[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119679-en":3,"doc-seo-119679-105":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},119679,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","High Dimensional Quantum Machine Learning With Small Quantum Computers","Quantum computers can accelerate machine learning, yet limited qubit counts hinder running large circuits directly. Circuit partitioning evaluates many smaller subcircuits on smaller devices and combines results to reproduce the larger circuit, but it becomes impractical due to the huge number of required evaluations. This work studies when subcircuits are unnecessary and proposes a machine learning model to estimate full-circuit outputs using far fewer evaluations. The method is tested on digit recognition and on approximating random 10-qubit parametrized quantum circuits via simulated access to a 5-qubit computer, outperforming a neural-network baseline and suggesting usefulness across the NISQ era.","High Dimensional Quantum Machine Learning With Small Quantum Computers  \narXiv :2203 . 13739v4 [ quant-ph] 12 Jul 2023  \nS. C. Marshall, C. Gyurik, and V. Dunjko  \nLeiden University, Leiden, The Netherlands  \nQuantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. To deal with this limitation the community has produced a set of techniques for evaluating large quantum circuits on smaller quantum devices. These techniques work by evaluating many smaller circuits on the smaller machine, that are then combined in a polynomial to replicate the output of the larger machine. This scheme requires more circuit evaluations than are practical for general circuits. However, we investigate the possibility that for certain applications many of these subcircuits are superfluous, and that a much smaller sum is sufficient to estimate the full circuit. We construct a machine learning model that may be capable of approximating the outputs of the larger circuit with much fewer circuit evaluations. We successfully apply our model to the task of digit recognition, using simulated quantum computers much smaller than the data dimension. The model is also applied to the task of approximating a random 10 qubit PQC with simulated access to a 5 qubit computer, even with only relatively modest number of circuits our model provides an accurate approximation of the 10 qubit PQCs output, superior toa neural network attempt. The developed method might be useful for implementing quantum models for larger data throughout the NISQ era.  \n1 Introduction  \nQuantum machine learning is often listed as oneof the most promising applications of a near term  \nS. C. Marshall: [s.c. marshall@liacs.leidenuniv.nl](s.c. marshall@liacs.leidenuniv.nl)  \nquantum computer [28], with important early successes in a range of problems, from classi􀀌cation [14, 31] to generative modelling [20] . However the broader roll out of these methods to real world problems is tempered, in part, by the limited size of quantum computers. Among other limitations, current quantum computers lack enough qubits to run large circuits. Some \\circuit partitioning schemes\" [6, 22 , 25] have been proposed to simulate larger circuits on smaller devices by partitioning the full circuit into a set of smaller circuits (see 􀀌gure 1) . However, the exponential number of circuits needed by these schemes is completely intractable formost applications, with billions of sub-circuit evaluations required for even modest quantum machine learning instances.  \nIn this work we examine the necessity of each subcircuit in producing an approximation of some partitioned circuit, presenting reasoning that a smaller amount of circuits could be suf-􀀌cient in some cases. We then use this as inspiration for a new machine learning technique, which reconciles the need for larger circuit instances with a􀀋ordable runtimes. Our new technique takes the same form as a given generic machine learning architecture that has been partitioned using the aforementioned techniques but with vastly fewer terms.  \nWe develop the basic theory behind this technique in Section 3, consider its generalisation error in Section 4 and test it experimentally in Section 6 on an instances of handwritten digit recognition using a 64 qubit ansatz with access to only a simulated 8 qubit computer (without use of excessive dimensionality reduction, such as dimensional principal component analysis) . We also include an experiment testing the model's ability to replicate the output of larger unpartitioned circuits. Error analysis and the speci􀀌cs of an evaluation and training schemes are presented in Section 5.  \nAccepted in  2023-03-01, click title to verify. Published under CC-BY 4 .0. 1  \nFigure 1: The fundamental notion of circuit partitioning. A potential partition (peach coloured and mint coloured) exists but is joined by a 2-qubit gate, G. By expressing G as a sum of single qubit u","cbCaimxBn8BGcldC","https://ap.wps.com/l/cbCaimxBn8BGcldC","pdf",1057190,1,17,"English","en",105,"# Introduction\n# Related work\n## Circuit partitioning and efficiency\n## Noise reduction and gradients\n# Method overview\n## Theory and generalisation\n## Experimental setup\n# Experiments\n## Handwritten digit recognition\n## Approximating unpartitioned circuits","[{\"question\":\"Why are circuit partitioning techniques needed for quantum machine learning on small quantum devices?\",\"answer\":\"Because current quantum computers have limited qubit counts, partitioning lets larger circuits be simulated by evaluating outputs from many smaller subcircuits on a smaller device.\"},{\"question\":\"What limitation does this paper address in existing partitioning approaches?\",\"answer\":\"It addresses the intractably large number of subcircuit evaluations required by standard partitioning schemes, which can become impractical for general quantum machine learning tasks.\"},{\"question\":\"How does the proposed model reduce the number of circuit evaluations?\",\"answer\":\"It builds a machine learning model that approximates the larger circuit output using a much smaller sum of subcircuits, leveraging cases where many subcircuits are superfluous.\"}]","High Dimensional Quantum Machine Learning With Small Quantum Computers | 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are circuit partitioning techniques needed for quantum machine learning on small quantum devices?","Question",{"text":75,"@type":76},"Because current quantum computers have limited qubit counts, partitioning lets larger circuits be simulated by evaluating outputs from many smaller subcircuits on a smaller device.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What limitation does this paper address in existing partitioning approaches?",{"text":80,"@type":76},"It addresses the intractably large number of subcircuit evaluations required by standard partitioning schemes, which can become impractical for general quantum machine learning tasks.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed model reduce the number of circuit evaluations?",{"text":84,"@type":76},"It builds a machine learning model that approximates the larger circuit output using a much smaller sum of subcircuits, leveraging cases where many subcircuits are 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