{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T12:49:39Z","timestamp":1725367779507},"reference-count":181,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T00:00:00Z","timestamp":1643760000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ERC","award":["758329"]},{"name":"MIUR Programme FARE","award":["817482"]},{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science","doi-asserted-by":"crossref","award":["Scholarship START"],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Science Foundation","award":["PHY-2144910"]},{"name":"DOE Office of Science, Office of Nuclear Physics","award":["DE-SC0021143"]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"crossref","award":["W911NF21P0003"],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"crossref","award":["N00014-20-1-2695"],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.<\/jats:p>","DOI":"10.22331\/q-2022-02-02-638","type":"journal-article","created":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T11:12:03Z","timestamp":1643800323000},"page":"638","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":58,"title":["Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains"],"prefix":"10.22331","volume":"6","author":[{"given":"Piotr","family":"Sierant","sequence":"first","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"},{"name":"Institute of Theoretical Physics, Jagiellonian University in Krakow, \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"}]},{"given":"Giuliano","family":"Chiriac\u00f2","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"},{"name":"SISSA \u2014 International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy"}]},{"given":"Federica M.","family":"Surace","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"},{"name":"SISSA \u2014 International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy"}]},{"given":"Shraddha","family":"Sharma","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"}]},{"given":"Xhek","family":"Turkeshi","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"},{"name":"SISSA \u2014 International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy"}]},{"given":"Marcello","family":"Dalmonte","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"},{"name":"SISSA \u2014 International School of Advanced Studies, via Bonomea 265, 34136 Trieste, Italy"}]},{"given":"Rosario","family":"Fazio","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy"},{"name":"Dipartimento di Fisica, Universit\u00e0 di Napoli ``Federico II'', Monte S. Angelo, I-80126 Napoli, Italy"}]},{"given":"Guido","family":"Pagano","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, TX 77005, USA"}]}],"member":"9598","published-online":{"date-parts":[[2022,2,2]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"L. M. Sieberer, M. Buchhold, and S. Diehl, Reports on Progress in Physics 79, 096001 (2016).","DOI":"10.1088\/0034-4885\/79\/9\/096001"},{"key":"1","doi-asserted-by":"publisher","unstructured":"T. E. Lee, S. Gopalakrishnan, and M. D. Lukin, Phys. Rev. Lett. 110, 257204 (2013).","DOI":"10.1103\/PhysRevLett.110.257204"},{"key":"2","doi-asserted-by":"publisher","unstructured":"J. Jin, A. Biella, O. Viyuela, L. Mazza, J. Keeling, R. Fazio, and D. Rossini, Phys. Rev. X 6, 031011 (2016).","DOI":"10.1103\/PhysRevX.6.031011"},{"key":"3","doi-asserted-by":"publisher","unstructured":"M. F. Maghrebi and A. V. Gorshkov, Physical Review B 93, 014307 (2016).","DOI":"10.1103\/PhysRevB.93.014307"},{"key":"4","doi-asserted-by":"publisher","unstructured":"V. R. Overbeck, M. F. Maghrebi, A. V. Gorshkov, and H. Weimer, Phys. Rev. A 95, 042133 (2017).","DOI":"10.1103\/PhysRevA.95.042133"},{"key":"5","doi-asserted-by":"publisher","unstructured":"M. Foss-Feig, J. T. Young, V. V. Albert, A. V. Gorshkov, and M. F. Maghrebi, Phys. Rev. Lett. 119, 190402 (2017).","DOI":"10.1103\/PhysRevLett.119.190402"},{"key":"6","doi-asserted-by":"publisher","unstructured":"J. Jin, A. Biella, O. Viyuela, C. Ciuti, R. Fazio, and D. Rossini, Phys. Rev. B 98, 241108 (2018).","DOI":"10.1103\/PhysRevB.98.241108"},{"key":"7","doi-asserted-by":"publisher","unstructured":"J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos, Phys. Rev. X 7, 011012 (2017).","DOI":"10.1103\/PhysRevX.7.011012"},{"key":"8","doi-asserted-by":"publisher","unstructured":"M. Fitzpatrick, N. M. Sundaresan, A. C. Y. Li, J. Koch, and A. A. Houck, Phys. Rev. X 7, 011016 (2017).","DOI":"10.1103\/PhysRevX.7.011016"},{"key":"9","doi-asserted-by":"publisher","unstructured":"N. Fl\u00e4schner, D. Vogel, M. Tarnowski, M. Tarnowski, B. S. Rem, D.-S. L\u00fchmann, M. Heyl, J. C. Budich, L. Mathey, K. Sengstock, and C. Weitenberg, Nature Physics 14, 265 (2018).","DOI":"10.1038\/s41567-017-0013-8"},{"key":"10","doi-asserted-by":"publisher","unstructured":"N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze, J. J. Garc\u00eda-Ripoll, J. I. Cirac, G. Rempe, and S. D\u00fcrr, Science 320, 1329 (2008).","DOI":"10.1126\/science.1155309"},{"key":"11","doi-asserted-by":"publisher","unstructured":"T. Tomita, S. Nakajima, I. Danshita, Y. Takasu, and Y. Takahashi, Science Advances 3, e1701513 (2017).","DOI":"10.1126\/sciadv.1701513"},{"key":"12","doi-asserted-by":"publisher","unstructured":"S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. P. B\u00fcchler, and P. Zoller, Nature Physics 4, 878 (2008).","DOI":"10.1038\/nphys1073"},{"key":"13","doi-asserted-by":"publisher","unstructured":"D. Poletti, J.-S. Bernier, A. Georges, and C. Kollath, Phys. Rev. Lett. 109, 045302 (2012).","DOI":"10.1103\/PhysRevLett.109.045302"},{"key":"14","doi-asserted-by":"publisher","unstructured":"D. Poletti, P. Barmettler, A. Georges, and C. Kollath, Phys. Rev. Lett. 111, 195301 (2013).","DOI":"10.1103\/PhysRevLett.111.195301"},{"key":"15","doi-asserted-by":"publisher","unstructured":"L. M. Sieberer, S. D. Huber, E. Altman, and S. Diehl, Phys. Rev. Lett. 110, 195301 (2013).","DOI":"10.1103\/PhysRevLett.110.195301"},{"key":"16","doi-asserted-by":"publisher","unstructured":"J. Marino and S. Diehl, Phys. Rev. Lett. 116, 070407 (2016).","DOI":"10.1103\/PhysRevLett.116.070407"},{"key":"17","doi-asserted-by":"publisher","unstructured":"M. Schir\u00f3, C. Joshi, M. Bordyuh, R. Fazio, J. Keeling, and