Optimizing a polynomial function on a quantum processor

Abstract The gradient descent method is central to numerical optimization and is the key ingredient in many machine learning algorithms. It promises to find a local minimum of a function by iteratively moving along the direction of the steepest descent. Since for high-dimensional problems the requir...

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Autores principales:	Keren Li, Shijie Wei, Pan Gao, Feihao Zhang, Zengrong Zhou, Tao Xin, Xiaoting Wang, Patrick Rebentrost, Guilu Long
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/ee291d3fa219422aa4c45b7a814186f3
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spelling	oai:doaj.org-article:ee291d3fa219422aa4c45b7a814186f32021-12-02T10:48:15ZOptimizing a polynomial function on a quantum processor10.1038/s41534-020-00351-52056-6387https://doaj.org/article/ee291d3fa219422aa4c45b7a814186f32021-01-01T00:00:00Zhttps://doi.org/10.1038/s41534-020-00351-5https://doaj.org/toc/2056-6387Abstract The gradient descent method is central to numerical optimization and is the key ingredient in many machine learning algorithms. It promises to find a local minimum of a function by iteratively moving along the direction of the steepest descent. Since for high-dimensional problems the required computational resources can be prohibitive, it is desirable to investigate quantum versions of the gradient descent, such as the recently proposed (Rebentrost et al.1). Here, we develop this protocol and implement it on a quantum processor with limited resources. A prototypical experiment is shown with a four-qubit nuclear magnetic resonance quantum processor, which demonstrates the iterative optimization process. Experimentally, the final point converged to the local minimum with a fidelity >94%, quantified via full-state tomography. Moreover, our method can be employed to a multidimensional scaling problem, showing the potential to outperform its classical counterparts. Considering the ongoing efforts in quantum information and data science, our work may provide a faster approach to solving high-dimensional optimization problems and a subroutine for future practical quantum computers.Keren LiShijie WeiPan GaoFeihao ZhangZengrong ZhouTao XinXiaoting WangPatrick RebentrostGuilu LongNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-7 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
spellingShingle	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Keren Li Shijie Wei Pan Gao Feihao Zhang Zengrong Zhou Tao Xin Xiaoting Wang Patrick Rebentrost Guilu Long Optimizing a polynomial function on a quantum processor
description	Abstract The gradient descent method is central to numerical optimization and is the key ingredient in many machine learning algorithms. It promises to find a local minimum of a function by iteratively moving along the direction of the steepest descent. Since for high-dimensional problems the required computational resources can be prohibitive, it is desirable to investigate quantum versions of the gradient descent, such as the recently proposed (Rebentrost et al.1). Here, we develop this protocol and implement it on a quantum processor with limited resources. A prototypical experiment is shown with a four-qubit nuclear magnetic resonance quantum processor, which demonstrates the iterative optimization process. Experimentally, the final point converged to the local minimum with a fidelity >94%, quantified via full-state tomography. Moreover, our method can be employed to a multidimensional scaling problem, showing the potential to outperform its classical counterparts. Considering the ongoing efforts in quantum information and data science, our work may provide a faster approach to solving high-dimensional optimization problems and a subroutine for future practical quantum computers.
format	article
author	Keren Li Shijie Wei Pan Gao Feihao Zhang Zengrong Zhou Tao Xin Xiaoting Wang Patrick Rebentrost Guilu Long
author_facet	Keren Li Shijie Wei Pan Gao Feihao Zhang Zengrong Zhou Tao Xin Xiaoting Wang Patrick Rebentrost Guilu Long
author_sort	Keren Li
title	Optimizing a polynomial function on a quantum processor
title_short	Optimizing a polynomial function on a quantum processor
title_full	Optimizing a polynomial function on a quantum processor
title_fullStr	Optimizing a polynomial function on a quantum processor
title_full_unstemmed	Optimizing a polynomial function on a quantum processor
title_sort	optimizing a polynomial function on a quantum processor
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/ee291d3fa219422aa4c45b7a814186f3
work_keys_str_mv	AT kerenli optimizingapolynomialfunctiononaquantumprocessor AT shijiewei optimizingapolynomialfunctiononaquantumprocessor AT pangao optimizingapolynomialfunctiononaquantumprocessor AT feihaozhang optimizingapolynomialfunctiononaquantumprocessor AT zengrongzhou optimizingapolynomialfunctiononaquantumprocessor AT taoxin optimizingapolynomialfunctiononaquantumprocessor AT xiaotingwang optimizingapolynomialfunctiononaquantumprocessor AT patrickrebentrost optimizingapolynomialfunctiononaquantumprocessor AT guilulong optimizingapolynomialfunctiononaquantumprocessor
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Optimizing a polynomial function on a quantum processor

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