Fermion-qudit quantum processors for simulating lattice gauge theories with matter

Torsten V. Zache1,2,3, Daniel González-Cuadra1,2,3, and Peter Zoller1,2

1Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
2Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
3These authors contributed equally to this work.

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Simulating the real-time dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this work, we present a complete Rydberg-based architecture, co-designed to digitally simulate the dynamics of general gauge theories coupled to matter fields in a hardware-efficient manner. Ref. [1] showed how a qudit processor, where non-abelian gauge fields are locally encoded and time-evolved, considerably reduces the required simulation resources compared to standard qubit-based quantum computers. Here we integrate the latter with a recently introduced fermionic quantum processor [2], where fermionic statistics are accounted for at the hardware level, allowing us to construct quantum circuits that preserve the locality of the gauge-matter interactions. We exemplify the flexibility of such a fermion-qudit processor by focusing on two paradigmatic high-energy phenomena. First, we present a resource-efficient protocol to simulate the Abelian-Higgs model, where the dynamics of confinement and string breaking can be investigated. Then, we show how to prepare hadrons made up of fermionic matter constituents bound by non-abelian gauge fields, and show how to extract the corresponding hadronic tensor. In both cases, we estimate the required resources, showing how quantum devices can be used to calculate experimentally-relevant quantities in particle physics.

► BibTeX data

► References

[1] Daniel González-Cuadra, Torsten V. Zache, Jose Carrasco, Barbara Kraus, and Peter Zoller. ``Hardware efficient quantum simulation of non-abelian gauge theories with qudits on rydberg platforms''. Phys. Rev. Lett. 129, 160501 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.129.160501

[2] D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. ``Fermionic quantum processing with programmable neutral atom arrays''. Proceedings of the National Academy of Sciences 120, e2304294120 (2023).
https:/​/​doi.org/​10.1073/​pnas.2304294120

[3] Steven Weinberg. ``The quantum theory of fields''. Volume 2. Cambridge university press. (1996).
https:/​/​doi.org/​10.1017/​CBO9781139644174

[4] István Montvay and Gernot Münster. ``Quantum fields on a lattice''. Cambridge University Press. (1994).
https:/​/​doi.org/​10.1017/​CBO9780511470783

[5] S. Aoki, Y. Aoki, D. Bečirević, T. Blum, G. Colangelo, S. Collins, M. Della Morte, P. Dimopoulos, S. Dürr, H. Fukaya, M. Golterman, Steven Gottlieb, R. Gupta, S. Hashimoto, U. M. Heller, G. Herdoiza, R. Horsley, A. Jüttner, T. Kaneko, C. J. D. Lin, E. Lunghi, R. Mawhinney, A. Nicholson, T. Onogi, C. Pena, A. Portelli, A. Ramos, S. R. Sharpe, J. N. Simone, S. Simula, R. Sommer, R. Van de Water, A. Vladikas, U. Wenger, and H. Wittig. ``Flag review 2019''. The European Physical Journal C 80, 113 (2020).
https:/​/​doi.org/​10.1140/​epjc/​s10052-019-7354-7

[6] Matthias Troyer and Uwe-Jens Wiese. ``Computational complexity and fundamental limitations to fermionic quantum monte carlo simulations''. Phys. Rev. Lett. 94, 170201 (2005).
https:/​/​doi.org/​10.1103/​PhysRevLett.94.170201

[7] N. Brambilla, S. Eidelman, P. Foka, S. Gardner, A. S. Kronfeld, M. G. Alford, R. Alkofer, M. Butenschoen, T. D. Cohen, J. Erdmenger, L. Fabbietti, M. Faber, J. L. Goity, B. Ketzer, H. W. Lin, F. J. Llanes-Estrada, H. B. Meyer, P. Pakhlov, E. Pallante, M. I. Polikarpov, H. Sazdjian, A. Schmitt, W. M. Snow, A. Vairo, R. Vogt, A. Vuorinen, H. Wittig, P. Arnold, P. Christakoglou, P. Di Nezza, Z. Fodor, X. Garcia i Tormo, R. Höllwieser, M. A. Janik, A. Kalweit, D. Keane, E. Kiritsis, A. Mischke, R. Mizuk, G. Odyniec, K. Papadodimas, A. Pich, R. Pittau, J. W. Qiu, G. Ricciardi, C. A. Salgado, K. Schwenzer, N. G. Stefanis, G. M. von Hippel, and V. I. Zakharov. ``Qcd and strongly coupled gauge theories: challenges and perspectives''. The European Physical Journal C 74, 2981 (2014).
https:/​/​doi.org/​10.1140/​epjc/​s10052-014-2981-5

[8] Jürgen Berges, Michal P. Heller, Aleksas Mazeliauskas, and Raju Venugopalan. ``Qcd thermalization: Ab initio approaches and interdisciplinary connections''. Rev. Mod. Phys. 93, 035003 (2021).
https:/​/​doi.org/​10.1103/​RevModPhys.93.035003