H. E. T\u00fcreci, Phys. Rev. Lett. 116, 143603 (2016).","DOI":"10.1103\/PhysRevLett.116.143603"},{"key":"18","doi-asserted-by":"publisher","unstructured":"F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Phys. Rev. A 98, 042118 (2018).","DOI":"10.1103\/PhysRevA.98.042118"},{"key":"19","doi-asserted-by":"publisher","unstructured":"R. Rota, F. Minganti, C. Ciuti, and V. Savona, Phys. Rev. Lett. 122, 110405 (2019).","DOI":"10.1103\/PhysRevLett.122.110405"},{"key":"20","doi-asserted-by":"publisher","unstructured":"J. T. Young, A. V. Gorshkov, M. Foss-Feig, and M. F. Maghrebi, Phys. Rev. X 10, 011039 (2020).","DOI":"10.1103\/PhysRevX.10.011039"},{"key":"21","doi-asserted-by":"crossref","unstructured":"D. A. Paz and M. F. Maghrebi, ``Driven-dissipative ising model: Dynamical crossover at weak dissipation,'' (2021), arXiv:1906.08278.","DOI":"10.1209\/0295-5075\/ac33cb"},{"key":"22","doi-asserted-by":"publisher","unstructured":"M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, Phys. Rev. Lett. 113, 210401 (2014).","DOI":"10.1103\/PhysRevLett.113.210401"},{"key":"23","unstructured":"K. Seetharam, A. Lerose, R. Fazio, and J. Marino, ``Correlation engineering via non-local dissipation,'' (2021), arXiv:2101.06445."},{"key":"24","doi-asserted-by":"publisher","unstructured":"V. R. Morrison, R. P. Chatelain, K. L. Tiwari, A. Hendaoui, A. Bruh\u00e1cs, M. Chaker, and B. J. Siwick, Science 346, 445 (2014).","DOI":"10.1126\/science.1253779"},{"key":"25","doi-asserted-by":"publisher","unstructured":"D. Fausti, R. I. Tobey, N. Dean, S. Kaiser, A. Dienst, M. C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Science 331, 189 (2011).","DOI":"10.1126\/science.1197294"},{"key":"26","doi-asserted-by":"publisher","unstructured":"M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Ricc\u00f2, S. R. Clark, D. Jaksch, and A. Cavalleri, Nature 530, 461 (2016).","DOI":"10.1038\/nature16522"},{"key":"27","doi-asserted-by":"publisher","unstructured":"A. Zong, A. Kogar, Y.-Q. Bie, T. Rohwer, C. Lee, E. Baldini, E. Erge\u00e7en, M. B. Yilmaz, B. Freelon, E. J. Sie, H. Zhou, J. Straquadine, P. Walmsley, P. E. Dolgirev, A. V. Rozhkov, I. R. Fisher, P. Jarillo-Herrero, B. V. Fine, and N. Gedik, Nature Physics 15, 27 (2019).","DOI":"10.1038\/s41567-018-0311-9"},{"key":"28","doi-asserted-by":"publisher","unstructured":"A. Kogar, A. Zong, P. E. Dolgirev, X. Shen, J. Straquadine, Y.-Q. Bie, X. Wang, T. Rohwer, I.-C. Tung, Y. Yang, R. Li, J. Yang, S. Weathersby, S. Park, M. E. Kozina, E. J. Sie, H. Wen, P. Jarillo-Herrero, I. R. Fisher, X. Wang, and N. Gedik, Nature Physics 16, 159 (2020).","DOI":"10.1038\/s41567-019-0705-3"},{"key":"29","doi-asserted-by":"publisher","unstructured":"T. F. Nova, A. S. Disa, M. Fechner, and A. Cavalleri, Science 364, 1075 (2019).","DOI":"10.1126\/science.aaw4911"},{"key":"30","doi-asserted-by":"publisher","unstructured":"A. Disa, M. Fechner, T. Nova, B. Liu, M. F\u00f6rst, D. Prabhakaran, P. Radaelli, and A. Cavalleri, Nature Physics 16, 937 (2020).","DOI":"10.1038\/s41567-020-0936-3"},{"key":"31","doi-asserted-by":"publisher","unstructured":"G. Chiriac\u00f2, A. J. Millis, and I. L. Aleiner, Phys. Rev. B 98, 220510(R) (2018).","DOI":"10.1103\/PhysRevB.98.220510"},{"key":"32","doi-asserted-by":"publisher","unstructured":"M. A. Sentef, A. Tokuno, A. Georges, and C. Kollath, Phys. Rev. Lett. 118, 087002 (2017).","DOI":"10.1103\/PhysRevLett.118.087002"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Z. Sun and A. J. Millis, Phys. Rev. X 10, 021028 (2020).","DOI":"10.1103\/PhysRevX.10.021028"},{"key":"34","doi-asserted-by":"publisher","unstructured":"S. Dhar and S. Dasgupta, Phys. Rev. A 93, 050103 (2016).","DOI":"10.1103\/PhysRevA.93.050103"},{"key":"35","doi-asserted-by":"publisher","unstructured":"A. Nahum, J. Ruhman, S. Vijay, and J. Haah, Phys. Rev. X 7, 031016 (2017).","DOI":"10.1103\/PhysRevX.7.031016"},{"key":"36","doi-asserted-by":"publisher","unstructured":"Y. Li, X. Chen, and M. P. A. Fisher, Phys. Rev. B 98, 205136 (2018).","DOI":"10.1103\/PhysRevB.98.205136"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Y. Li, X. Chen, and M. P. Fisher, Physical Review B 100, 134306 (2019).","DOI":"10.1103\/PhysRevB.100.134306"},{"key":"38","doi-asserted-by":"publisher","unstructured":"Y. Li, X. Chen, A. W. W. Ludwig, and M. P. A. Fisher, Phys. Rev. B 104, 104305 (2021).","DOI":"10.1103\/PhysRevB.104.104305"},{"key":"39","doi-asserted-by":"publisher","unstructured":"Y. Li and M. P. A. Fisher, Phys. Rev. B 103, 104306 (2021).","DOI":"10.1103\/PhysRevB.103.104306"},{"key":"40","doi-asserted-by":"publisher","unstructured":"A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, Phys. Rev. B 99, 224307 (2019).","DOI":"10.1103\/PhysRevB.99.224307"},{"key":"41","doi-asserted-by":"publisher","unstructured":"T. Zhou and A. Nahum, Phys. Rev. B 99, 174205 (2019).","DOI":"10.1103\/PhysRevB.99.174205"},{"key":"42","doi-asserted-by":"publisher","unstructured":"B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019).","DOI":"10.1103\/PhysRevX.9.031009"},{"key":"43","doi-asserted-by":"publisher","unstructured":"Y. Bao, S. Choi, and E. Altman, Physical Review B 101, 104301 (2020).","DOI":"10.1103\/PhysRevB.101.104301"},{"key":"44","doi-asserted-by":"publisher","unstructured":"C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, Phys. Rev. B 101, 104302 (2020).","DOI":"10.1103\/PhysRevB.101.104302"},{"key":"45","doi-asserted-by":"publisher","unstructured":"M. J. Gullans and D. A. Huse, Phys. Rev. Lett. 125, 070606 (2020a).","DOI":"10.1103\/PhysRevLett.125.070606"},{"key":"46","doi-asserted-by":"publisher","unstructured":"M. J. Gullans and D. A. Huse, Phys. Rev. X 10, 041020 (2020b).","DOI":"10.1103\/PhysRevX.10.041020"},{"key":"47","doi-asserted-by":"publisher","unstructured":"S. Gopalakrishnan and M. J. Gullans, Phys. Rev. Lett. 126, 170503 (2021).","DOI":"10.1103\/PhysRevLett.126.170503"},{"key":"48","doi-asserted-by":"publisher","unstructured":"X. Turkeshi, R. Fazio, and M. Dalmonte, Phys. Rev. B 102, 014315 (2020).","DOI":"10.1103\/PhysRevB.102.014315"},{"key":"49","doi-asserted-by":"publisher","unstructured":"X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and