Generalized concurrence in boson sampling

Abstract A fundamental question in linear optical quantum computing is to understand the origin of the quantum supremacy in the physical system. It is found that the multimode linear optical transition amplitudes are calculated through the permanents of transition operator matrices, which is a hard...

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Autores principales:	Seungbeom Chin, Joonsuk Huh
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/9f74875e30b441d5bb48733c449fbb59
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spelling	oai:doaj.org-article:9f74875e30b441d5bb48733c449fbb592021-12-02T15:08:45ZGeneralized concurrence in boson sampling10.1038/s41598-018-24302-52045-2322https://doaj.org/article/9f74875e30b441d5bb48733c449fbb592018-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-24302-5https://doaj.org/toc/2045-2322Abstract A fundamental question in linear optical quantum computing is to understand the origin of the quantum supremacy in the physical system. It is found that the multimode linear optical transition amplitudes are calculated through the permanents of transition operator matrices, which is a hard problem for classical simulations (boson sampling problem). We can understand this problem by considering a quantum measure that directly determines the runtime for computing the transition amplitudes. In this paper, we suggest a quantum measure named “Fock state concurrence sum” C S , which is the summation over all the members of “the generalized Fock state concurrence” (a measure analogous to the generalized concurrences of entanglement and coherence). By introducing generalized algorithms for computing the transition amplitudes of the Fock state boson sampling with an arbitrary number of photons per mode, we show that the minimal classical runtime for all the known algorithms directly depends on C S . Therefore, we can state that the Fock state concurrence sum C S behaves as a collective measure that controls the computational complexity of Fock state BS. We expect that our observation on the role of the Fock state concurrence in the generalized algorithm for permanents would provide a unified viewpoint to interpret the quantum computing power of linear optics.Seungbeom ChinJoonsuk HuhNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-9 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Seungbeom Chin Joonsuk Huh Generalized concurrence in boson sampling
description	Abstract A fundamental question in linear optical quantum computing is to understand the origin of the quantum supremacy in the physical system. It is found that the multimode linear optical transition amplitudes are calculated through the permanents of transition operator matrices, which is a hard problem for classical simulations (boson sampling problem). We can understand this problem by considering a quantum measure that directly determines the runtime for computing the transition amplitudes. In this paper, we suggest a quantum measure named “Fock state concurrence sum” C S , which is the summation over all the members of “the generalized Fock state concurrence” (a measure analogous to the generalized concurrences of entanglement and coherence). By introducing generalized algorithms for computing the transition amplitudes of the Fock state boson sampling with an arbitrary number of photons per mode, we show that the minimal classical runtime for all the known algorithms directly depends on C S . Therefore, we can state that the Fock state concurrence sum C S behaves as a collective measure that controls the computational complexity of Fock state BS. We expect that our observation on the role of the Fock state concurrence in the generalized algorithm for permanents would provide a unified viewpoint to interpret the quantum computing power of linear optics.
format	article
author	Seungbeom Chin Joonsuk Huh
author_facet	Seungbeom Chin Joonsuk Huh
author_sort	Seungbeom Chin
title	Generalized concurrence in boson sampling
title_short	Generalized concurrence in boson sampling
title_full	Generalized concurrence in boson sampling
title_fullStr	Generalized concurrence in boson sampling
title_full_unstemmed	Generalized concurrence in boson sampling
title_sort	generalized concurrence in boson sampling
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/9f74875e30b441d5bb48733c449fbb59
work_keys_str_mv	AT seungbeomchin generalizedconcurrenceinbosonsampling AT joonsukhuh generalizedconcurrenceinbosonsampling
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Generalized concurrence in boson sampling

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