[9] U.-J. Wiese. ``Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories''. Annalen der Physik 525, 777–796 (2013).
https:/​/​doi.org/​10.1002/​andp.201300104

[10] Erez Zohar, J Ignacio Cirac, and Benni Reznik. ``Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices''. Reports on Progress in Physics 79, 014401 (2015).
https:/​/​doi.org/​10.1088/​0034-4885/​79/​1/​014401

[11] M. Dalmonte and S. Montangero. ``Lattice gauge theory simulations in the quantum information era''. Contemporary Physics 57, 388–412 (2016).
https:/​/​doi.org/​10.1080/​00107514.2016.1151199

[12] Mari Carmen Bañuls, Rainer Blatt, Jacopo Catani, Alessio Celi, Juan Ignacio Cirac, Marcello Dalmonte, Leonardo Fallani, Karl Jansen, Maciej Lewenstein, Simone Montangero, Christine A. Muschik, Benni Reznik, Enrique Rico, Luca Tagliacozzo, Karel Van Acoleyen, Frank Verstraete, Uwe-Jens Wiese, Matthew Wingate, Jakub Zakrzewski, and Peter Zoller. ``Simulating lattice gauge theories within quantum technologies''. The European Physical Journal D 74, 165 (2020).
https:/​/​doi.org/​10.1140/​epjd/​e2020-100571-8

[13] Monika Aidelsburger, Luca Barbiero, Alejandro Bermudez, Titas Chanda, Alexandre Dauphin, Daniel González-Cuadra, Przemysław R. Grzybowski, Simon Hands, Fred Jendrzejewski, Johannes Jünemann, Gediminas Juzeliūnas, Valentin Kasper, Angelo Piga, Shi-Ju Ran, Matteo Rizzi, Germán Sierra, Luca Tagliacozzo, Emanuele Tirrito, Torsten V. Zache, Jakub Zakrzewski, Erez Zohar, and Maciej Lewenstein. ``Cold atoms meet lattice gauge theory''. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, 20210064 (2022).
https:/​/​doi.org/​10.1098/​rsta.2021.0064

[14] Erez Zohar. ``Quantum simulation of lattice gauge theories in more than one space dimension - requirements, challenges and methods''. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, 20210069 (2022).
https:/​/​doi.org/​10.1098/​rsta.2021.0069

[15] Alberto Di Meglio, Karl Jansen, Ivano Tavernelli, Constantia Alexandrou, Srinivasan Arunachalam, Christian W. Bauer, Kerstin Borras, Stefano Carrazza, Arianna Crippa, Vincent Croft, Roland de Putter, Andrea Delgado, Vedran Dunjko, Daniel J. Egger, Elias Fernandez-Combarro, Elina Fuchs, Lena Funcke, Daniel Gonzalez-Cuadra, Michele Grossi, Jad C. Halimeh, Zoe Holmes, Stefan Kuhn, Denis Lacroix, Randy Lewis, Donatella Lucchesi, Miriam Lucio Martinez, Federico Meloni, Antonio Mezzacapo, Simone Montangero, Lento Nagano, Voica Radescu, Enrique Rico Ortega, Alessandro Roggero, Julian Schuhmacher, Joao Seixas, Pietro Silvi, Panagiotis Spentzouris, Francesco Tacchino, Kristan Temme, Koji Terashi, Jordi Tura, Cenk Tuysuz, Sofia Vallecorsa, Uwe-Jens Wiese, Shinjae Yoo, and Jinglei Zhang. ``Quantum computing for high-energy physics: State of the art and challenges. summary of the qc4hep working group'' (2023). arXiv:2307.03236.
arXiv:2307.03236

[16] Esteban A. Martinez, Christine A. Muschik, Philipp Schindler, Daniel Nigg, Alexander Erhard, Markus Heyl, Philipp Hauke, Marcello Dalmonte, Thomas Monz, Peter Zoller, and Rainer Blatt. ``Real-time dynamics of lattice gauge theories with a few-qubit quantum computer''. Nature 534, 516–519 (2016).
https:/​/​doi.org/​10.1038/​nature18318

[17] Christian Schweizer, Fabian Grusdt, Moritz Berngruber, Luca Barbiero, Eugene Demler, Nathan Goldman, Immanuel Bloch, and Monika Aidelsburger. ``Floquet approach to $\mathbb{Z}_2$ lattice gauge theories with ultracold atoms in optical lattices''. Nature Physics 15, 1168–1173 (2019).
https:/​/​doi.org/​10.1038/​s41567-019-0649-7

[18] C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller. ``Self-verifying variational quantum simulation of lattice models''. Nature 569, 355–360 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1177-4

[19] Alexander Mil, Torsten V. Zache, Apoorva Hegde, Andy Xia, Rohit P. Bhatt, Markus K. Oberthaler, Philipp Hauke, Jürgen Berges, and Fred Jendrzejewski. ``A scalable realization of local u(1) gauge invariance in cold atomic mixtures''. Science 367, 1128–1130 (2020).
https:/​/​doi.org/​10.1126/​science.aaz5312