M. Schir\u00f3, Phys. Rev. B 103, 224210 (2021).","DOI":"10.1103\/PhysRevB.103.224210"},{"key":"50","doi-asserted-by":"publisher","unstructured":"M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, Phys. Rev. X 11, 011030 (2021).","DOI":"10.1103\/PhysRevX.11.011030"},{"key":"51","doi-asserted-by":"publisher","unstructured":"M. Buchhold, Y. Minoguchi, A. Altland, and S. Diehl, Phys. Rev. X 11, 041004 (2021).","DOI":"10.1103\/PhysRevX.11.041004"},{"key":"52","doi-asserted-by":"publisher","unstructured":"T. Minato, K. Sugimoto, T. Kuwahara, and K. Saito, Phys. Rev. Lett. 128, 010603 (2022).","DOI":"10.1103\/PhysRevLett.128.010603"},{"key":"53","doi-asserted-by":"publisher","unstructured":"M. Block, Y. Bao, S. Choi, E. Altman, and N. Y. Yao, Phys. Rev. Lett. 128, 010604 (2022).","DOI":"10.1103\/PhysRevLett.128.010604"},{"key":"54","unstructured":"S. Sharma, X. Turkeshi, R. Fazio, and M. Dalmonte, ``Measurement-induced criticality in extended and long-range unitary circuits,'' (2021), arXiv:2110.14403."},{"key":"55","unstructured":"T. Hashizume, G. Bentsen, and A. J. Daley, ``Measurement-induced phase transitions in sparse nonlocal scramblers,'' (2021), arXiv:2109.10944."},{"key":"56","unstructured":"S. Sahu, S.-K. Jian, G. Bentsen, and B. Swingle, ``Entanglement phases in large-n hybrid brownian circuits with long-range couplings,'' (2021), arXiv:2109.00013."},{"key":"57","doi-asserted-by":"publisher","unstructured":"X. Chen, Y. Li, M. P. A. Fisher, and A. Lucas, Phys. Rev. Research 2, 033017 (2020).","DOI":"10.1103\/PhysRevResearch.2.033017"},{"key":"58","doi-asserted-by":"publisher","unstructured":"A. Biella and M. Schir\u00f3, Quantum 5, 528 (2021).","DOI":"10.22331\/q-2021-08-19-528"},{"key":"59","doi-asserted-by":"publisher","unstructured":"Q. Tang, X. Chen, and W. Zhu, Phys. Rev. B 103, 174303 (2021).","DOI":"10.1103\/PhysRevB.103.174303"},{"key":"60","doi-asserted-by":"crossref","unstructured":"P. Zhang, C. Liu, S.-K. Jian, and X. Chen, ``Universal entanglement transitions of free fermions with long-range non-unitary dynamics,'' (2021a), arXiv:2105.08895.","DOI":"10.22331\/q-2022-05-27-723"},{"key":"61","doi-asserted-by":"publisher","unstructured":"S.-K. Jian, C. Liu, X. Chen, B. Swingle, and P. Zhang, Phys. Rev. Lett. 127, 140601 (2021).","DOI":"10.1103\/PhysRevLett.127.140601"},{"key":"62","doi-asserted-by":"publisher","unstructured":"P. Zhang, S.-K. Jian, C. Liu, and X. Chen, Quantum 5, 579 (2021b).","DOI":"10.22331\/q-2021-11-16-579"},{"key":"63","doi-asserted-by":"publisher","unstructured":"T. M\u00fcller, S. Diehl, and M. Buchhold, Phys. Rev. Lett. 128, 010605 (2022).","DOI":"10.1103\/PhysRevLett.128.010605"},{"key":"64","doi-asserted-by":"publisher","unstructured":"O. Lunt, M. Szyniszewski, and A. Pal, Phys. Rev. B 104, 155111 (2021).","DOI":"10.1103\/PhysRevB.104.155111"},{"key":"65","doi-asserted-by":"publisher","unstructured":"O. Alberton, M. Buchhold, and S. Diehl, Phys. Rev. Lett. 126, 170602 (2021).","DOI":"10.1103\/PhysRevLett.126.170602"},{"key":"66","doi-asserted-by":"publisher","unstructured":"L. Zhang, J. A. Reyes, S. Kourtis, C. Chamon, E. R. Mucciolo, and A. E. Ruckenstein, Phys. Rev. B 101, 235104 (2020).","DOI":"10.1103\/PhysRevB.101.235104"},{"key":"67","doi-asserted-by":"publisher","unstructured":"R. Vasseur, A. C. Potter, Y.