{"id":520522,"date":"2026-04-09T00:31:14","date_gmt":"2026-04-09T00:31:14","guid":{"rendered":"https:\/\/www.newsbeep.com\/uk\/520522\/"},"modified":"2026-04-09T00:31:14","modified_gmt":"2026-04-09T00:31:14","slug":"protected-quantum-gates-using-qubit-doublons-in-dynamical-optical-lattices","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/uk\/520522\/","title":{"rendered":"Protected quantum gates using qubit doublons in dynamical optical lattices"},"content":{"rendered":"<p class=\"c-article-references__text\" id=\"ref-CR1\">Jaksch, D., Briegel, H.-J., Cirac, J. I., Gardiner, C. W. &amp; Zoller, P. Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975\u20131978 (1999).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.82.1975\" data-track-item_id=\"10.1103\/PhysRevLett.82.1975\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.82.1975\" aria-label=\"Article reference 1\" data-doi=\"10.1103\/PhysRevLett.82.1975\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1999PhRvL..82.1975J\" aria-label=\"ADS reference 1\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DyaK1MXhtlertLw%3D\" aria-label=\"CAS reference 1\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 1\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Entanglement%20of%20atoms%20via%20cold%20controlled%20collisions&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.82.1975&amp;volume=82&amp;pages=1975-1978&amp;publication_year=1999&amp;author=Jaksch%2CD&amp;author=Briegel%2CH-J&amp;author=Cirac%2CJI&amp;author=Gardiner%2CCW&amp;author=Zoller%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR2\">Brennen, G. K., Caves, C. M., Jessen, P. S. &amp; Deutsch, I. H. Quantum logic gates in optical lattices. Phys. Rev. Lett. 82, 1060\u20131063 (1999).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.82.1060\" data-track-item_id=\"10.1103\/PhysRevLett.82.1060\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.82.1060\" aria-label=\"Article reference 2\" data-doi=\"10.1103\/PhysRevLett.82.1060\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1999PhRvL..82.1060B\" aria-label=\"ADS reference 2\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DyaK1MXotV2ntg%3D%3D\" aria-label=\"CAS reference 2\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 2\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20logic%20gates%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.82.1060&amp;volume=82&amp;pages=1060-1063&amp;publication_year=1999&amp;author=Brennen%2CGK&amp;author=Caves%2CCM&amp;author=Jessen%2CPS&amp;author=Deutsch%2CIH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR3\">S\u00f8rensen, A. &amp; M\u00f8lmer, K. Spin-spin interaction and spin squeezing in an optical lattice. Phys. Rev. Lett. 83, 2274\u20132277 (1999).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.83.2274\" data-track-item_id=\"10.1103\/PhysRevLett.83.2274\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.83.2274\" aria-label=\"Article reference 3\" data-doi=\"10.1103\/PhysRevLett.83.2274\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1999PhRvL..83.2274S\" aria-label=\"ADS reference 3\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 3\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spin-spin%20interaction%20and%20spin%20squeezing%20in%20an%20optical%20lattice&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.83.2274&amp;volume=83&amp;pages=2274-2277&amp;publication_year=1999&amp;author=S%C3%B8rensen%2CA&amp;author=M%C3%B8lmer%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR4\">Calarco, T. et al. Quantum gates with neutral atoms: controlling collisional interactions in time-dependent traps. Phys. Rev. A 61, 022304 (2000).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.61.022304\" data-track-item_id=\"10.1103\/PhysRevA.61.022304\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.61.022304\" aria-label=\"Article reference 4\" data-doi=\"10.1103\/PhysRevA.61.022304\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2000PhRvA..61b2304C\" aria-label=\"ADS reference 4\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 4\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20gates%20with%20neutral%20atoms%3A%20controlling%20collisional%20interactions%20in%20time-dependent%20traps&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.61.022304&amp;volume=61&amp;publication_year=2000&amp;author=Calarco%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR5\">Hayes, D., Julienne, P. S. &amp; Deutsch, I. H. Quantum logic via the exchange blockade in ultracold collisions. Phys. Rev. Lett. 98, 070501 (2007).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.98.070501\" data-track-item_id=\"10.1103\/PhysRevLett.98.070501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.98.070501\" aria-label=\"Article reference 5\" data-doi=\"10.1103\/PhysRevLett.98.070501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2007PhRvL..98g0501H\" aria-label=\"ADS reference 5\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=17359003\" aria-label=\"PubMed reference 5\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 5\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20logic%20via%20the%20exchange%20blockade%20in%20ultracold%20collisions&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.98.070501&amp;volume=98&amp;publication_year=2007&amp;author=Hayes%2CD&amp;author=Julienne%2CPS&amp;author=Deutsch%2CIH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR6\">Daley, A. J., Boyd, M. M., Ye, J. &amp; Zoller, P. Quantum computing with alkaline-earth-metal atoms. Phys. Rev. Lett. 101, 170504 (2008).