[20] Bing Yang, Hui Sun, Robert Ott, Han-Yi Wang, Torsten V. Zache, Jad C. Halimeh, Zhen-Sheng Yuan, Philipp Hauke, and Jian-Wei Pan. ``Observation of gauge invariance in a 71-site bose–hubbard quantum simulator''. Nature 587, 392–396 (2020).
https:/​/​doi.org/​10.1038/​s41586-020-2910-8

[21] Zhao-Yu Zhou, Guo-Xian Su, Jad C. Halimeh, Robert Ott, Hui Sun, Philipp Hauke, Bing Yang, Zhen-Sheng Yuan, Jürgen Berges, and Jian-Wei Pan. ``Thermalization dynamics of a gauge theory on a quantum simulator''. Science 377, 311–314 (2022).
https:/​/​doi.org/​10.1126/​science.abl6277

[22] Nhung H. Nguyen, Minh C. Tran, Yingyue Zhu, Alaina M. Green, C. Huerta Alderete, Zohreh Davoudi, and Norbert M. Linke. ``Digital quantum simulation of the schwinger model and symmetry protection with trapped ions''. PRX Quantum 3, 020324 (2022).
https:/​/​doi.org/​10.1103/​PRXQuantum.3.020324

[23] J. Ignacio Cirac and Peter Zoller. ``Goals and opportunities in quantum simulation''. Nature Physics 8, 264–266 (2012).
https:/​/​doi.org/​10.1038/​nphys2275

[24] I. M. Georgescu, S. Ashhab, and Franco Nori. ``Quantum simulation''. Rev. Mod. Phys. 86, 153–185 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.153

[25] Christian Gross and Immanuel Bloch. ``Quantum simulations with ultracold atoms in optical lattices''. Science 357, 995–1001 (2017).
https:/​/​doi.org/​10.1126/​science.aal3837

[26] Antoine Browaeys and Thierry Lahaye. ``Many-body physics with individually controlled rydberg atoms''. Nature Physics 16, 132–142 (2020).
https:/​/​doi.org/​10.1038/​s41567-019-0733-z

[27] R. Blatt and C. F. Roos. ``Quantum simulations with trapped ions''. Nature Physics 8, 277–284 (2012).
https:/​/​doi.org/​10.1038/​nphys2252

[28] C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao. ``Programmable quantum simulations of spin systems with trapped ions''. Rev. Mod. Phys. 93, 025001 (2021).
https:/​/​doi.org/​10.1103/​RevModPhys.93.025001

[29] Tim Byrnes and Yoshihisa Yamamoto. ``Simulating lattice gauge theories on a quantum computer''. Phys. Rev. A 73, 022328 (2006).
https:/​/​doi.org/​10.1103/​PhysRevA.73.022328

[30] Henry Lamm, Scott Lawrence, and Yukari Yamauchi. ``General methods for digital quantum simulation of gauge theories''. Phys. Rev. D 100, 034518 (2019).
https:/​/​doi.org/​10.1103/​PhysRevD.100.034518

[31] Andrei Alexandru, Paulo F. Bedaque, Siddhartha Harmalkar, Henry Lamm, Scott Lawrence, and Neill C. Warrington. ``Gluon field digitization for quantum computers''. Phys. Rev. D 100, 114501 (2019).
https:/​/​doi.org/​10.1103/​PhysRevD.100.114501

[32] Yao Ji, Henry Lamm, and Shuchen Zhu. ``Gluon field digitization via group space decimation for quantum computers''. Phys. Rev. D 102, 114513 (2020).
https:/​/​doi.org/​10.1103/​PhysRevD.102.114513

[33] Simon V. Mathis, Guglielmo Mazzola, and Ivano Tavernelli. ``Toward scalable simulations of lattice gauge theories on quantum computers''. Phys. Rev. D 102, 094501 (2020).
https:/​/​doi.org/​10.1103/​PhysRevD.102.094501

[34] David B. Kaplan and Jesse R. Stryker. ``Gauss's law, duality, and the hamiltonian formulation of u(1) lattice gauge theory''. Phys. Rev. D 102, 094515 (2020).
https:/​/​doi.org/​10.1103/​PhysRevD.102.094515

[35] Richard C. Brower, David Berenstein, and Hiroki Kawai. ``Lattice Gauge Theory for a Quantum Computer'' (2020). arXiv:2002.10028.
arXiv:2002.10028

[36] Alexander F. Shaw, Pavel Lougovski, Jesse R. Stryker, and Nathan Wiebe. ``Quantum Algorithms for Simulating the Lattice Schwinger Model''. Quantum 4, 306 (2020).
https:/​/​doi.org/​10.22331/​q-2020-08-10-306

[37] Natalie Klco, Martin J. Savage, and Jesse R. Stryker. ``Su(2) non-abelian gauge field theory in one dimension on digital quantum computers''. Phys. Rev. D 101, 074512 (2020).
https:/​/​doi.org/​10.1103/​PhysRevD.101.074512

