[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122633-en":3,"doc-seo-122633-105":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},122633,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Massively parallel hybrid quantum-classical machine learning for kernelized time-series classification - arXiv:2305.05881","Supervised time-series classification is widely used across finance, astronomy, biosensors, and other domains. This work develops hybrid quantum-classical machine learning that infers pairwise temporal relationships via a time-series Hamiltonian kernel (TSHK). The TSHK is built from sums of quantum-state inner products generated with a parameterized time evolution operator and then optimally weighted using multiple-kernel-learning ideas. Treating kernel weighting as differentiable convex optimization yields an end-to-end learnable QCC-net whose TSHK generalizes for kernelized methods like SVM, implemented in parallel on quantum hardware.","Massively parallel hybrid quantum-classical machine learning for kernelized  \ntime-series classi􀀌cation  \narXiv :2305 .05881v1 [ quant-ph] 10 May 2023  \nJack S. Baker 1 , Gilchan Park2 , Kwangmin Yu2 ,􀀃 Ara Ghukasyan 1 , Oktay Goktas 1 , and Santosh Kumar Radha 1y  \n1 Agnostiq Inc. , 325 Front St W, Toronto, ON M5V 2Y1 and  \n2 Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA (Dated: May 11, 2023)  \nSupervised time-series classi􀀌cation garners widespread interest because of its applicability throughout a broad application domain including 􀀌nance, astronomy, biosensors, and many others. In this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a time-series Hamiltonian kernel (TSHK) . A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as adi􀀋erentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM) . Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the e􀀎cient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.  \nI. INTRODUCTION  \nProcesses and systems which produce observable characteristics evolving with time are present in topics as disparate as 􀀌nance, sensor technologies, medicine, astronomy and many others. As a result, new techniques for time-series analysis have become among the most sought after in machine learning where we seek to learn temporal trends and correlations from time-series data to perform classi􀀌cation [1], anomaly detection [2, 3], regression [4], forecasting [5, 6] and to generate synthetic time-series instances [7] . Focusing on classi􀀌cation, classical machine learning has provided a zoo of algorithms where the present state-of-the-artis centered around deep learning. Popular approaches include recurrent neural networks like long-short-termmemory [8] (and its variations [9, 10]), gated recurrent units and, more recently, transformer networks [11{13] .  \nWhile popular for static data (i.e. data without time dependence), kernelized methods like the wellknown support vector machine (SVM) [14] see limited use in time-series analysis. Although time-series kernel methods have been proposed [15{18], none are tailored to encode temporal trends by way of an explicit and learnable time-dependent inner product space. In this work, we show that time evolution as generated by a parameterized Hamiltonian operator within quantum mechanics is a natural approach for achieving such an objective. Indeed, by combining inner products evolved to di􀀋erent points of time, we achieve a quantum kernel function adapted for time-series data which we call the Time-Series Hamiltonian Kernel (TSHK) .  \n􀀃 [kyu@bnl.gov](kyu@bnl.gov)[ ](kyu@bnl.gov)[y](y research@agnostiq.ai)[ research@agnostiq.ai](y research@agnostiq.ai)  \nThe construction of the TSHK is tied to a 􀀌eld known as Multiple Kernel Learning (MKL) . In MKL, multiple kernel functions are combined using various tactics [19, 20] to give rise to a combined kernel that is by some measure superior. The TSHK is a combined kernel built using a weighted linear combination of quantum kernel functions each de􀀌ned at di􀀋erent instances of time t. These weights are chosen to maximize the separation between labeled data classes as was proposed in the well-known EasyMKL [20] algorithm. Furthermore, as was originally suggested in [2","cbCaibooGeLN0Ufq","https://ap.wps.com/l/cbCaibooGeLN0Ufq","pdf",4448527,1,23,"English","en",105,"# Introduction\n## Time-series classification and kernelized methods\n## Time-series Hamiltonian kernel (TSHK) and QCC-net\n## Efficient NISQ implementation and parallel deployment","[{\"question\":\"What is the main goal of the proposed method for time-series classification?\",\"answer\":\"It targets supervised time-series classification by learning temporal relationships using a hybrid quantum-classical approach based on a time-series Hamiltonian kernel (TSHK).\"},{\"question\":\"How is the TSHK constructed in the method?\",\"answer\":\"The TSHK is formed by summing inner products from quantum states evolved under a parameterized time evolution operator, then optimally weighting those kernel components using techniques from multiple kernel learning.\"},{\"question\":\"What allows the approach to be efficiently run on NISQ quantum processors?\",\"answer\":\"The method uses shallow variational circuits for time evolution (leveraging an eigendecomposition-based strategy) and parallelizes the kernel-matrix computations, enabling deployment on multi-programmed superconducting processors.\"}]","Massively parallel hybrid quantum-classical machine learning for kernelized time-series classification - 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