Optimal provable robustness of quantum classification via quantum hypothesis testing

Abstract Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for...

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Autores principales:	Maurice Weber, Nana Liu, Bo Li, Ce Zhang, Zhikuan Zhao
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/4da0084235ce432aaa2a4943af0014d9
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spelling	oai:doaj.org-article:4da0084235ce432aaa2a4943af0014d92021-12-02T14:59:13ZOptimal provable robustness of quantum classification via quantum hypothesis testing10.1038/s41534-021-00410-52056-6387https://doaj.org/article/4da0084235ce432aaa2a4943af0014d92021-05-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00410-5https://doaj.org/toc/2056-6387Abstract Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.Maurice WeberNana LiuBo LiCe ZhangZhikuan ZhaoNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-12 (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 Maurice Weber Nana Liu Bo Li Ce Zhang Zhikuan Zhao Optimal provable robustness of quantum classification via quantum hypothesis testing
description	Abstract Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.
format	article
author	Maurice Weber Nana Liu Bo Li Ce Zhang Zhikuan Zhao
author_facet	Maurice Weber Nana Liu Bo Li Ce Zhang Zhikuan Zhao
author_sort	Maurice Weber
title	Optimal provable robustness of quantum classification via quantum hypothesis testing
title_short	Optimal provable robustness of quantum classification via quantum hypothesis testing
title_full	Optimal provable robustness of quantum classification via quantum hypothesis testing
title_fullStr	Optimal provable robustness of quantum classification via quantum hypothesis testing
title_full_unstemmed	Optimal provable robustness of quantum classification via quantum hypothesis testing
title_sort	optimal provable robustness of quantum classification via quantum hypothesis testing
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/4da0084235ce432aaa2a4943af0014d9
work_keys_str_mv	AT mauriceweber optimalprovablerobustnessofquantumclassificationviaquantumhypothesistesting AT nanaliu optimalprovablerobustnessofquantumclassificationviaquantumhypothesistesting AT boli optimalprovablerobustnessofquantumclassificationviaquantumhypothesistesting AT cezhang optimalprovablerobustnessofquantumclassificationviaquantumhypothesistesting AT zhikuanzhao optimalprovablerobustnessofquantumclassificationviaquantumhypothesistesting
_version_	1718389198351761408

Optimal provable robustness of quantum classification via quantum hypothesis testing

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