[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120773-en":3,"doc-seo-120773-105":30,"detail-sidebar-cat-0-en-105":83},{"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},120773,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Encoding optimization for quantum machine learning demonstrated on a superconducting transmon qutrit","Three-level qutrits can realize quantum circuits with fewer components than two-level qubits, motivating their use in quantum machine learning classification. The work studies qutrit parametric circuits for classification and evaluates multiple data-encoding schemes, showing that accuracy depends strongly on the chosen encoding. An encoding-optimization training method is proposed to obtain consistently high classification accuracy. Theory and numerical simulations indicate that a qutrit classifier can reach high accuracy with fewer circuit elements than a comparable qubit system, and experiments on a superconducting transmon qutrit confirm practicality on noisy hardware.","arXiv :2309 . 13036v1 [ quant-ph] 22 Sep 2023  \nEncoding optimization for quantum machine learning demonstrated on a  \nsuperconducting transmon qutrit  \nShuxiang Cao 1 ,∗ Weixi Zhang2 ,∗ Jules Tilly3 , Abhishek Agarwal2 , Mustafa Bakr 1 , Giulio Campanaro 1 , Simone DFasciati 1 , James Wills 1 , Boris Shteynas 1 , Vivek Chidambaram 1 , Peter Leek 1 , and Ivan Rungger2†  \n1 Clarendon Laboratory, Department of Physics,  \nUniversity of Oxford, Oxford, OX1 3PU, United Kingdom  \n2 National Physical Laboratory, Teddington, TW11 0LW, United Kingdom and  \n3 InstaDeep, London, W2 1AY, United Kingdom  \nQutrits, three-level quantum systems, have the advantage of potentially requiring fewer components than the typically used two-level qubits to construct equivalent quantum circuits. This work investigates the potential of qutrit parametric circuits in machine learning classification applications. We propose and evaluate different data-encoding schemes for qutrits, and find that the classification accuracy varies significantly depending on the used encoding. We therefore propose a training method for encoding optimization that allows to consistently achieve high classification accuracy. Our theoretical analysis and numerical simulations indicate that the qutrit classifier can achieve high classification accuracy using fewer components than a comparable qubit system. We showcase the qutrit classification using the optimized encoding method on a superconducting transmon qutrit, demonstrating the practicality of the proposed method on noisy hardware. Our work demonstrates high-precision ternary classification using fewer circuit elements, establishing qutrit parametric quantum circuits as a viable and efficient tool for quantum machine learning applications.  \nI. INTRODUCTION  \nLying at the intersection between quantum computation and machine learning (ML), quantum machine learning (QML) has become a field of growing interest in recent years [1–9] . QML encompasses a large number of techniques and learning tasks, including variational quantum optimization problems [10], resolution of molecular electronic structure problems [11–13], and more general ML tasks, such as using quantum neural networks (QNN) to perform a classification task on classical data [14–21] .  \nQNNs acting on classical input data require the definition of a process to encode the classical information into quantum information [22, 23] . A parameterized quantum circuit is then used as ansatz for the classifier, and its parameters are optimized to minimize a loss function, in analogy to classical neural networks [24] . The most common quantum circuits used as QNNs are tree tensor networks (TTN) [25], multi-scale entanglement renormalization ans¨atze (MERA) [26–28], and their extensions, which include a quantum version of convolutional neural networks (QCNN) [29] . While the cost of encoding classical data onto quantum states in terms of the required circuit depth can limit QML in its potential to bring an advantage over classical methods [7, 30], there are indications that QML may be able to perform tasks that require degrees of entanglement which would be intractable for classical ML [15, 24] .  \nEfficient encoding of classical data into quantum data is understood to be the likely critical driver for the ad-  \n∗ These two authors contributed equally † [ivan.rungger@npl.co.uk](ivan.rungger@npl.co.uk)  \nvantage of QML over classical ML [22, 23 , 31] . One can decide to encode the data onto the amplitudes of the wave function of the quantum state, encoding a vector of O (2􀀣 ) data point onto 􀀣 qubits. This may however require exponential circuit depth to implement, negating any advantage brought from using quantum computing [30] . To reduce the encoding circuit depth at the expense of using more qubits, one can use an encoding scheme based on an unentangled product state of 􀀣 qubits, with the amplitude of the wavefunction coefficient of each qubit encoding a single data point, a","cbCaifEF4yjGKrFO","https://ap.wps.com/l/cbCaifEF4yjGKrFO","pdf",852756,1,14,"English","en",105,"# Introduction\n## Encoding classical data into quantum states\n## Qutrits and qudits for efficient quantum circuits\n## Qutrit quantum classification and hardware implementation","[{\"question\":\"How is the method validated on real hardware?\",\"answer\":\"The optimized encoding method is demonstrated for qutrit classification on a superconducting transmon qutrit. The results showcase practicality under noisy hardware conditions.\"}]","Encoding optimization for quantum machine learning demonstrated on a superconducting transmon qutrit | PDF",1785731971,35,{"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":78,"head_meta":80,"extra_data":82,"updated_unix":28},"encoding-optimization-for-quantum-machine-learning-demonstrated-on-a-superconducting-transmon-qutrit","",{"@graph":36,"@context":77},[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-optimization-for-quantum-machine-learning-demonstrated-on-a-superconducting-transmon-qutrit/120773/",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":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"How is the method validated on real hardware?","Question",{"text":75,"@type":76},"The optimized encoding method is demonstrated for qutrit classification on a superconducting transmon qutrit. 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