[38] Anthony Ciavarella, Natalie Klco, and Martin J. Savage. ``Trailhead for quantum simulation of su(3) yang-mills lattice gauge theory in the local multiplet basis''. Phys. Rev. D 103, 094501 (2021).
https:/​/​doi.org/​10.1103/​PhysRevD.103.094501

[39] Andrei Alexandru, Paulo F. Bedaque, Ruairí Brett, and Henry Lamm. ``Spectrum of digitized qcd: Glueballs in a $s(1080)$ gauge theory''. Phys. Rev. D 105, 114508 (2022).
https:/​/​doi.org/​10.1103/​PhysRevD.105.114508

[40] Jan F. Haase, Luca Dellantonio, Alessio Celi, Danny Paulson, Angus Kan, Karl Jansen, and Christine A. Muschik. ``A resource efficient approach for quantum and classical simulations of gauge theories in particle physics''. Quantum 5, 393 (2021).
https:/​/​doi.org/​10.22331/​q-2021-02-04-393

[41] Christian W. Bauer and Dorota M. Grabowska. ``Efficient Representation for Simulating U(1) Gauge Theories on Digital Quantum Computers at All Values of the Coupling'' (2021). arXiv:2111.08015.
arXiv:2111.08015

[42] Angus Kan and Yunseong Nam. ``Lattice Quantum Chromodynamics and Electrodynamics on a Universal Quantum Computer'' (2021). arXiv:2107.12769.
arXiv:2107.12769

[43] Zohreh Davoudi, Indrakshi Raychowdhury, and Andrew Shaw. ``Search for efficient formulations for hamiltonian simulation of non-abelian lattice gauge theories''. Phys. Rev. D 104, 074505 (2021).
https:/​/​doi.org/​10.1103/​PhysRevD.104.074505

[44] Natalie Klco, Alessandro Roggero, and Martin J Savage. ``Standard model physics and the digital quantum revolution: thoughts about the interface''. Reports on Progress in Physics 85, 064301 (2022).
https:/​/​doi.org/​10.1088/​1361-6633/​ac58a4

[45] Christine Muschik, Markus Heyl, Esteban Martinez, Thomas Monz, Philipp Schindler, Berit Vogell, Marcello Dalmonte, Philipp Hauke, Rainer Blatt, and Peter Zoller. ``U(1) wilson lattice gauge theories in digital quantum simulators''. New Journal of Physics 19, 103020 (2017).
https:/​/​doi.org/​10.1088/​1367-2630/​aa89ab

[46] Danny Paulson, Luca Dellantonio, Jan F. Haase, Alessio Celi, Angus Kan, Andrew Jena, Christian Kokail, Rick van Bijnen, Karl Jansen, Peter Zoller, and Christine A. Muschik. ``Simulating 2d effects in lattice gauge theories on a quantum computer''. PRX Quantum 2, 030334 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.030334

[47] Zohreh Davoudi, Norbert M. Linke, and Guido Pagano. ``Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach''. Phys. Rev. Research 3, 043072 (2021).
https:/​/​doi.org/​10.1103/​PhysRevResearch.3.043072

[48] L. Tagliacozzo, A. Celi, P. Orland, M. W. Mitchell, and M. Lewenstein. ``Simulation of non-abelian gauge theories with optical lattices''. Nature Communications 4, 2615 (2013).
https:/​/​doi.org/​10.1038/​ncomms3615

[49] L. Tagliacozzo, A. Celi, A. Zamora, and M. Lewenstein. ``Optical abelian lattice gauge theories''. Annals of Physics 330, 160–191 (2013).
https:/​/​doi.org/​10.1016/​j.aop.2012.11.009

[50] Erez Zohar, Alessandro Farace, Benni Reznik, and J. Ignacio Cirac. ``Digital quantum simulation of $\mathbb{Z}_{2}$ lattice gauge theories with dynamical fermionic matter''. Phys. Rev. Lett. 118, 070501 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.070501

[51] Erez Zohar, Alessandro Farace, Benni Reznik, and J. Ignacio Cirac. ``Digital lattice gauge theories''. Phys. Rev. A 95, 023604 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.023604

[52] Julian Bender, Erez Zohar, Alessandro Farace, and J Ignacio Cirac. ``Digital quantum simulation of lattice gauge theories in three spatial dimensions''. New Journal of Physics 20, 093001 (2018).
https:/​/​doi.org/​10.1088/​1367-2630/​aadb71

[53] A. Mezzacapo, E. Rico, C. Sabín, I. L. Egusquiza, L. Lamata, and E. Solano. ``Non-abelian su(2) lattice gauge theories in superconducting circuits''. Phys. Rev. Lett. 115, 240502 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.240502

[54] N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, M. Sanz, E. Solano, P. Lougovski, and M. J. Savage. ``Quantum-classical computation of schwinger model dynamics using quantum computers''. Phys. Rev. A 98, 032331 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.032331