-Z. You, and A. W. W. Ludwig, Phys. Rev. B 100, 134203 (2019).","DOI":"10.1103\/PhysRevB.100.134203"},{"key":"68","doi-asserted-by":"publisher","unstructured":"J. Lopez-Piqueres, B. Ware, and R. Vasseur, Phys. Rev. B 102, 064202 (2020).","DOI":"10.1103\/PhysRevB.102.064202"},{"key":"69","doi-asserted-by":"publisher","unstructured":"A. Nahum, S. Roy, B. Skinner, and J. Ruhman, PRX Quantum 2, 010352 (2021).","DOI":"10.1103\/PRXQuantum.2.010352"},{"key":"70","doi-asserted-by":"publisher","unstructured":"X. Cao, A. Tilloy, and A. D. Luca, SciPost Phys. 7, 24 (2019).","DOI":"10.21468\/SciPostPhys.7.2.024"},{"key":"71","doi-asserted-by":"publisher","unstructured":"S. Maity, S. Bandyopadhyay, S. Bhattacharjee, and A. Dutta, Phys. Rev. B 101, 180301 (2020).","DOI":"10.1103\/PhysRevB.101.180301"},{"key":"72","doi-asserted-by":"publisher","unstructured":"Y. Fuji and Y. Ashida, Phys. Rev. B 102, 054302 (2020).","DOI":"10.1103\/PhysRevB.102.054302"},{"key":"73","doi-asserted-by":"publisher","unstructured":"M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. Lett. 125, 210602 (2020).","DOI":"10.1103\/PhysRevLett.125.210602"},{"key":"74","doi-asserted-by":"publisher","unstructured":"N. Lang and H. P. B\u00fcchler, Phys. Rev. A 92, 012128 (2015).","DOI":"10.1103\/PhysRevA.92.012128"},{"key":"75","unstructured":"S. Vijay, ``Measurement-driven phase transition within a volume-law entangled phase,'' (2020), arXiv:2005.03052."},{"key":"76","doi-asserted-by":"publisher","unstructured":"J. Iaconis, A. Lucas, and X. Chen, Phys. Rev. B 102, 224311 (2020).","DOI":"10.1103\/PhysRevB.102.224311"},{"key":"77","doi-asserted-by":"publisher","unstructured":"G. S. Bentsen, S. Sahu, and B. Swingle, Phys. Rev. B 104, 094304 (2021).","DOI":"10.1103\/PhysRevB.104.094304"},{"key":"78","doi-asserted-by":"publisher","unstructured":"T. Botzung, S. Diehl, and M. M\u00fcller, Phys. Rev. B 104, 184422 (2021).","DOI":"10.1103\/PhysRevB.104.184422"},{"key":"79","doi-asserted-by":"publisher","unstructured":"J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Nature 551, 601 (2017).","DOI":"10.1038\/nature24654"},{"key":"80","doi-asserted-by":"publisher","unstructured":"C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Rev. Mod. Phys. 93, 025001 (2021).","DOI":"10.1103\/RevModPhys.93.025001"},{"key":"81","doi-asserted-by":"publisher","unstructured":"W. L. Tan, P. Becker, F. Liu, G. Pagano, K. S. Collins, A. De, L. Feng, H. B. Kaplan, A. Kyprianidis, R. Lundgren, W. Morong, S. Whitsitt, A. V. Gorshkov, and C. Monroe, Nature Physics 17, 742 (2021).","DOI":"10.1038\/s41567-021-01194-3"},{"key":"82","doi-asserted-by":"publisher","unstructured":"A. Kyprianidis, F. Machado, W. Morong, P. Becker, K. S. Collins, D. V. Else, L. Feng, P. W. Hess, C. Nayak, G. Pagano, N. Y. Yao, and C. Monroe, Science 