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.101.170504\" data-track-item_id=\"10.1103\/PhysRevLett.101.170504\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.101.170504\" aria-label=\"Article reference 6\" data-doi=\"10.1103\/PhysRevLett.101.170504\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2008PhRvL.101q0504D\" aria-label=\"ADS reference 6\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=18999733\" aria-label=\"PubMed reference 6\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 6\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20computing%20with%20alkaline-earth-metal%20atoms&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.101.170504&amp;volume=101&amp;publication_year=2008&amp;author=Daley%2CAJ&amp;author=Boyd%2CMM&amp;author=Ye%2CJ&amp;author=Zoller%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR7\">Weitenberg, C., Kuhr, S., M\u00f8lmer, K. &amp; Sherson, J. F. Quantum computation architecture using optical tweezers. Phys. Rev. A 84, 032322 (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.84.032322\" data-track-item_id=\"10.1103\/PhysRevA.84.032322\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.84.032322\" aria-label=\"Article reference 7\" data-doi=\"10.1103\/PhysRevA.84.032322\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2011PhRvA..84c2322W\" aria-label=\"ADS reference 7\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 7\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20computation%20architecture%20using%20optical%20tweezers&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.84.032322&amp;volume=84&amp;publication_year=2011&amp;author=Weitenberg%2CC&amp;author=Kuhr%2CS&amp;author=M%C3%B8lmer%2CK&amp;author=Sherson%2CJF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR8\">Nemirovsky, J. &amp; Sagi, Y. Fast universal two-qubit gate for neutral fermionic atoms in optical tweezers. Phys. Rev. Res. 3, 013113 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevResearch.3.013113\" data-track-item_id=\"10.1103\/PhysRevResearch.3.013113\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.3.013113\" aria-label=\"Article reference 8\" data-doi=\"10.1103\/PhysRevResearch.3.013113\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3MXovVajurk%3D\" aria-label=\"CAS reference 8\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 8\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fast%20universal%20two-qubit%20gate%20for%20neutral%20fermionic%20atoms%20in%20optical%20tweezers&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.3.013113&amp;volume=3&amp;publication_year=2021&amp;author=Nemirovsky%2CJ&amp;author=Sagi%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR9\">Zhou, Y. et al. A scheme to create and verify scalable entanglement in optical lattice. npj Quantum Inf. 8, 99 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41534-022-00609-0\" data-track-item_id=\"10.1038\/s41534-022-00609-0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41534-022-00609-0\" aria-label=\"Article reference 9\" data-doi=\"10.1038\/s41534-022-00609-0\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022npjQI...8...99Z\" aria-label=\"ADS reference 9\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 9\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20scheme%20to%20create%20and%20verify%20scalable%20entanglement%20in%20optical%20lattice&amp;journal=npj%20Quantum%20Inf.&amp;doi=10.1038%2Fs41534-022-00609-0&amp;volume=8&amp;publication_year=2022&amp;author=Zhou%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR10\">Singh, J., Reuter, J. A.P., Calarco, T., Motzoi, F. &amp; Zeier, R. Optimizing two-qubit gates for ultracold atoms using Fermi-Hubbard models. Phys. Rev. Appl. 24, 034007 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/xqzw-m27l\" data-track-item_id=\"10.1103\/xqzw-m27l\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2Fxqzw-m27l\" aria-label=\"Article reference 10\" data-doi=\"10.1103\/xqzw-m27l\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025PhRvP..24c4007S\" aria-label=\"ADS reference 10\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2MXisVOnt77P\" aria-label=\"CAS reference 10\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 10\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optimizing%20two-qubit%20gates%20for%20ultracold%20atoms%20using%20Fermi-Hubbard%20models&amp;journal=Phys.%20Rev.%20Appl.&amp;doi=10.1103%2Fxqzw-m27l&amp;volume=24&amp;publication_year=2025&amp;author=Singh%2CJ&amp;author=Reuter%2CJAP&amp;author=Calarco%2CT&amp;author=Motzoi%2CF&amp;author=Zeier%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR11\">Mandel, O. et al. Controlled collisions for multi-particle entanglement of optically trapped atoms. Nature 425, 937\u2013940 (2003).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature02008\" data-track-item_id=\"10.1038\/nature02008\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature02008\" aria-label=\"Article reference 11\" data-doi=\"10.1038\/nature02008\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2003Natur.425..937M\" aria-label=\"ADS reference 11\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BD3sXosVOhtrg%3D\" aria-label=\"CAS reference 11\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=14586463\" aria-label=\"PubMed reference 11\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 11\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Controlled%20collisions%20for%20multi-particle%20entanglement%20of%20optically%20trapped%20atoms&amp;journal=Nature&amp;doi=10.1038%2Fnature02008&amp;volume=425&amp;pages=937-940&amp;publication_year=2003&amp;author=Mandel%2CO\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR12\">Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452\u2013456 (2007).