[55] Yasar Y. Atas, Jinglei Zhang, Randy Lewis, Amin Jahanpour, Jan F. Haase, and Christine A. Muschik. ``Su(2) hadrons on a quantum computer via a variational approach''. Nature Communications 12, 6499 (2021).
https:/​/​doi.org/​10.1038/​s41467-021-26825-4

[56] Tsafrir Armon, Shachar Ashkenazi, Gerardo García-Moreno, Alejandro González-Tudela, and Erez Zohar. ``Photon-mediated stroboscopic quantum simulation of a $\mathbb{Z}_{2}$ lattice gauge theory''. Phys. Rev. Lett. 127, 250501 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.127.250501

[57] John Preskill. ``Quantum Computing in the NISQ era and beyond''. Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[58] Andrew J. Daley, Immanuel Bloch, Christian Kokail, Stuart Flannigan, Natalie Pearson, Matthias Troyer, and Peter Zoller. ``Practical quantum advantage in quantum simulation''. Nature 607, 667–676 (2022).
https:/​/​doi.org/​10.1038/​s41586-022-04940-6

[59] Sepehr Ebadi, Tout T. Wang, Harry Levine, Alexander Keesling, Giulia Semeghini, Ahmed Omran, Dolev Bluvstein, Rhine Samajdar, Hannes Pichler, Wen Wei Ho, Soonwon Choi, Subir Sachdev, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin. ``Quantum phases of matter on a 256-atom programmable quantum simulator''. Nature 595, 227–232 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03582-4

[60] Pascal Scholl, Michael Schuler, Hannah J. Williams, Alexander A. Eberharter, Daniel Barredo, Kai-Niklas Schymik, Vincent Lienhard, Louis-Paul Henry, Thomas C. Lang, Thierry Lahaye, Andreas M. Läuchli, and Antoine Browaeys. ``Quantum simulation of 2d antiferromagnets with hundreds of rydberg atoms''. Nature 595, 233–238 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03585-1

[61] Adam M. Kaufman and Kang-Kuen Ni. ``Quantum science with optical tweezer arrays of ultracold atoms and molecules''. Nature Physics 17, 1324–1333 (2021).
https:/​/​doi.org/​10.1038/​s41567-021-01357-2

[62] M Saffman. ``Quantum computing with atomic qubits and rydberg interactions: progress and challenges''. Journal of Physics B: Atomic, Molecular and Optical Physics 49, 202001 (2016).
https:/​/​doi.org/​10.1088/​0953-4075/​49/​20/​202001

[63] Harry Levine, Alexander Keesling, Giulia Semeghini, Ahmed Omran, Tout T. Wang, Sepehr Ebadi, Hannes Bernien, Markus Greiner, Vladan Vuletić, Hannes Pichler, and Mikhail D. Lukin. ``Parallel implementation of high-fidelity multiqubit gates with neutral atoms''. Phys. Rev. Lett. 123, 170503 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.170503

[64] Loïc Henriet, Lucas Beguin, Adrien Signoles, Thierry Lahaye, Antoine Browaeys, Georges-Olivier Reymond, and Christophe Jurczak. ``Quantum computing with neutral atoms''. Quantum 4, 327 (2020).
https:/​/​doi.org/​10.22331/​q-2020-09-21-327

[65] Ivaylo S. Madjarov, Jacob P. Covey, Adam L. Shaw, Joonhee Choi, Anant Kale, Alexandre Cooper, Hannes Pichler, Vladimir Schkolnik, Jason R. Williams, and Manuel Endres. ``High-fidelity entanglement and detection of alkaline-earth rydberg atoms''. Nature Physics 16, 857–861 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0903-z

[66] Sam R. Cohen and Jeff D. Thompson. ``Quantum computing with circular rydberg atoms''. PRX Quantum 2, 030322 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.030322

[67] Dolev Bluvstein, Harry Levine, Giulia Semeghini, Tout T. Wang, Sepehr Ebadi, Marcin Kalinowski, Alexander Keesling, Nishad Maskara, Hannes Pichler, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin. ``A quantum processor based on coherent transport of entangled atom arrays''. Nature 604, 451–456 (2022).
https:/​/​doi.org/​10.1038/​s41586-022-04592-6

[68] Andrew J. Daley, Martin M. Boyd, Jun Ye, and Peter Zoller. ``Quantum computing with alkaline-earth-metal atoms''. Phys. Rev. Lett. 101, 170504 (2008).
https:/​/​doi.org/​10.1103/​PhysRevLett.101.170504

[69] John Kogut and Leonard Susskind. ``Hamiltonian formulation of wilson's lattice gauge theories''. Phys. Rev. D 11, 395–408 (1975).
https:/​/​doi.org/​10.1103/​PhysRevD.11.395

[70] Alexandre Cooper, Jacob P. Covey, Ivaylo S. Madjarov, Sergey G. Porsev, Marianna S. Safronova, and Manuel Endres. ``Alkaline-earth atoms in optical tweezers''. Phys. Rev. X 8, 041055 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.041055

