[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122576-en":3,"doc-seo-122576-105":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":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":27,"seo_description":14,"update_tm":28,"read_time":29},122576,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Encoding molecular structures in quantum machine learning","Quantum machine learning (QML) offers strong potential for analyzing chemical datasets, but conventional quantum data-encoding methods such as fingerprint encoding struggle to represent molecular substructures accurately. The work proposes the quantum molecular structure encoding (QMSE) scheme, embedding molecular bond orders and interatomic couplings as a hybrid Coulomb-adjacency matrix through direct one- and two-qubit rotations in parametrised circuits. Results show improved, interpretable state separability and robust trainability for classification and regression tasks. The paper also proves a fidelity-preserving chain-contraction theorem that reuses substructures to reduce qubit counts, demonstrated on long-chain fatty acids.","Mach. Learn.: Sci. Technol. 6 (2025) 045076 [https://doi.org/10.1088/2632-2153/ae304f](https://doi.org/10.1088/2632-2153/ae304f)  \n|  |\n| --- |\n|  |\n| OPEN ACCESS\u003Cbr>RECEIVED\u003Cbr>27 July 2025\u003Cbr>REVISED\u003Cbr>20 November 2025\u003Cbr>ACCEPTED FOR PUBLICATION 22 December 2025\u003Cbr>PUBLISHED\u003Cbr>31 December 2025 |\n\nOriginal content from this work may be used under the terms of the  \nCreative Commons Attribution 4 .0 licence.  \nAny further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  \nPAPER  \nEncoding molecular structures in quantum machine learning  \nChoy Boy1,2, ∗􀁂, Edoardo Altamura1,2,4􀁂, Dilhan Manawadu2􀁂, Ivano Tavernelli3􀁂, Stefano Mensa2􀁂 and David J Wales1􀁂  \n1 2  \n3 4  \n∗  \nYusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom  \nIBM Quantum, IBM Research Zurich, Rüschlikon 8803, Switzerland Shared first-authorship.  \nAuthor to whom any correspondence should be addressed.  \n[E-mail: bc537@cam.ac.uk](E-mail: bc537@cam.ac.uk)  \nKeywords: quantum computing, computational chemistry, emerging technologies  \nAbstract  \nQuantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of chemical moieties in such datasets. In this contribution, we introduce the quantum molecular structure encoding (QMSE) scheme, which encodes the molecular bond orders and interatomic couplings expressed as a hybrid Coulomb-adjacency matrix, directly as one-and two-qubit rotations within parametrised circuits. We show that this strategy provides an efficient and interpretable method in improving state separability between encoded molecules compared to other fingerprint encoding methods, which is especially crucial for the success in preparing feature maps in QML workflows. To benchmark our method, we train a parametrised ansatz on molecular datasets to perform classification of state phases and regression on boiling points, demonstrating the competitive trainability and generalisation capabilities of QMSE. We further prove a fidelity-preserving chain-contraction theorem that reuses common substructures to cut qubit counts, with an application to long-chain fatty acids. We expect this scalable and interpretable encoding framework to greatly pave the way for practical QML applications of molecular datasets.  \n1. Introduction  \nThe integration of machine learning (ML) techniques in chemistry has led to significant advances, such as improved prediction of protein structures [1] and the estimation of blood-brain barrier permeability for small molecules as potential drug candidates [2] . Quantum computing is a promising approach for enhancing ML pipelines involving classical and quantum data [3] . In this context, quantum machine learning (QML) algorithms have been proposed to improve in-silico screening and quantum-assisted drug design [4–6] . In the near term, QML may continue to deliver practical advantages in specialised tasks, such as learning from quantum data, simulating physical systems, and employing quantum feature spaces, particularly when paired with hybrid quantum–classical architectures. As quantum hardware is set to improve with longer qubit coherence times [7–9], reduced leakage [10], and suppressed cross-talk [11], QML models may outperform their classical counterparts in representing and optimising high-dimensional, structured, and entangled data, especially in domains like quantum chemistry, material science, and drug discovery. This potential is expected to become even more significant in the fault-tolerant quantum computing (FTQC) regime, where QML is expected to offer competitive speedups for variational [12] and kernel methods, feature selection [13], and generative ","cbCaip6eqg0OLxHY","https://ap.wps.com/l/cbCaip6eqg0OLxHY","pdf",1610286,1,20,"English","en",105,"# Abstract\n# Introduction\n## Motivation for quantum machine learning in chemistry\n## Molecular representation learning and classical encodings\n## Quantum encoding schemes for QML","[{\"question\":\"Why are conventional quantum data-encoding schemes difficult for chemical datasets?\",\"answer\":\"Conventional schemes like fingerprint encoding are generally unfeasible for accurate representation of chemical moieties, limiting how well molecular substructures can be captured.\"},{\"question\":\"What does the QMSE encoding scheme do?\",\"answer\":\"QMSE encodes molecular bond orders and interatomic couplings using a hybrid Coulomb-adjacency matrix, implemented directly via one- and two-qubit rotations in parametrised circuits.\"},{\"question\":\"How does QMSE improve QML performance for molecular tasks?\",\"answer\":\"QMSE provides an efficient and interpretable way to improve state separability between encoded molecules, which is especially important for feature map preparation in QML workflows. Experiments show competitive trainability and generalisation.\"}]","Encoding molecular structures in quantum machine learning | PDF",1785811404,50,{"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},"encoding-molecular-structures-in-quantum-machine-learning","",{"@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/encoding-molecular-structures-in-quantum-machine-learning/122576/",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","2026-08-04",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},"Why are conventional quantum data-encoding schemes difficult for chemical datasets?","Question",{"text":75,"@type":76},"Conventional schemes like fingerprint encoding are generally unfeasible for accurate representation of chemical moieties, limiting how well molecular substructures can be captured.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does the QMSE encoding scheme do?",{"text":80,"@type":76},"QMSE encodes molecular bond orders and interatomic couplings using a hybrid Coulomb-adjacency matrix, implemented directly via one- and two-qubit rotations in parametrised circuits.",{"name":82,"@type":73,"acceptedAnswer":83},"How does QMSE improve QML performance for molecular tasks?",{"text":84,"@type":76},"QMSE provides an efficient and interpretable way to improve state separability between encoded molecules, which is especially important for feature map preparation in QML workflows. 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