From the Jaynes-Cummings model to non-abelian gauge theories: A guided tour for the quantum engineer

Valentin Kasper; Gediminas Juzeliūnas; Maciej Lewenstein; Fred Jendrzejewski; Erez Zohar

doi:10.1088/1367-2630/abb961

From the Jaynes-Cummings model to non-abelian gauge theories: A guided tour for the quantum engineer

Valentin Kasper^*, Gediminas Juzeliūnas, Maciej Lewenstein, Fred Jendrzejewski, Erez Zohar

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of abelian gauge theories, the quantum simulation of non-abelian gauge theories appears still elusive. In this paper we present minimal non-abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.

Original language	American English
Article number	103027
Journal	New Journal of Physics
Volume	22
Issue number	10
DOIs	https://doi.org/10.1088/1367-2630/abb961
State	Published - Oct 2020

Bibliographical note

Funding Information:
Original content from this work may be used under the terms of the . Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. European Union Regional Development Fund ERDF Operational Program of Catalonia 2014-2020 (O Fundaci�n Cellex https://doi.org/10.13039/100008050 Generalitat de Catalunya https://doi.org/10.13039/501100002809 AGAUR Grant No. 2017 SGR 1341 CERCA/Program Fundaci� MIR-PUIG Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 Emmy Noether 377616843 SFB 1225 (ISOQUANT) Ministerium f�r Wissenschaft, Forschung und Kunst Baden-W�rttemberg https://doi.org/10.13039/501100003542 Juniorprofessorenprogramm European Social Fund https://doi.org/10.13039/501100004895 Narodowe Centrum Nauki https://doi.org/10.13039/501100004281 Poland-Symfonia Grant No. 2016/20/W/ST4/00314 Ministerio de Econom�a y Competitividad https://doi.org/10.13039/501100003329 EU QUANTERA MAQS (PCI2019-111828-2 / 10.13039/5011 FISICATEAMO No. FIS2016-79508-P FPI SEVERO OCHOA No. SEV-2015-0522 yes � 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft Creative Commons Attribution 4.0 licence

Publisher Copyright:
© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.

Keywords

lattice gauge theory
quantum optics
quantum simulation

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10.1088/1367-2630/abb961

Cite this

@article{df7b541fd1304cae9573ede0de95d8e1,

title = "From the Jaynes-Cummings model to non-abelian gauge theories: A guided tour for the quantum engineer",

abstract = "The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of abelian gauge theories, the quantum simulation of non-abelian gauge theories appears still elusive. In this paper we present minimal non-abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.",

keywords = "lattice gauge theory, quantum optics, quantum simulation",

author = "Valentin Kasper and Gediminas Juzeliūnas and Maciej Lewenstein and Fred Jendrzejewski and Erez Zohar",

note = "Funding Information: Original content from this work may be used under the terms of the . Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. European Union Regional Development Fund ERDF Operational Program of Catalonia 2014-2020 (O Fundaci�n Cellex https://doi.org/10.13039/100008050 Generalitat de Catalunya https://doi.org/10.13039/501100002809 AGAUR Grant No. 2017 SGR 1341 CERCA/Program Fundaci� MIR-PUIG Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 Emmy Noether 377616843 SFB 1225 (ISOQUANT) Ministerium f�r Wissenschaft, Forschung und Kunst Baden-W�rttemberg https://doi.org/10.13039/501100003542 Juniorprofessorenprogramm European Social Fund https://doi.org/10.13039/501100004895 Narodowe Centrum Nauki https://doi.org/10.13039/501100004281 Poland-Symfonia Grant No. 2016/20/W/ST4/00314 Ministerio de Econom�a y Competitividad https://doi.org/10.13039/501100003329 EU QUANTERA MAQS (PCI2019-111828-2 / 10.13039/5011 FISICATEAMO No. FIS2016-79508-P FPI SEVERO OCHOA No. SEV-2015-0522 yes � 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft Creative Commons Attribution 4.0 licence Publisher Copyright: {\textcopyright} 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.",

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doi = "10.1088/1367-2630/abb961",

language = "American English",

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AU - Jendrzejewski, Fred

AU - Zohar, Erez

N1 - Funding Information: Original content from this work may be used under the terms of the . Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. European Union Regional Development Fund ERDF Operational Program of Catalonia 2014-2020 (O Fundaci�n Cellex https://doi.org/10.13039/100008050 Generalitat de Catalunya https://doi.org/10.13039/501100002809 AGAUR Grant No. 2017 SGR 1341 CERCA/Program Fundaci� MIR-PUIG Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 Emmy Noether 377616843 SFB 1225 (ISOQUANT) Ministerium f�r Wissenschaft, Forschung und Kunst Baden-W�rttemberg https://doi.org/10.13039/501100003542 Juniorprofessorenprogramm European Social Fund https://doi.org/10.13039/501100004895 Narodowe Centrum Nauki https://doi.org/10.13039/501100004281 Poland-Symfonia Grant No. 2016/20/W/ST4/00314 Ministerio de Econom�a y Competitividad https://doi.org/10.13039/501100003329 EU QUANTERA MAQS (PCI2019-111828-2 / 10.13039/5011 FISICATEAMO No. FIS2016-79508-P FPI SEVERO OCHOA No. SEV-2015-0522 yes � 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft Creative Commons Attribution 4.0 licence Publisher Copyright: © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.

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N2 - The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of abelian gauge theories, the quantum simulation of non-abelian gauge theories appears still elusive. In this paper we present minimal non-abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.

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From the Jaynes-Cummings model to non-abelian gauge theories: A guided tour for the quantum engineer

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Keywords

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