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature06011\" data-track-item_id=\"10.1038\/nature06011\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature06011\" aria-label=\"Article reference 12\" data-doi=\"10.1038\/nature06011\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2007Natur.448..452A\" aria-label=\"ADS reference 12\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BD2sXotFajurg%3D\" aria-label=\"CAS reference 12\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=17653187\" aria-label=\"PubMed reference 12\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 12\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Controlled%20exchange%20interaction%20between%20pairs%20of%20neutral%20atoms%20in%20an%20optical%20lattice&amp;journal=Nature&amp;doi=10.1038%2Fnature06011&amp;volume=448&amp;pages=452-456&amp;publication_year=2007&amp;author=Anderlini%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR13\">Kaufman, A. M. et al. Entangling two transportable neutral atoms via local spin exchange. Nature 527, 208\u2013211 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature16073\" data-track-item_id=\"10.1038\/nature16073\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature16073\" aria-label=\"Article reference 13\" data-doi=\"10.1038\/nature16073\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015Natur.527..208K\" aria-label=\"ADS reference 13\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC2MXhslOrtb7M\" aria-label=\"CAS reference 13\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=26524533\" aria-label=\"PubMed reference 13\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 13\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Entangling%20two%20transportable%20neutral%20atoms%20via%20local%20spin%20exchange&amp;journal=Nature&amp;doi=10.1038%2Fnature16073&amp;volume=527&amp;pages=208-211&amp;publication_year=2015&amp;author=Kaufman%2CAM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR14\">F\u00f6lling, S. et al. Direct observation of second-order atom tunnelling. Nature 448, 1029\u20131032 (2007).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature06112\" data-track-item_id=\"10.1038\/nature06112\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature06112\" aria-label=\"Article reference 14\" data-doi=\"10.1038\/nature06112\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2007Natur.448.1029F\" aria-label=\"ADS reference 14\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=17728753\" aria-label=\"PubMed reference 14\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 14\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Direct%20observation%20of%20second-order%20atom%20tunnelling&amp;journal=Nature&amp;doi=10.1038%2Fnature06112&amp;volume=448&amp;pages=1029-1032&amp;publication_year=2007&amp;author=F%C3%B6lling%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR15\">Trotzky, S., Chen, Y.-A., Schnorrberger, U., Cheinet, P. &amp; Bloch, I. Controlling and detecting spin correlations of ultracold atoms in optical lattices. Phys. Rev. Lett. 105, 265303 (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.105.265303\" data-track-item_id=\"10.1103\/PhysRevLett.105.265303\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.105.265303\" aria-label=\"Article reference 15\" data-doi=\"10.1103\/PhysRevLett.105.265303\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2010PhRvL.105z5303T\" aria-label=\"ADS reference 15\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=21231676\" aria-label=\"PubMed reference 15\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 15\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Controlling%20and%20detecting%20spin%20correlations%20of%20ultracold%20atoms%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.105.265303&amp;volume=105&amp;publication_year=2010&amp;author=Trotzky%2CS&amp;author=Chen%2CY-A&amp;author=Schnorrberger%2CU&amp;author=Cheinet%2CP&amp;author=Bloch%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR16\">Zhu, Z. et al. Splitting and connecting singlets in atomic quantum circuits. Phys. Rev. X 15, 041032 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB28XivVGhtL4%3D\" aria-label=\"CAS reference 16\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 16\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Splitting%20and%20connecting%20singlets%20in%20atomic%20quantum%20circuits&amp;journal=Phys.%20Rev.%20X&amp;volume=15&amp;publication_year=2025&amp;author=Zhu%2CZ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR17\">Chalopin, T. et al. Optical superlattice for engineering Hubbard couplings in quantum simulation. Phys. Rev. Lett. 134, 053402 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.134.053402\" data-track-item_id=\"10.1103\/PhysRevLett.134.053402\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.134.053402\" aria-label=\"Article reference 17\" data-doi=\"10.1103\/PhysRevLett.134.053402\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025PhRvL.134e3402C\" aria-label=\"ADS reference 17\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2MXltFOlsLk%3D\" aria-label=\"CAS reference 17\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=39983179\" aria-label=\"PubMed reference 17\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 17\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optical%20superlattice%20for%20engineering%20Hubbard%20couplings%20in%20quantum%20simulation&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.134.053402&amp;volume=134&amp;publication_year=2025&amp;author=Chalopin%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR18\">Yang, B. et al. Cooling and entangling ultracold atoms in optical lattices. Science 369, 550\u2013553 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aaz6801\" data-track-item_id=\"10.1126\/science.aaz6801\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aaz6801\" aria-label=\"Article reference 18\" data-doi=\"10.1126\/science.aaz6801\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020Sci...369..550Y\" aria-label=\"ADS reference 18\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3cXhsFWgsbvF\" aria-label=\"CAS reference 18\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=32554628\" aria-label=\"PubMed reference 18\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 18\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Cooling%20and%20entangling%20ultracold%20atoms%20in%20optical%20lattices&amp;journal=Science&amp;doi=10.1126%2Fscience.aaz6801&amp;volume=369&amp;pages=550-553&amp;publication_year=2020&amp;author=Yang%2CB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR19\">Zhang, W.