372, 1192 (2021).","DOI":"10.1126\/science.abg8102"},{"key":"83","doi-asserted-by":"crossref","unstructured":"W. Happer, Rev. Mod. Phys. 44, 169 (1972).","DOI":"10.1103\/RevModPhys.44.169"},{"key":"84","doi-asserted-by":"publisher","unstructured":"R. Noek, G. Vrijsen, D. Gaultney, E. Mount, T. Kim, P. Maunz, and J. Kim, Opt. Lett. 38, 4735 (2013a).","DOI":"10.1364\/OL.38.004735"},{"key":"85","doi-asserted-by":"publisher","unstructured":"J. E. Christensen, D. Hucul, W. C. Campbell, and E. R. Hudson, npj Quantum Information 6, 35 (2020).","DOI":"10.1038\/s41534-020-0265-5"},{"key":"86","doi-asserted-by":"publisher","unstructured":"S. Sang and T. H. Hsieh, Phys. Rev. Research 3, 023200 (2021).","DOI":"10.1103\/PhysRevResearch.3.023200"},{"key":"87","doi-asserted-by":"publisher","unstructured":"Y. Bao, S. Choi, and E. Altman, Annals of Physics 435, 168618 (2021).","DOI":"10.1016\/j.aop.2021.168618"},{"key":"88","doi-asserted-by":"publisher","unstructured":"A. Schnell, A. Eckardt, and S. Denisov, Phys. Rev. B 101, 100301 (2020).","DOI":"10.1103\/PhysRevB.101.100301"},{"key":"89","doi-asserted-by":"publisher","unstructured":"M. Bukov, L. D'Alessio, and A. Polkovnikov, Advances in Physics 64, 139 (2015).","DOI":"10.1080\/00018732.2015.1055918"},{"key":"90","doi-asserted-by":"publisher","unstructured":"B. \u017dunkovi\u010d, M. Heyl, M. Knap, and A. Silva, Phys. Rev. Lett. 120, 130601 (2018).","DOI":"10.1103\/PhysRevLett.120.130601"},{"key":"91","doi-asserted-by":"publisher","unstructured":"P. Hauke and L. Tagliacozzo, Phys. Rev. Lett. 111, 207202 (2013).","DOI":"10.1103\/PhysRevLett.111.207202"},{"key":"92","doi-asserted-by":"publisher","unstructured":"J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley, Phys. Rev. X 3, 031015 (2013).","DOI":"10.1103\/PhysRevX.3.031015"},{"key":"93","doi-asserted-by":"publisher","unstructured":"A. Lerose and S. Pappalardi, Phys. Rev. Research 2, 012041 (2020a).","DOI":"10.1103\/PhysRevResearch.2.012041"},{"key":"94","doi-asserted-by":"publisher","unstructured":"S. Pappalardi, A. Russomanno, B. \u017dunkovi\u010d, F. Iemini, A. Silva, and R. Fazio, Phys. Rev. B 98, 134303 (2018).","DOI":"10.1103\/PhysRevB.98.134303"},{"key":"95","doi-asserted-by":"publisher","unstructured":"A. Lerose and S. Pappalardi, Phys. Rev. A 102, 032404 (2020b).","DOI":"10.1103\/PhysRevA.102.032404"},{"key":"96","doi-asserted-by":"publisher","unstructured":"M. B. Plenio and P. L. Knight, Rev. Mod. Phys. 70, 101 (1998).","DOI":"10.1103\/RevModPhys.70.101"},{"key":"97","unstructured":"H. Carmichael, An open systems approach to quantum optics: lectures presented at the Universit\u00e9 Libre de Bruxelles, October 28 to November 4, 1991, Vol. 18 (Springer Science & Business Media, 2009)."