Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators

Abstract A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the p...

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Autores principales:	Hayato Goto, Zhirong Lin, Yasunobu Nakamura
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b33b4b268e8a482f8a152920ce337603
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spelling	oai:doaj.org-article:b33b4b268e8a482f8a152920ce3376032021-12-02T12:33:00ZBoltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators10.1038/s41598-018-25492-82045-2322https://doaj.org/article/b33b4b268e8a482f8a152920ce3376032018-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-25492-8https://doaj.org/toc/2045-2322Abstract A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.Hayato GotoZhirong LinYasunobu NakamuraNature 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 Hayato Goto Zhirong Lin Yasunobu Nakamura Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators
description	Abstract A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.
format	article
author	Hayato Goto Zhirong Lin Yasunobu Nakamura
author_facet	Hayato Goto Zhirong Lin Yasunobu Nakamura
author_sort	Hayato Goto
title	Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators
title_short	Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators
title_full	Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators
title_fullStr	Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators
title_full_unstemmed	Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators
title_sort	boltzmann sampling from the ising model using quantum heating of coupled nonlinear oscillators
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/b33b4b268e8a482f8a152920ce337603
work_keys_str_mv	AT hayatogoto boltzmannsamplingfromtheisingmodelusingquantumheatingofcouplednonlinearoscillators AT zhironglin boltzmannsamplingfromtheisingmodelusingquantumheatingofcouplednonlinearoscillators AT yasunobunakamura boltzmannsamplingfromtheisingmodelusingquantumheatingofcouplednonlinearoscillators
_version_	1718393880018157568

Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators

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