Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations

Abstract The scalability, error correction and practical problem solving are important challenges for quantum computing (QC) as more emphasized by quantum supremacy (QS) experiments. Quantum path computing (QPC), recently introduced for linear optic based QCs as an unconventional design, targets to...

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Autor principal:	Burhan Gulbahar
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2020
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/ca5ecba615da4ce797e5580f577ac7ac
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spelling	oai:doaj.org-article:ca5ecba615da4ce797e5580f577ac7ac2021-12-02T16:32:12ZTheory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations10.1038/s41598-020-67364-02045-2322https://doaj.org/article/ca5ecba615da4ce797e5580f577ac7ac2020-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-020-67364-0https://doaj.org/toc/2045-2322Abstract The scalability, error correction and practical problem solving are important challenges for quantum computing (QC) as more emphasized by quantum supremacy (QS) experiments. Quantum path computing (QPC), recently introduced for linear optic based QCs as an unconventional design, targets to obtain scalability and practical problem solving. It samples the intensity from the interference of exponentially increasing number of propagation paths obtained in multi-plane diffraction (MPD) of classical particle sources. QPC exploits MPD based quantum temporal correlations of the paths and freely entangled projections at different time instants, for the first time, with the classical light source and intensity measurement while not requiring photon interactions or single photon sources and receivers. In this article, photonic QPC is defined, theoretically modeled and numerically analyzed for arbitrary Fourier optical or quadratic phase set-ups while utilizing both Gaussian and Hermite-Gaussian source laser modes. Problem solving capabilities already including partial sum of Riemann theta functions are extended. Important future applications, implementation challenges and open issues such as universal computation and quantum circuit implementations determining the scope of QC capabilities are discussed. The applications include QS experiments reaching more than $$2^{100}$$ 2100 Feynman paths, quantum neuron implementations and solutions of nonlinear Schrödinger equation.Burhan GulbaharNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 10, Iss 1, Pp 1-23 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Burhan Gulbahar Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations
description	Abstract The scalability, error correction and practical problem solving are important challenges for quantum computing (QC) as more emphasized by quantum supremacy (QS) experiments. Quantum path computing (QPC), recently introduced for linear optic based QCs as an unconventional design, targets to obtain scalability and practical problem solving. It samples the intensity from the interference of exponentially increasing number of propagation paths obtained in multi-plane diffraction (MPD) of classical particle sources. QPC exploits MPD based quantum temporal correlations of the paths and freely entangled projections at different time instants, for the first time, with the classical light source and intensity measurement while not requiring photon interactions or single photon sources and receivers. In this article, photonic QPC is defined, theoretically modeled and numerically analyzed for arbitrary Fourier optical or quadratic phase set-ups while utilizing both Gaussian and Hermite-Gaussian source laser modes. Problem solving capabilities already including partial sum of Riemann theta functions are extended. Important future applications, implementation challenges and open issues such as universal computation and quantum circuit implementations determining the scope of QC capabilities are discussed. The applications include QS experiments reaching more than $$2^{100}$$ 2100 Feynman paths, quantum neuron implementations and solutions of nonlinear Schrödinger equation.
format	article
author	Burhan Gulbahar
author_facet	Burhan Gulbahar
author_sort	Burhan Gulbahar
title	Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations
title_short	Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations
title_full	Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations
title_fullStr	Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations
title_full_unstemmed	Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations
title_sort	theory of quantum path computing with fourier optics and future applications for quantum supremacy, neural networks and nonlinear schrödinger equations
publisher	Nature Portfolio
publishDate	2020
url	https://doaj.org/article/ca5ecba615da4ce797e5580f577ac7ac
work_keys_str_mv	AT burhangulbahar theoryofquantumpathcomputingwithfourieropticsandfutureapplicationsforquantumsupremacyneuralnetworksandnonlinearschrodingerequations
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Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations

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