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Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many prob...

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Autores principales: Li, Zhaokai, Yung, Man-Hong, Chen, Hongwei, Lu, Dawei, Whitfield, James D., Peng, Xinhua, Aspuru-Guzik, Alán, Du, Jiangfeng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2011
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3216574/
https://www.ncbi.nlm.nih.gov/pubmed/22355607
http://dx.doi.org/10.1038/srep00088
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author Li, Zhaokai
Yung, Man-Hong
Chen, Hongwei
Lu, Dawei
Whitfield, James D.
Peng, Xinhua
Aspuru-Guzik, Alán
Du, Jiangfeng
author_facet Li, Zhaokai
Yung, Man-Hong
Chen, Hongwei
Lu, Dawei
Whitfield, James D.
Peng, Xinhua
Aspuru-Guzik, Alán
Du, Jiangfeng
author_sort Li, Zhaokai
collection PubMed
description Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10(−5) decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers
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spelling pubmed-32165742011-12-22 Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance Li, Zhaokai Yung, Man-Hong Chen, Hongwei Lu, Dawei Whitfield, James D. Peng, Xinhua Aspuru-Guzik, Alán Du, Jiangfeng Sci Rep Article Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10(−5) decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers Nature Publishing Group 2011-09-09 /pmc/articles/PMC3216574/ /pubmed/22355607 http://dx.doi.org/10.1038/srep00088 Text en Copyright © 2011, Macmillan Publishers Limited. All rights reserved http://creativecommons.org/licenses/by-nc-nd/3.0/ This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/
spellingShingle Article
Li, Zhaokai
Yung, Man-Hong
Chen, Hongwei
Lu, Dawei
Whitfield, James D.
Peng, Xinhua
Aspuru-Guzik, Alán
Du, Jiangfeng
Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
title Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
title_full Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
title_fullStr Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
title_full_unstemmed Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
title_short Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
title_sort solving quantum ground-state problems with nuclear magnetic resonance
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3216574/
https://www.ncbi.nlm.nih.gov/pubmed/22355607
http://dx.doi.org/10.1038/srep00088
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