-Y. et al. Scalable multipartite entanglement created by spin exchange in an optical lattice. Phys. Rev. Lett. 131, 073401 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.131.073401\" data-track-item_id=\"10.1103\/PhysRevLett.131.073401\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.131.073401\" aria-label=\"Article reference 19\" data-doi=\"10.1103\/PhysRevLett.131.073401\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023PhRvL.131g3401Z\" aria-label=\"ADS reference 19\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXhvF2isrzO\" aria-label=\"CAS reference 19\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=37656862\" aria-label=\"PubMed reference 19\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 19\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Scalable%20multipartite%20entanglement%20created%20by%20spin%20exchange%20in%20an%20optical%20lattice&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.131.073401&amp;volume=131&amp;publication_year=2023&amp;author=Zhang%2CW-Y\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR20\">Bojovi\u0107, P. et al. High-fidelity collisional quantum gates with fermionic atoms. Nature <a href=\"https:\/\/doi.org\/10.1038\/s41586-026-10356-3\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41586-026-10356-3\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41586-026-10356-3<\/a> (2026).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR21\">Murmann, S. et al. Two fermions in a double well: exploring a fundamental building block of the Hubbard model. Phys. Rev. Lett. 114, 080402 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.114.080402\" data-track-item_id=\"10.1103\/PhysRevLett.114.080402\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.114.080402\" aria-label=\"Article reference 21\" data-doi=\"10.1103\/PhysRevLett.114.080402\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015PhRvL.114h0402M\" aria-label=\"ADS reference 21\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=25768739\" aria-label=\"PubMed reference 21\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 21\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Two%20fermions%20in%20a%20double%20well%3A%20exploring%20a%20fundamental%20building%20block%20of%20the%20Hubbard%20model&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.114.080402&amp;volume=114&amp;publication_year=2015&amp;author=Murmann%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR22\">Hartke, T., Oreg, B., Jia, N. &amp; Zwierlein, M. Quantum register of fermion pairs. Nature 601, 537\u2013541 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-021-04205-8\" data-track-item_id=\"10.1038\/s41586-021-04205-8\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-021-04205-8\" aria-label=\"Article reference 22\" data-doi=\"10.1038\/s41586-021-04205-8\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022Natur.601..537H\" aria-label=\"ADS reference 22\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XitFGlu7w%3D\" aria-label=\"CAS reference 22\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=35082420\" aria-label=\"PubMed reference 22\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 22\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20register%20of%20fermion%20pairs&amp;journal=Nature&amp;doi=10.1038%2Fs41586-021-04205-8&amp;volume=601&amp;pages=537-541&amp;publication_year=2022&amp;author=Hartke%2CT&amp;author=Oreg%2CB&amp;author=Jia%2CN&amp;author=Zwierlein%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR23\">Sj\u00f6qvist, E. Geometric phases in quantum information. Int. J. Quant. Chem. 115, 1311\u20131326 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1002\/qua.24941\" data-track-item_id=\"10.1002\/qua.24941\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1002%2Fqua.24941\" aria-label=\"Article reference 23\" data-doi=\"10.1002\/qua.24941\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 23\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Geometric%20phases%20in%20quantum%20information&amp;journal=Int.%20J.%20Quant.%20Chem.&amp;doi=10.1002%2Fqua.24941&amp;volume=115&amp;pages=1311-1326&amp;publication_year=2015&amp;author=Sj%C3%B6qvist%2CE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR24\">Duan, L.-M., Cirac, J. I. &amp; Zoller, P. Geometric manipulation of trapped ions for quantum computation. Science 292, 1695\u20131697 (2001).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.1058835\" data-track-item_id=\"10.1126\/science.1058835\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.1058835\" aria-label=\"Article reference 24\" data-doi=\"10.1126\/science.1058835\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2001Sci...292.1695D\" aria-label=\"ADS reference 24\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BD3MXkt1SltL4%3D\" aria-label=\"CAS reference 24\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=11387469\" aria-label=\"PubMed reference 24\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 24\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Geometric%20manipulation%20of%20trapped%20ions%20for%20quantum%20computation&amp;journal=Science&amp;doi=10.1126%2Fscience.1058835&amp;volume=292&amp;pages=1695-1697&amp;publication_year=2001&amp;author=Duan%2CL-M&amp;author=Cirac%2CJI&amp;author=Zoller%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR25\">Desbuquois, R. et al. Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system. Phys. Rev. A 96, 053602 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.96.053602\" data-track-item_id=\"10.1103\/PhysRevA.96.053602\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.96.053602\" aria-label=\"Article reference 25\" data-doi=\"10.1103\/PhysRevA.96.053602\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvA..96e3602D\" aria-label=\"ADS reference 25\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 25\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Controlling%20the%20Floquet%20state%20population%20and%20observing%20micromotion%20in%20a%20periodically%20driven%20two-body%20quantum%20system&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.96.053602&amp;volume=96&amp;publication_year=2017&amp;author=Desbuquois%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR26\">Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. &amp; Petta, J. R. Semiconductor spin qubits. Rev. Mod. Phys. 95, 025003 