Department of Physics, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India  \n2eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE  \n3Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD, Abu Dhabi, UAE  \n[prashantkchoudhary.rs.phy22@iitbhu.ac.in nouhaila.innan@nyu.edu muhammad.shafique@nyu.edu rajeevs.phy@iitbhu.ac.in](prashantkchoudhary.rs.phy22@iitbhu.ac.in nouhaila.innan@nyu.edu muhammad.shafique@nyu.edu rajeevs.phy@iitbhu.ac.in)  \narXiv :2512 .09586v2 [ quant-ph] 12 Jul 2026  \nAbstract. Quantum circuit design is a key bottleneck for practical quantum machine learning on complex, real-world data. We present an automated framework that discovers and refines variational quantum circuits (VQCs) using graph-based Bayesian optimization with a graph neural network (GNN) surrogate. Circuits are represented as graphs, mutated and selected via an expected improvement acquisition function informed by surrogate uncertainty with Monte Carlo dropout. Candidate circuits are evaluated with a hybrid quantum–classical variational classifier on the next-generation firewall-telemetry and network internet of things (NF-ToN-IoT-V2) cybersecurity dataset, after feature selection and scaling for quantum embedding. We benchmark our pipeline against an MLP-based surrogate, random search, and greedy GNN selection. The GNN-guided optimizer consistently finds circuits with lower complexity and competitive or superior classification accuracy compared to all baselines. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit-flip noise. The implementation is fully reproducible, with time benchmarking and export of best-found circuits, providing a scalable and interpretable route to automated quantum circuit discovery.  \nKeywords: Quantum Machine Learning, Variational Quantum Circuits, Bayesian Optimization, Graph Neural Networks, Quantum Architecture Search, Surrogate Modeling  \n1 Introduction  \nVariational quantum circuits (VQCs) have become a central computational primitive for many near-term quantum algorithms, including variational quantum classifier (VQ-C), Quantum Neural Network (QNN), quantum generative adversarial network (QGAN), variational quantum eigensolver (VQE), and quantum approximate optimization algorithm (QAOA)[1–13] . The performance of a VQC depends critically on both its parameter values and architectural design, defined by the arrangement, type, and connectivity of quantum gates within the circuit [14–17] . Designing VQC architectures for noisy intermediate-scale quantum (NISQ) devices thus presents a high-dimensional, non-convex optimization problem, with a combinatorial search space that quickly renders brute-force or exhaustive enumeration intractable as the number of qubits and circuit depth increase [18, 19] .  \nTo address this challenge, recent work on automated quantum architecture search has adopted techniques from classical neural architecture search (NAS) [20, 21], evolutionary strategies, and black-box optimization to systematically explore the quantum circuit design space [22–27] . In particular, Bayesian optimization (BO) provides a principled and sample-efficient framework for global optimization of expensive-to-evaluate objectives, making it highly suitable for quantum circuit architecture search, where each candidate must be validated via simulation or hardware execution [28–32] .  \nOne of the main challenges in BO lies in constructing a surrogate model that can both accurately predict a circuit’s performance and provide calibrated epistemic (model) uncertainty that shrinks with data, as opposed to aleatoric (n","cbCais4ewcBBFJXC","https://ap.wps.com/l/cbCais4ewcBBFJXC","pdf",2155064,1,17,"English","en",105,"# 1 Introduction\n## Variational quantum circuits and architecture search challenges\n## Bayesian optimization and surrogate modeling\n## Need for structure-aware surrogates using GNNs\n# 2 Related Concepts (excerpt)","[{\"question\":\"How does the proposed method represent and search for quantum circuit architectures?\",\"answer\":\"Quantum circuits are represented as graphs, then mutated and selected using a Bayesian optimization expected-improvement acquisition function that leverages surrogate uncertainty calibrated by Monte Carlo dropout.\"},{\"question\":\"What role does the graph neural network surrogate play in the optimization process?\",\"answer\":\"A GNN surrogate predicts circuit performance while preserving graph-structured information (gate connectivity/topology) and provides calibrated epistemic uncertainty to guide sample-efficient architecture search.\"},{\"question\":\"How are candidate circuits evaluated and how is robustness tested?\",\"answer\":\"Candidates are evaluated using a hybrid quantum–classical variational classifier after feature selection and scaling for quantum embedding on the NF-ToN-IoT-V2 dataset. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit-flip noise.\"}]",1784203910,43,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"graph-based-bayesian-optimization-for-quantum-circuit-architecture-search-with-uncertainty-calibrated-surrogates","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/graph-based-bayesian-optimization-for-quantum-circuit-architecture-search-with-uncertainty-calibrated-surrogates/85480/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the proposed method represent and search for quantum circuit architectures?","Question",{"text":75,"@type":76},"Quantum circuits are represented as graphs, then mutated and selected using a Bayesian optimization expected-improvement acquisition function that leverages surrogate uncertainty calibrated by Monte Carlo dropout.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What role does the graph neural network surrogate play in the optimization process?",{"text":80,"@type":76},"A GNN surrogate predicts circuit performance while preserving graph-structured information (gate connectivity/topology) and provides calibrated epistemic uncertainty to guide sample-efficient architecture search.",{"name":82,"@type":73,"acceptedAnswer":83},"How are candidate circuits evaluated and how is robustness tested?",{"text":84,"@type":76},"Candidates are evaluated using a hybrid quantum–classical variational classifier after feature selection and scaling for quantum embedding on the NF-ToN-IoT-V2 dataset. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit-flip noise.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"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":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]