[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118284-en":3,"doc-seo-118284-105":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},118284,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Hybrid Heuristic Algorithms for Adiabatic Quantum Machine Learning Models","Adiabatic quantum machine learning (AQML) methods grounded in the quadratic unconstrained binary optimization (QUBO) formulation have attracted research and industry interest. Many classical learning models can be converted into QUBO, but the training phase becomes a computational bottleneck. Heuristic quantum-annealing solvers, including simulated annealing and multiple start tabu search, are used to accelerate AQML training, yet face scalability limits on large QUBO instances. A hybrid heuristic embedding an r-flip strategy is introduced to improve solution quality and reduce computing time versus the state-of-the-art MSTS approach, validated through benchmark and large-scale experiments under CPU time limits.","Hybrid Heuristic Algorithms for Adiabatic Quantum  \nMachine Learning Models  \nBahram Alidaee, Department of Marketing, School of Business Administration, University of Mississippi, Oxford,  \nMS, USA (e-mail: [balidaee@bus.olemiss.edu](balidaee@bus.olemiss.edu)).  \nHaibo Wang, Division of International Business and Technology Studies, Texas A&MInternational University,  \nLaredo, Texas, USA (e-mail: [hwang@tamiu.edu](hwang@tamiu.edu)).  \nLutfu S.Sua, Department of Management and Marketing, Southern University andA&M College, Baton Rouge,  \nLA, USA (e-mail: [lutfu.sagbansua@subr.edu](lutfu.sagbansua@subr.edu)).  \nWade W. Liu, Department of Computer Science, School of Engineering, University of Mississippi, Oxford, MS,  \nUSA ([e-mail: wliu6636@yahoo.com](e-mail: wliu6636@yahoo.com)).  \nAbstract— The recent developments of adiabatic quantum machine learning (AQML) methods and applications based on the quadratic unconstrained binary optimization (QUBO) model have received attention from academics and practitioners. Traditional machine learning methods such as support vector machines, balanced k-means clustering, linear regression, Decision Tree Splitting, Restricted Boltzmann Machines, and Deep Belief Networks can be transformed into a QUBO model. The training of adiabatic quantum machine learning models is the bottleneck for computation. Heuristics-based quantum annealing solvers such as Simulated Annealing and Multiple Start Tabu Search (MSTS) are implemented to speed up the training ofAQML based on the QUBO model.  \nThe main purpose of this paper is to present a hybrid heuristic embedding an r-flip strategy to solve large-scale QUBO with an improved solution and shorter computing time compared to the state-of-the-art MSTS method. The results of the substantial computational experiments are reported to compare an r-flip strategy embedded hybrid heuristic and a multiple start tabu search algorithm on a set of benchmark instances and three large-scale QUBO instances. The r-flip strategy embedded algorithm provides very high-quality solutions within the CPU time limits of 60 and 600 seconds.  \nIndex Terms—Machine Learning, Quadratic unconstrained binary optimization, Local optimality, r-flip local optimality  \nI. INTRODUCTION  \nTThe recent developments of adiabatic quantum machine learning (AQML) methods and applications based on the quadratic  \nunconstrained binary optimization (QUBO) model have received attention from academics and practitioners (Biamonte et al., 2017; Date et al., 2021; Guan et al., 2021; Hatakeyama-Sato et al., 2022; Orús et al., 2019; von Lilienfeld, 2018) .  \nTraditional machine learning methods such as support vector machines (SVM) (Biamonte et al., 2017; Date et al., 2021) , balanced k-means clustering(BKC)(Date et al., 2021), linear regression(LR)(Date & Potok, 2021), Feature subset selection (FSS)(Chakraborty et al., 2020; Mücke et al., 2023; Otgonbaatar & Datcu, 2021) , Decision Tree Splitting(DTS)(Yawata et al., 2022), Restricted Boltzmann Machines (RBMs)(Xu & Oates, 2021) and Deep Belief Networks (DBNs)(Date et al., 2021) can be transformed into a QUBO model. AQML methods have been applied to many areas, for example, AQML is used to select candidates in materials development(Guan et al., 2021; Hatakeyama-Sato et al., 2022; von Lilienfeld, 2018; Haibo Wang & Alidaee, 2019), to detect the fraud in finance(Grossi et al., 2022; H. Wang et al., 2022), to improve the traffic scheduling(Daugherty et al., 2019), to classify remote sensing data(Cavallaro et al., 2020; Delilbasic et al., 2021), to detect anomaly(Liu & Rebentrost, 2018), to process sensor data and enable quantum walk-in robotic systems (Petschnigg et al., 2019), and to enhance the prediction in renewable energy development(Ajagekar & You, 2022) .  \nThe training process ofAQML models is the bottleneck for implementation. Heuristics-based quantum annealing solvers such as Simulated Annealing (SA)(D-Wave Inc, 2021a) and Multiple Start Tabu Search (MST","cbCaippXahopENDp","https://ap.wps.com/l/cbCaippXahopENDp","pdf",591826,1,14,"English","en",105,"# Introduction\n## AQML and QUBO Formulation\n## Heuristic Quantum Annealing and Scalability Limits\n## Local Search and r-flip Theoretical Results\n## QUBO Model Definition","[{\"question\":\"Why is training AQML models a computational bottleneck?\",\"answer\":\"AQML training requires solving the corresponding QUBO problem. This step becomes computation-heavy, and existing quantum-annealing approaches suffer from scalability issues when QUBO instances grow large.\"},{\"question\":\"How do simulated annealing and multiple start tabu search help in AQML training?\",\"answer\":\"They act as heuristic quantum-annealing solvers to speed up the training process by finding good solutions to the QUBO-based formulation.\"},{\"question\":\"What does the proposed hybrid heuristic with an r-flip strategy achieve?\",\"answer\":\"It embeds an r-flip local search strategy into a hybrid heuristic to obtain higher-quality solutions with shorter computing time than the MSTS method, demonstrated on benchmark and large-scale QUBO instances.\"}]","Hybrid Heuristic Algorithms for Adiabatic Quantum Machine Learning Models | PDF",1785682806,35,{"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},"hybrid-heuristic-algorithms-for-adiabatic-quantum-machine-learning-models","",{"@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/hybrid-heuristic-algorithms-for-adiabatic-quantum-machine-learning-models/118284/",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","2026-08-02",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 is training AQML models a computational bottleneck?","Question",{"text":75,"@type":76},"AQML training requires solving the corresponding QUBO problem. This step becomes computation-heavy, and existing quantum-annealing approaches suffer from scalability issues when QUBO instances grow large.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do simulated annealing and multiple start tabu search help in AQML training?",{"text":80,"@type":76},"They act as heuristic quantum-annealing solvers to speed up the training process by finding good solutions to the QUBO-based formulation.",{"name":82,"@type":73,"acceptedAnswer":83},"What does the proposed hybrid heuristic with an r-flip strategy achieve?",{"text":84,"@type":76},"It embeds an r-flip local search strategy into a hybrid heuristic to obtain higher-quality solutions with shorter computing time than the MSTS method, demonstrated on benchmark and large-scale QUBO instances.","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"]