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.95.025003\" data-track-item_id=\"10.1103\/RevModPhys.95.025003\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.95.025003\" aria-label=\"Article reference 26\" data-doi=\"10.1103\/RevModPhys.95.025003\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023RvMP...95b5003B\" aria-label=\"ADS reference 26\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXhsFKhsLfE\" aria-label=\"CAS reference 26\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 26\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Semiconductor%20spin%20qubits&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.95.025003&amp;volume=95&amp;publication_year=2023&amp;author=Burkard%2CG&amp;author=Ladd%2CTD&amp;author=Pan%2CA&amp;author=Nichol%2CJM&amp;author=Petta%2CJR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR27\">Hu, X. &amp; Das Sarma, S. Gate errors in solid-state quantum-computer architectures. Phys. Rev. A 66, 012312 (2002).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.66.012312\" data-track-item_id=\"10.1103\/PhysRevA.66.012312\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.66.012312\" aria-label=\"Article reference 27\" data-doi=\"10.1103\/PhysRevA.66.012312\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2002PhRvA..66a2312H\" aria-label=\"ADS reference 27\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 27\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Gate%20errors%20in%20solid-state%20quantum-computer%20architectures&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.66.012312&amp;volume=66&amp;publication_year=2002&amp;author=Hu%2CX&amp;author=Sarma%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR28\">Kaplan, T. A. &amp; Piermarocchi, C. Spin swap versus double occupancy in quantum gates. Phys. Rev. B 70, 161311 (2004).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.70.161311\" data-track-item_id=\"10.1103\/PhysRevB.70.161311\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.70.161311\" aria-label=\"Article reference 28\" data-doi=\"10.1103\/PhysRevB.70.161311\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2004PhRvB..70p1311K\" aria-label=\"ADS reference 28\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 28\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spin%20swap%20versus%20double%20occupancy%20in%20quantum%20gates&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.70.161311&amp;volume=70&amp;publication_year=2004&amp;author=Kaplan%2CTA&amp;author=Piermarocchi%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR29\">Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 1994).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR30\">Vitanov, N. V., Rangelov, A. A., Shore, B. W. &amp; Bergmann, K. Stimulated Raman adiabatic passage in physics, chemistry, and beyond. Rev. Mod. Phys. 89, 015006 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.89.015006\" data-track-item_id=\"10.1103\/RevModPhys.89.015006\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.89.015006\" aria-label=\"Article reference 30\" data-doi=\"10.1103\/RevModPhys.89.015006\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017RvMP...89a5006V\" aria-label=\"ADS reference 30\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 30\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Stimulated%20Raman%20adiabatic%20passage%20in%20physics%2C%20chemistry%2C%20and%20beyond&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.89.015006&amp;volume=89&amp;publication_year=2017&amp;author=Vitanov%2CNV&amp;author=Rangelov%2CAA&amp;author=Shore%2CBW&amp;author=Bergmann%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR31\">Aharonov, Y. &amp; Anandan, J. Phase change during a cyclic quantum evolution. Phys. Rev. Lett. 58, 1593\u20131596 (1987).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.58.1593\" data-track-item_id=\"10.1103\/PhysRevLett.58.1593\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.58.1593\" aria-label=\"Article reference 31\" data-doi=\"10.1103\/PhysRevLett.58.1593\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1987PhRvL..58.1593A\" aria-label=\"ADS reference 31\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=884314\" aria-label=\"MathSciNet reference 31\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:STN:280:DC%2BC2sfotFyltQ%3D%3D\" aria-label=\"CAS reference 31\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=10034484\" aria-label=\"PubMed reference 31\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 31\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Phase%20change%20during%20a%20cyclic%20quantum%20evolution&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.58.1593&amp;volume=58&amp;pages=1593-1596&amp;publication_year=1987&amp;author=Aharonov%2CY&amp;author=Anandan%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR32\">Greif, D., Uehlinger, T., Jotzu, G., Tarruell, L. &amp; Esslinger, T. Short-range quantum magnetism of ultracold fermions in an optical lattice. Science 340, 1307\u20131310 (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.1236362\" data-track-item_id=\"10.1126\/science.1236362\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.1236362\" aria-label=\"Article reference 32\" data-doi=\"10.1126\/science.1236362\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013Sci...340.1307G\" aria-label=\"ADS reference 32\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC3sXptFKjsrw%3D\" aria-label=\"CAS reference 32\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=23704375\" aria-label=\"PubMed reference 32\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 32\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Short-range%20quantum%20magnetism%20of%20ultracold%20fermions%20in%20an%20optical%20lattice&amp;journal=Science&amp;doi=10.1126%2Fscience.1236362&amp;volume=340&amp;pages=1307-1310&amp;publication_year=2013&amp;author=Greif%2CD&amp;author=Uehlinger%2CT&amp;author=Jotzu%2CG&amp;author=Tarruell%2CL&amp;author=Esslinger%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR33\">Chin, C., Grimm, R., Julienne, P. &amp; Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225\u20131286 (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.82.1225\" data-track-item_id=\"10.1103\/RevModPhys.82.1225\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.82.1225\" aria-label=\"Article reference 33\" data-doi=\"10.1103\/RevModPhys.82.1225\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2010RvMP...82.1225C\" aria-label=\"ADS reference 33\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC3cXos1Gmur4%3D\" aria-label=\"CAS reference 33\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 33\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Feshbach%20resonances%20in%20ultracold%20gases&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.82.1225&amp;volume=82&amp;pages=1225-1286&amp;publication_year=2010&amp;author=Chin%2CC&amp;author=Grimm%2CR&amp;author=Julienne%2CP&amp;author=Tiesinga%2CE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR34\">Kasevich, M. &amp; Chu, S. Laser cooling below a photon recoil with three-level atoms. Phys. Rev. Lett. 69, 1741\u20131744 (1992).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.69.1741\" data-track-item_id=\"10.1103\/PhysRevLett.69.1741\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.69.1741\" aria-label=\"Article reference 34\" data-doi=\"10.1103\/PhysRevLett.69.1741\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1992PhRvL..69.1741K\" aria-label=\"ADS reference 34\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DyaK38XlvF2jsbk%3D\" aria-label=\"CAS reference 34\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=10046302\" aria-label=\"PubMed reference 34\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 34\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Laser%20cooling%20below%20a%20photon%20recoil%20with%20three-level%20atoms&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.69.1741&amp;volume=69&amp;pages=1741-1744&amp;publication_year=1992&amp;author=Kasevich%2CM&amp;author=Chu%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR35\">Fern\u00e1ndez, P. &amp; Martin-Delgado, M. A. Implementing the Grover algorithm in homomorphic encryption schemes. Phys. Rev. Res. 6, 043109 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevResearch.6.043109\" data-track-item_id=\"10.1103\/PhysRevResearch.6.043109\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.6.043109\" aria-label=\"Article reference 35\" data-doi=\"10.1103\/PhysRevResearch.6.043109\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 35\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Implementing%20the%20Grover%20algorithm%20in%20homomorphic%20encryption%20schemes&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.6.043109&amp;volume=6&amp;publication_year=2024&amp;author=Fern%C3%A1ndez%2CP&amp;author=Martin-Delgado%2CMA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR36\">Andersen, C. K. &amp; Greplov\u00e1, E. Small quantum low parity density check codes for near-term experiments. Preprint at <a href=\"https:\/\/doi.org\/10.48550\/arXiv.2507.09690\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.48550\/arXiv.2507.09690\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.48550\/arXiv.2507.09690<\/a> (2025).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR37\">Tan, B. &amp; Cong, J. Optimal layout synthesis for quantum computing. In Proc. 39th International Conference on Computer-Aided Design pp. 1\u20139 (ACM, 2020).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR38\">Camps, D., Van Beeumen, R. &amp; Yang, C. Quantum Fourier transform revisited. Numer. Linear Algebra Appl. 28, e2331 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1002\/nla.2331\" data-track-item_id=\"10.1002\/nla.2331\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1002%2Fnla.2331\" aria-label=\"Article reference 38\" data-doi=\"10.1002\/nla.2331\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4184087\" aria-label=\"MathSciNet reference 38\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 38\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20Fourier%20transform%20revisited&amp;journal=Numer.%20Linear%20Algebra%20Appl.&amp;doi=10.1002%2Fnla.2331&amp;volume=28&amp;publication_year=2021&amp;author=Camps%2CD&amp;author=Beeumen%2CR&amp;author=Yang%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR39\">Blekos, K. et al. A review on quantum approximate optimization algorithm and its variants. Phys. Rep. 1068, 1\u201366 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.physrep.2024.03.002\" data-track-item_id=\"10.1016\/j.physrep.2024.03.002\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.physrep.2024.03.002\" aria-label=\"Article reference 39\" data-doi=\"10.1016\/j.physrep.2024.03.002\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024PhR..1068....1B\" aria-label=\"ADS reference 39\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4718366\" aria-label=\"MathSciNet reference 39\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 39\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20review%20on%20quantum%20approximate%20optimization%20algorithm%20and%20its%20variants&amp;journal=Phys.%20Rep.&amp;doi=10.1016%2Fj.physrep.2024.03.002&amp;volume=1068&amp;pages=1-66&amp;publication_year=2024&amp;author=Blekos%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR40\">Evered, S. J. et al. High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 622, 268\u2013272 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-023-06481-y\" data-track-item_id=\"10.1038\/s41586-023-06481-y\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-023-06481-y\" aria-label=\"Article reference 40\" data-doi=\"10.1038\/s41586-023-06481-y\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023Natur.622..268E\" aria-label=\"ADS reference 40\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXitFWlsLrL\" aria-label=\"CAS reference 40\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=37821591\" aria-label=\"PubMed reference 40\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC10567572\" aria-label=\"PubMed Central reference 40\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 40\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-fidelity%20parallel%20entangling%20gates%20on%20a%20neutral-atom%20quantum%20computer&amp;journal=Nature&amp;doi=10.1038%2Fs41586-023-06481-y&amp;volume=622&amp;pages=268-272&amp;publication_year=2023&amp;author=Evered%2CSJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR41\">Rines, R. et al. Demonstration of a logical architecture uniting motion and in-place entanglement: Shor\u2019s algorithm, constant-depth CNOT ladder, and many-hypercube code. Preprint at <a href=\"http:\/\/arxiv.org\/abs\/2509.13247\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"http:\/\/arxiv.org\/abs\/2509.13247\" rel=\"nofollow noopener\" target=\"_blank\">arxiv.org\/abs\/2509.13247<\/a> (2025).