[71] Jacob P. Covey, Ivaylo S. Madjarov, Alexandre Cooper, and Manuel Endres. ``2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays''. Phys. Rev. Lett. 122, 173201 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.173201

[72] Kevin Singh, Shraddha Anand, Andrew Pocklington, Jordan T. Kemp, and Hannes Bernien. ``Dual-element, two-dimensional atom array with continuous-mode operation''. Phys. Rev. X 12, 011040 (2022).
https:/​/​doi.org/​10.1103/​PhysRevX.12.011040

[73] Paolo Zanardi and Mario Rasetti. ``Holonomic quantum computation''. Physics Letters A 264, 94–99 (1999).
https:/​/​doi.org/​10.1016/​S0375-9601(99)00803-8

[74] Benjamin M. Spar, Elmer Guardado-Sanchez, Sungjae Chi, Zoe Z. Yan, and Waseem S. Bakr. ``Realization of a fermi-hubbard optical tweezer array''. Phys. Rev. Lett. 128, 223202 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.128.223202

[75] Zoe Z. Yan, Benjamin M. Spar, Max L. Prichard, Sungjae Chi, Hao-Tian Wei, Eduardo Ibarra-García-Padilla, Kaden R. A. Hazzard, and Waseem S. Bakr. ``Two-dimensional programmable tweezer arrays of fermions''. Phys. Rev. Lett. 129, 123201 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.129.123201

[76] Simon Murmann, Andrea Bergschneider, Vincent M. Klinkhamer, Gerhard Zürn, Thomas Lompe, and Selim Jochim. ``Two fermions in a double well: Exploring a fundamental building block of the hubbard model''. Phys. Rev. Lett. 114, 080402 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.114.080402

[77] Andrea Bergschneider, Vincent M. Klinkhamer, Jan Hendrik Becher, Ralf Klemt, Lukas Palm, Gerhard Zürn, Selim Jochim, and Philipp M. Preiss. ``Experimental characterization of two-particle entanglement through position and momentum correlations''. Nature Physics 15, 640–644 (2019).
https:/​/​doi.org/​10.1038/​s41567-019-0508-6

[78] J. H. Becher, E. Sindici, R. Klemt, S. Jochim, A. J. Daley, and P. M. Preiss. ``Measurement of identical particle entanglement and the influence of antisymmetrization''. Phys. Rev. Lett. 125, 180402 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.180402

[79] Aaron W. Young, William J. Eckner, Nathan Schine, Andrew M. Childs, and Adam M. Kaufman. ``Tweezer-programmable 2d quantum walks in a hubbard-regime lattice''. Science 377, 885–889 (2022).
https:/​/​doi.org/​10.1126/​science.abo0608

[80] D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller. ``Entanglement of atoms via cold controlled collisions''. Phys. Rev. Lett. 82, 1975–1978 (1999).
https:/​/​doi.org/​10.1103/​PhysRevLett.82.1975

[81] Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch. ``Coherent transport of neutral atoms in spin-dependent optical lattice potentials''. Phys. Rev. Lett. 91, 010407 (2003).
https:/​/​doi.org/​10.1103/​PhysRevLett.91.010407

[82] Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch. ``Controlled collisions for multi-particle entanglement of optically trapped atoms''. Nature 425, 937–940 (2003).
https:/​/​doi.org/​10.1038/​nature02008

[83] Noomen Belmechri, Leonid Förster, Wolfgang Alt, Artur Widera, Dieter Meschede, and Andrea Alberti. ``Microwave control of atomic motional states in a spin-dependent optical lattice''. Journal of Physics B: Atomic, Molecular and Optical Physics 46, 104006 (2013).
https:/​/​doi.org/​10.1088/​0953-4075/​46/​10/​104006

[84] Carsten Robens, Wolfgang Alt, Dieter Meschede, Clive Emary, and Andrea Alberti. ``Ideal negative measurements in quantum walks disprove theories based on classical trajectories''. Phys. Rev. X 5, 011003 (2015).
https:/​/​doi.org/​10.1103/​PhysRevX.5.011003

[85] Manolo R. Lam, Natalie Peter, Thorsten Groh, Wolfgang Alt, Carsten Robens, Dieter Meschede, Antonio Negretti, Simone Montangero, Tommaso Calarco, and Andrea Alberti. ``Demonstration of quantum brachistochrones between distant states of an atom''. Phys. Rev. X 11, 011035 (2021).
https:/​/​doi.org/​10.1103/​PhysRevX.11.011035

[86] Wei-Yong Zhang, Ming-Gen He, Hui Sun, Yong-Guang Zheng, Ying Liu, An Luo, Han-Yi Wang, Zi-Hang Zhu, Pei-Yue Qiu, Ying-Chao Shen, Xuan-Kai Wang, Wan Lin, Song-Tao Yu, Bin-Chen Li, Bo Xiao, Meng-Da Li, Yu-Meng Yang, Xiao Jiang, Han-Ning Dai, You Zhou, Xiongfeng Ma, Zhen-Sheng Yuan, and Jian-Wei Pan. ``Scalable multipartite entanglement created by spin exchange in an optical lattice''. Phys. Rev. Lett. 131, 073401 (2023).
https:/​/​doi.org/​10.1103/​PhysRevLett.131.073401

[87] Immanuel Bloch. private communication (2023).

