[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117308-en":3,"doc-seo-117308-105":30,"detail-sidebar-cat-0-en-105":90},{"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":21,"is_downloadable":21,"audit_status":21,"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},117308,687207024643,"Oliver","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Machine Learning on Quantum Systems - Quantum Machine Learning Approaches Overview","Quantum machine learning applies machine learning ideas to quantum devices, targeting advantages over classical ML through exponentially large feature maps, native quantum input processing, and non-classical correlations from entanglement. The material contrasts two QML views: a gate-based method using parameterized quantum circuits where data are embedded with unitary gates and trainable ansatz parameters are optimized via classical optimizers, and a complex-dynamics method using quantum reservoir computing with fixed quantum dynamics (e.g., TFIM) as the reservoir. The project goal is to explain mechanisms, compare capabilities, and evaluate expressivity via eigentasks and resolvable expressive capacity.","Machine Learning on Quantum Systems  \nNils-Erik Schütte*1,2 , Niclas Götting2 , Hauke Müntinga 1 , Meike List 1,3 and Christopher Gies2  \n1 German Aerospace Center (DLR), Institute for Satellite Geodesy and Inertial Sensing, Bremen  \n2 Institute for Theoretical Physics, University of Bremen, Bremen  \n3 University of Bremen, Bremen  \n* [nils-erik.schuette@dlr.de](nils-erik.schuette@dlr.de)  \nWhy do we want to do quantum machine learning?  \nMachine learning (ML) enables us to use computer systems for human-like tasks.  \nNeural networks are inspired by the human brain and consist of neurons that are connected by edges modelling the synapses of a brain.  \nQuantum computing describes information processing with a device, whose working principles are governed by the laws of quantum mechanics.  \nQuantum systems possess unique properties that scientists try to exploit to gain advantagesand functionalities beyond classical ML:  \n• feature maps into exponentially large phase spaces   \n• native processing of quantum input   \n• non-classical correlations via entanglement   \nQuantum machine learning (QML) can be viewed as A) implementing algorithms through quantum gates on quantum computers, or B) using the inherent temporal dynamics of quantum systems as input-output map.  \nA) Gate-Based Approach:  \nParameterized Quantum Circuits (PQCs)  \nClassical Computer  \n• basic unit of information: bit (0 or 1)  \n• NOT-gate is the only non-trivial singlebit gate  \n• AND-gate as example for a two-bit gate  \nParameterized Quantum Circuits (PQCs)  \n• gates are represented by unitary matrices  \nQuantum Computer  \n• information is stored in quantum bits (qubits)  \n• infinite number of single-qubit gates, which rotate the state on the Bloch sphere  \n• arbitrary superpositions are possible  \n• PQCs are realized by making the unitary matrices dependent on real parameters  \nWorkflow:  \n1. use unitary gates 􀜵(􀝔) to embed data into the quantum system  \n2. use a block of parameterized gates 􀜷 (􀟠) (called ansatz) as trainable part of the circuit  \n3. perform measurement on the system  \n4. use an optimizer on a classical computer to update the parameters  \nWhy does it work-an example:  \n• use a single qubit PQC to fit a sine curve  \n• inputs:  ~~ ~~   \n• parameter:  ~~ ~~   \n• the measured expectation value is analytically by  \nnoisy  \ngiven  \nB) Complex Dynamics Approach: Quantum Reservoir Computing (QRC)  \nClassical Reservoir Computing  \n• inspired by the human brain  \n• a reservoir computer is a recurrent neural network with fixed weights; only the weights of the linear readout layer are trained with a simple linear regression  \n• computation may be viewed as any transformation of an input signal to an output signal arising from the intrinsic system dynamics  \n• physical RC: the reservoir is realized by a real physical system, [e.g. an](e.g. an) origami-structure [1]  \nQuantum Reservoir Computing (QRC)  \n• quantum system is used as reservoir  \n• example is the transverse-field Ising model (TFIM):   \n• dynamics of the system are described by the unitary time-evolution operator:  \n[1] Bhovad et al., Sci Rep 11 , 13002 (2021)  \nGoal of the Quantum Fellowship Project  \nUnderstand the working mechanisms of QML algorithms that rely on either of the two approaches and compare their capabilities and limitations.  \nFirst connection: Embed the TFIM on a gate-based quantum computing architecture and compare it with a PQC.  \nOne goal is to quantify and compare the expressivities of both approaches [2, 3], via calculation of  \n• eigentasks: set of orthogonal functions which can be optimally approximated by the system  \n• resolvable expressive capacity (REC): quantification of how many linearly independent functions can be expressed by the system  \n[2] Schuld et al., Phys. Rev. A 103 , 032430 (2021)  \n[3] Hu et al., Phys. Rev. X 13 , 041020 (2023)  \nQML Strategies Side by Side  \nA) Gate-based approach:  \n• potential to be realized on currently available noisy intermediate s","cbCaiiYufmBH93Ky","https://ap.wps.com/l/cbCaiiYufmBH93Ky","pdf",1177834,2,1,"English","en",105,"# Why do we want to do quantum machine learning?\n## Quantum advantages over classical ML\n# QML viewpoints and approaches\n## A) Gate-based approach: Parameterized Quantum Circuits (PQCs)\n## B) Complex dynamics approach: Quantum Reservoir Computing (QRC)\n# Goal of the Quantum Fellowship Project\n## Embedding TFIM and comparing expressivity\n# QML strategies side by side\n## Gate-based vs complex dynamics\n# Conclusion","[{\"question\":\"What advantages does quantum machine learning aim to achieve over classical machine learning?\",\"answer\":\"It targets benefits from exponentially large phase-space feature maps, native processing of quantum inputs, and non-classical correlations produced by entanglement.\"},{\"question\":\"How does the gate-based approach using parameterized quantum circuits (PQCs) work?\",\"answer\":\"Data are embedded with unitary gates, a trainable ansatz block applies parameterized gates, the system is measured to obtain expectation values, and a classical optimizer updates circuit parameters.\"},{\"question\":\"What is quantum reservoir computing (QRC) and how does it train?\",\"answer\":\"A quantum system acts as a reservoir, using fixed intrinsic dynamics; training focuses on a linear readout layer (via linear regression), and noise can even improve performance to some extent.\"}]","Machine Learning on Quantum Systems - Quantum Machine Learning Approaches Overview | PDF",1785675104,3,{"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":85,"head_meta":87,"extra_data":89,"updated_unix":28},"machine-learning-on-quantum-systems-quantum-machine-learning-approaches-overview","",{"@graph":36,"@context":84},[37,52,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,49],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":29},"https://docshare.wps.com/document/research-report/",{"item":50,"name":13,"@type":43,"position":51},"https://docshare.wps.com/document/machine-learning-on-quantum-systems-quantum-machine-learning-approaches-overview/117308/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":41,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-09-05","2026-08-02",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What advantages does quantum machine learning aim to achieve over classical machine learning?","Question",{"text":74,"@type":75},"It targets benefits from exponentially large phase-space feature maps, native processing of quantum inputs, and non-classical correlations produced by entanglement.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the gate-based approach using parameterized quantum circuits (PQCs) work?",{"text":79,"@type":75},"Data are embedded with unitary gates, a trainable ansatz block applies parameterized gates, the system is measured to obtain expectation values, and a classical optimizer updates circuit parameters.",{"name":81,"@type":72,"acceptedAnswer":82},"What is quantum reservoir computing (QRC) and how does it train?",{"text":83,"@type":75},"A quantum system acts as a reservoir, using fixed intrinsic dynamics; 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