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR42\">Peper, M. et al. Spectroscopy and modeling of 171Yb Rydberg states for high-fidelity two-qubit gates. Phys. Rev. X 15, 011009 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2MXovFGisLs%3D\" aria-label=\"CAS reference 42\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 42\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spectroscopy%20and%20modeling%20of%20171Yb%20Rydberg%20states%20for%20high-fidelity%20two-qubit%20gates&amp;journal=Phys.%20Rev.%20X&amp;volume=15&amp;publication_year=2025&amp;author=Peper%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR43\">Muniz, J. A. et al. High-fidelity universal gates in the 171Yb ground-state nuclear-spin qubit. PRX Quantum 6, 020334 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PRXQuantum.6.020334\" data-track-item_id=\"10.1103\/PRXQuantum.6.020334\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPRXQuantum.6.020334\" aria-label=\"Article reference 43\" data-doi=\"10.1103\/PRXQuantum.6.020334\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025PRXQ....6b0334M\" aria-label=\"ADS reference 43\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 43\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-fidelity%20universal%20gates%20in%20the%20171Yb%20ground-state%20nuclear-spin%20qubit&amp;journal=PRX%20Quantum&amp;doi=10.1103%2FPRXQuantum.6.020334&amp;volume=6&amp;publication_year=2025&amp;author=Muniz%2CJA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR44\">Senoo, A. et al. High-fidelity entanglement and coherent multi-qubit mapping in an atom array. Preprint at <a href=\"http:\/\/arxiv.org\/abs\/2506.13632\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"http:\/\/arxiv.org\/abs\/2506.13632\" rel=\"nofollow noopener\" target=\"_blank\">arxiv.org\/abs\/2506.13632<\/a> (2025).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR45\">Bravyi, S. B. &amp; Kitaev, A. Y. Fermionic quantum computation. Ann. Phys. 298, 210\u2013226 (2002).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1006\/aphy.2002.6254\" data-track-item_id=\"10.1006\/aphy.2002.6254\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1006%2Faphy.2002.6254\" aria-label=\"Article reference 45\" data-doi=\"10.1006\/aphy.2002.6254\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2002AnPhy.298..210B\" aria-label=\"ADS reference 45\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1910092\" aria-label=\"MathSciNet reference 45\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BD38Xktlals7k%3D\" aria-label=\"CAS reference 45\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 45\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fermionic%20quantum%20computation&amp;journal=Ann.%20Phys.&amp;doi=10.1006%2Faphy.2002.6254&amp;volume=298&amp;pages=210-226&amp;publication_year=2002&amp;author=Bravyi%2CSB&amp;author=Kitaev%2CAY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR46\">Gonz\u00e1lez-Cuadra, D. et al. Fermionic quantum processing with programmable neutral atom arrays. Proc. Natl Acad. Sci. USA 120, e2304294120 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1073\/pnas.2304294120\" data-track-item_id=\"10.1073\/pnas.2304294120\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1073%2Fpnas.2304294120\" aria-label=\"Article reference 46\" data-doi=\"10.1073\/pnas.2304294120\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4648070\" aria-label=\"MathSciNet reference 46\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=37607226\" aria-label=\"PubMed reference 46\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC10468619\" aria-label=\"PubMed Central reference 46\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 46\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fermionic%20quantum%20processing%20with%20programmable%20neutral%20atom%20arrays&amp;journal=Proc.%20Natl%20Acad.%20Sci.%20USA&amp;doi=10.1073%2Fpnas.2304294120&amp;volume=120&amp;publication_year=2023&amp;author=Gonz%C3%A1lez-Cuadra%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR47\">Zhu, C. et al. Quantum compiler design for qubit mapping and routing: a cross-architectural survey of superconducting, trapped-ion, and neutral atom systems. Preprint at <a href=\"http:\/\/arxiv.org\/abs\/2505.16891\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"http:\/\/arxiv.org\/abs\/2505.16891\" rel=\"nofollow noopener\" target=\"_blank\">arxiv.org\/abs\/2505.16891<\/a> (2025).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR48\">Zhou, Y.-C. et al. High-fidelity geometric quantum gates exceeding 99.9% in germanium quantum dots. Nat. Commun. 16, 7953 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-025-63241-4\" data-track-item_id=\"10.1038\/s41467-025-63241-4\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-025-63241-4\" aria-label=\"Article reference 48\" data-doi=\"10.1038\/s41467-025-63241-4\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025NatCo..16.7953Z\" aria-label=\"ADS reference 48\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2MXitFGjsrjE\" aria-label=\"CAS reference 48\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=40858587\" aria-label=\"PubMed reference 48\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC12381234\" aria-label=\"PubMed Central reference 48\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 48\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-fidelity%20geometric%20quantum%20gates%20exceeding%2099.9%25%20in%20germanium%20quantum%20dots&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-025-63241-4&amp;volume=16&amp;publication_year=2025&amp;author=Zhou%2CY-C\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR49\">Chiu, C.