[88] N. Henkel, R. Nath, and T. Pohl. ``Three-dimensional roton excitations and supersolid formation in rydberg-excited bose-einstein condensates''. Phys. Rev. Lett. 104, 195302 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.104.195302

[89] X. Zhang, M. Bishof, S. L. Bromley, C. V. Kraus, M. S. Safronova, P. Zoller, A. M. Rey, and J. Ye. ``Spectroscopic observation of su($n$)-symmetric interactions in sr orbital magnetism''. Science 345, 1467–1473 (2014).
https:/​/​doi.org/​10.1126/​science.1254978

[90] A. Goban, R. B. Hutson, G. E. Marti, S. L. Campbell, M. A. Perlin, P. S. Julienne, J. P. D'Incao, A. M. Rey, and J. Ye. ``Emergence of multi-body interactions in a fermionic lattice clock''. Nature 563, 369–373 (2018).
https:/​/​doi.org/​10.1038/​s41586-018-0661-6

[91] Eduardo Fradkin and Stephen H. Shenker. ``Phase diagrams of lattice gauge theories with higgs fields''. Phys. Rev. D 19, 3682–3697 (1979).
https:/​/​doi.org/​10.1103/​PhysRevD.19.3682

[92] Daniel González-Cuadra, Erez Zohar, and J Ignacio Cirac. ``Quantum simulation of the abelian-higgs lattice gauge theory with ultracold atoms''. New Journal of Physics 19, 063038 (2017).
https:/​/​doi.org/​10.1088/​1367-2630/​aa6f37

[93] Eduardo Fradkin. ``Field theories of condensed matter physics''. Cambridge University Press. (2013). 2 edition.
https:/​/​doi.org/​10.1017/​CBO9781139015509

[94] F. F. Assaad and Tarun Grover. ``Simple fermionic model of deconfined phases and phase transitions''. Phys. Rev. X 6, 041049 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.041049

[95] Xiao-Gang Wen. ``Colloquium: Zoo of quantum-topological phases of matter''. Rev. Mod. Phys. 89, 041004 (2017).
https:/​/​doi.org/​10.1103/​RevModPhys.89.041004

[96] Daniel González-Cuadra, Luca Tagliacozzo, Maciej Lewenstein, and Alejandro Bermudez. ``Robust topological order in fermionic $\mathbb{Z}_{2}$ gauge theories: From aharonov-bohm instability to soliton-induced deconfinement''. Phys. Rev. X 10, 041007 (2020).
https:/​/​doi.org/​10.1103/​PhysRevX.10.041007

[97] Umberto Borla, Bhilahari Jeevanesan, Frank Pollmann, and Sergej Moroz. ``Quantum phases of two-dimensional $\mathbb{Z}_{2}$ gauge theory coupled to single-component fermion matter''. Phys. Rev. B 105, 075132 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.105.075132

[98] Thomas Iadecola and Michael Schecter. ``Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals''. Phys. Rev. B 101, 024306 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.024306

[99] Adith Sai Aramthottil, Utso Bhattacharya, Daniel González-Cuadra, Maciej Lewenstein, Luca Barbiero, and Jakub Zakrzewski. ``Scar states in deconfined $\mathbb{Z}_{2}$ lattice gauge theories''. Phys. Rev. B 106, L041101 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.106.L041101

[100] Jad C. Halimeh, Luca Barbiero, Philipp Hauke, Fabian Grusdt, and Annabelle Bohrdt. ``Robust quantum many-body scars in lattice gauge theories''. Quantum 7, 1004 (2023).
https:/​/​doi.org/​10.22331/​q-2023-05-15-1004

[101] F. Hebenstreit, J. Berges, and D. Gelfand. ``Real-time dynamics of string breaking''. Phys. Rev. Lett. 111, 201601 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.111.201601

[102] D. Petcher and D. H. Weingarten. ``Monte Ć arlo calculations and a model of the phase structure for gauge theories on discrete subgroups of su(2)''. Phys. Rev. D 22, 2465–2477 (1980).
https:/​/​doi.org/​10.1103/​PhysRevD.22.2465

[103] C.J. Hamer. ``Lattice model calculations for su(2) yang-mills theory in 1 + 1 dimensions''. Nuclear Physics B 121, 159–175 (1977).
https:/​/​doi.org/​10.1016/​0550-3213(77)90334-0

[104] Henry Lamm, Scott Lawrence, and Yukari Yamauchi. ``Parton physics on a quantum computer''. Phys. Rev. Res. 2, 013272 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.013272

[105] Jian Liang, Terrence Draper, Keh-Fei Liu, Alexander Rothkopf, and Yi-Bo Yang. ``Towards the nucleon hadronic tensor from lattice qcd''. Phys. Rev. D 101, 114503 (2020).
https:/​/​doi.org/​10.1103/​PhysRevD.101.114503

[106] Torsten V. Zache, Daniel González-Cuadra, and Peter Zoller. ``Quantum and classical spin network algorithms for $q$-deformed kogut-susskind gauge theories'' (2023). arXiv:2304.02527.
arXiv:2304.02527

Cited by

[1] Anthony N. Ciavarella, "Quantum simulation of lattice QCD with improved Hamiltonians", Physical Review D 108 9, 094513 (2023).