-K., Teo, J. C., Schnyder, A. P. &amp; Ryu, S. Classification of topological quantum matter with symmetries. Rev. Mod. Phys. 88, 035005 (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.88.035005\" data-track-item_id=\"10.1103\/RevModPhys.88.035005\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.88.035005\" aria-label=\"Article reference 49\" data-doi=\"10.1103\/RevModPhys.88.035005\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016RvMP...88c5005C\" aria-label=\"ADS reference 49\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 49\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Classification%20of%20topological%20quantum%20matter%20with%20symmetries&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.88.035005&amp;volume=88&amp;publication_year=2016&amp;author=Chiu%2CC-K&amp;author=Teo%2CJC&amp;author=Schnyder%2CAP&amp;author=Ryu%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR50\">Neef, V., Heinrich, M., Wolterink, T. A. W. &amp; Szameit, A. Pairing particles into holonomies. Sci. Adv. 12, eady3856 (2026).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/sciadv.ady3856\" data-track-item_id=\"10.1126\/sciadv.ady3856\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fsciadv.ady3856\" aria-label=\"Article reference 50\" data-doi=\"10.1126\/sciadv.ady3856\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB28XosVKmsr4%3D\" aria-label=\"CAS reference 50\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=41564170\" aria-label=\"PubMed reference 50\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC12822637\" aria-label=\"PubMed Central reference 50\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 50\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Pairing%20particles%20into%20holonomies&amp;journal=Sci.%20Adv.&amp;doi=10.1126%2Fsciadv.ady3856&amp;volume=12&amp;publication_year=2026&amp;author=Neef%2CV&amp;author=Heinrich%2CM&amp;author=Wolterink%2CTAW&amp;author=Szameit%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR51\">Walter, A.-S. et al. Quantization and its breakdown in a Hubbard-Thouless pump. Nat. Phys. 19, 1471\u20131475 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-023-02145-w\" data-track-item_id=\"10.1038\/s41567-023-02145-w\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-023-02145-w\" aria-label=\"Article reference 51\" data-doi=\"10.1038\/s41567-023-02145-w\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXhsFCksrzL\" aria-label=\"CAS reference 51\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=37841998\" aria-label=\"PubMed reference 51\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC10567560\" aria-label=\"PubMed Central reference 51\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 51\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantization%20and%20its%20breakdown%20in%20a%20Hubbard-Thouless%20pump&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-023-02145-w&amp;volume=19&amp;pages=1471-1475&amp;publication_year=2023&amp;author=Walter%2CA-S\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR52\">Xu, M. et al. A neutral-atom Hubbard quantum simulator in the cryogenic regime. Nature 642, 909\u2013915 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-025-09112-w\" data-track-item_id=\"10.1038\/s41586-025-09112-w\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-025-09112-w\" aria-label=\"Article reference 52\" data-doi=\"10.1038\/s41586-025-09112-w\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025Natur.642..909X\" aria-label=\"ADS reference 52\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2MXhsFCgs7vM\" aria-label=\"CAS reference 52\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=40500449\" aria-label=\"PubMed reference 52\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC12221996\" aria-label=\"PubMed Central reference 52\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 52\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20neutral-atom%20Hubbard%20quantum%20simulator%20in%20the%20cryogenic%20regime&amp;journal=Nature&amp;doi=10.1038%2Fs41586-025-09112-w&amp;volume=642&amp;pages=909-915&amp;publication_year=2025&amp;author=Xu%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR53\">Kiefer, Y. et al. Dataset for \u201cProtected quantum gates using qubit doublons in dynamical optical lattices\u201d. <a href=\"https:\/\/doi.org\/10.3929\/ethz-c-000794455\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.3929\/ethz-c-000794455\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.3929\/ethz-c-000794455<\/a> (ETH Research Collection, 2026).<\/p>\n","protected":false},"excerpt":{"rendered":"Jaksch, D., Briegel, H.-J., Cirac, J. I., Gardiner, C. W. &amp; Zoller, P. Entanglement of atoms via cold&hellip;\n","protected":false},"author":2,"featured_media":520523,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[4230,4231,2302,4835,90,12668,56,30212,54,55],"class_list":{"0":"post-520522","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-humanities-and-social-sciences","9":"tag-multidisciplinary","10":"tag-physics","11":"tag-quantum-information","12":"tag-science","13":"tag-topological-matter","14":"tag-uk","15":"tag-ultracold-gases","16":"tag-united-kingdom","17":"tag-unitedkingdom"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/520522","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/comments?post=520522"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/520522\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media\/520523"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media?parent=520522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/categories?post=520522"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/tags?post=520522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}