[2] Marc Illa, Caroline E. P. Robin, and Martin J. Savage, "Quantum simulations of SO(5) many-fermion systems using qudits", Physical Review C 108 6, 064306 (2023).

[3] Erik J. Gustafson, Henry Lamm, and Felicity Lovelace, "Primitive quantum gates for an SU(2) discrete subgroup: Binary octahedral", Physical Review D 109 5, 054503 (2024).

[4] Torsten V. Zache, Daniel González-Cuadra, and Peter Zoller, "Quantum and Classical Spin-Network Algorithms for q -Deformed Kogut-Susskind Gauge Theories", Physical Review Letters 131 17, 171902 (2023).

[5] Jacob Bringewatt, Jonathan Kunjummen, and Niklas Mueller, "Randomized measurement protocols for lattice gauge theories", Quantum 8, 1300 (2024).

[6] Pavel P. Popov, Michael Meth, Maciej Lewestein, Philipp Hauke, Martin Ringbauer, Erez Zohar, and Valentin Kasper, "Variational quantum simulation of U(1) lattice gauge theories with qudit systems", Physical Review Research 6 1, 013202 (2024).

[7] Qingyu Li, Chiranjib Mukhopadhyay, and Abolfazl Bayat, "Fermionic simulators for enhanced scalability of variational quantum simulation", Physical Review Research 5 4, 043175 (2023).

[8] Alberto Di Meglio, Karl Jansen, Ivano Tavernelli, Constantia Alexandrou, Srinivasan Arunachalam, Christian W. Bauer, Kerstin Borras, Stefano Carrazza, Arianna Crippa, Vincent Croft, Roland de Putter, Andrea Delgado, Vedran Dunjko, Daniel J. Egger, Elias Fernandez-Combarro, Elina Fuchs, Lena Funcke, Daniel Gonzalez-Cuadra, Michele Grossi, Jad C. Halimeh, Zoe Holmes, Stefan Kuhn, Denis Lacroix, Randy Lewis, Donatella Lucchesi, Miriam Lucio Martinez, Federico Meloni, Antonio Mezzacapo, Simone Montangero, Lento Nagano, Voica Radescu, Enrique Rico Ortega, Alessandro Roggero, Julian Schuhmacher, Joao Seixas, Pietro Silvi, Panagiotis Spentzouris, Francesco Tacchino, Kristan Temme, Koji Terashi, Jordi Tura, Cenk Tuysuz, Sofia Vallecorsa, Uwe-Jens Wiese, Shinjae Yoo, and Jinglei Zhang, "Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group", arXiv:2307.03236, (2023).

[9] Sivaprasad Omanakuttan and T. J. Volkoff, "Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles", Physical Review A 108 2, 022428 (2023).

[10] Sivaprasad Omanakuttan, Anupam Mitra, Eric J. Meier, Michael J. Martin, and Ivan H. Deutsch, "Qudit Entanglers Using Quantum Optimal Control", PRX Quantum 4 4, 040333 (2023).

[11] D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller, "Fermionic quantum processing with programmable neutral atom arrays", Proceedings of the National Academy of Science 120 35, e2304294120 (2023).

[12] Giovanni Cataldi, Giuseppe Magnifico, Pietro Silvi, and Simone Montangero, "(2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density via tensor networks", arXiv:2307.09396, (2023).

[13] Marc Illa, Caroline E. P. Robin, and Martin J. Savage, "Qu8its for Quantum Simulations of Lattice Quantum Chromodynamics", arXiv:2403.14537, (2024).

[14] Giuseppe Calajò, Giuseppe Magnifico, Claire Edmunds, Martin Ringbauer, Simone Montangero, and Pietro Silvi, "Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits", arXiv:2402.07987, (2024).

[15] Marcela Carena, Henry Lamm, Ying-Ying Li, and Wanqiang Liu, "Quantum error thresholds for gauge-redundant digitizations of lattice field theories", arXiv:2402.16780, (2024).

[16] Urban F. P. Seifert and Sergej Moroz, "Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids", arXiv:2306.09405, (2023).

[17] Sivaprasad Omanakuttan, "Quantum Computation Using Large Spin Qudits", arXiv:2405.07885, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 20:19:51) and SAO/NASA ADS (last updated successfully 2024-05-24 20:19:52). The list may be incomplete as not all publishers provide suitable and complete citation data.