},{"key":"98","doi-asserted-by":"publisher","unstructured":"A. J. Daley, Advances in Physics 63, 77 (2014).","DOI":"10.1080\/00018732.2014.933502"},{"key":"99","doi-asserted-by":"publisher","unstructured":"A. S\u00f8rensen and K. M\u00f8lmer, Phys. Rev. Lett. 82, 1971 (1999).","DOI":"10.1103\/PhysRevLett.82.1971"},{"key":"100","doi-asserted-by":"publisher","unstructured":"A. Das, K. Sengupta, D. Sen, and B. K. Chakrabarti, Phys. Rev. B 74, 144423 (2006).","DOI":"10.1103\/PhysRevB.74.144423"},{"key":"101","doi-asserted-by":"publisher","unstructured":"B. Sciolla and G. Biroli, Phys. Rev. Lett. 105, 220401 (2010).","DOI":"10.1103\/PhysRevLett.105.220401"},{"key":"102","doi-asserted-by":"publisher","unstructured":"M. Snoek, EuroPhys. Lett. 95, 30006 (2011).","DOI":"10.1209\/0295-5075\/95\/30006"},{"key":"103","doi-asserted-by":"publisher","unstructured":"B. Sciolla and G. Biroli, Journal of Statistical Mechanics: Theory and Experiment 2011, P11003 (2011).","DOI":"10.1088\/1742-5468\/2011\/11\/p11003"},{"key":"104","doi-asserted-by":"publisher","unstructured":"Fino and Algazi, IEEE Transactions on Computers C-25, 1142 (1976).","DOI":"10.1109\/TC.1976.1674569"},{"key":"105","doi-asserted-by":"crossref","unstructured":"J. Arndt, Matters Computational \u2013 Ideas, Algorithms, Source Code (Springer-Verlag, Berlin Heidelberg, 2011).","DOI":"10.1007\/978-3-642-14764-7"},{"key":"106","doi-asserted-by":"publisher","unstructured":"T. Prosen, Phys. Rev. Lett. 80, 1808 (1998).","DOI":"10.1103\/PhysRevLett.80.1808"},{"key":"107","doi-asserted-by":"publisher","unstructured":"T. Prosen, Phys. Rev. E 60, 3949 (1999).","DOI":"10.1103\/PhysRevE.60.3949"},{"key":"108","doi-asserted-by":"publisher","unstructured":"T. L. M. Lezama, S. Bera, and J. H. Bardarson, Phys. Rev. B 99, 161106 (2019).","DOI":"10.1103\/PhysRevB.99.161106"},{"key":"109","doi-asserted-by":"publisher","unstructured":"S. Sarkar and J. S. Satchell, Journal of Physics A: Mathematical and General 20, 2147 (1987).","DOI":"10.1088\/0305-4470\/20\/8\/028"},{"key":"110","doi-asserted-by":"publisher","unstructured":"B. A. Chase and J. M. Geremia, Phys. Rev. A 78, 052101 (2008).","DOI":"10.1103\/PhysRevA.78.052101"},{"key":"111","doi-asserted-by":"publisher","unstructured":"B. Q. Baragiola, B. A. Chase, and J. Geremia, Phys. Rev. A 81, 032104 (2010).","DOI":"10.1103\/PhysRevA.81.032104"},{"key":"112","doi-asserted-by":"publisher","unstructured":"T. E. Lee, H. H\u00e4ffner, and M. C. Cross, Phys. Rev. Lett. 108, 023602 (2012).","DOI":"10.1103\/PhysRevLett.108.023602"},{"key":"113","doi-asserted-by":"publisher","unstructured":"M. Xu, D. A. Tieri, and M. J. Holland, Phys. Rev. A 87, 062101 (2013).","DOI":"10.1103\/PhysRevA.87.062101"},{"key":"114","doi-asserted-by":"publisher","unstructured":"M. Bola\u00f1os and P. Barberis-Blostein, Journal of Physics A: Mathematical and Theoretical 48, 445301 (2015).","DOI":"10.1088\/1751-8113\/48\/44\/445301"},{"key":"115","doi-asserted-by":"publisher","unstructured":"M. Gegg and M. Richter, New Journal of Physics 18, 043037 (2016).","DOI":"10.1088\/1367-2630\/18\/4\/043037"},{"key":"116","doi-asserted-by":"publisher","unstructured":"M. Gegg and M. Richter, Scientific Reports 7, 16304 (2017).","DOI":"10.1038\/s41598-017-16178-8"},{"key":"117","doi-asserted-by":"publisher","unstructured":"M. Gegg, A. Carmele, A. Knorr, and M. Richter, New Journal of Physics 20, 013006 (2018).","DOI":"10.1088\/1367-2630\/aa9cdd"},{"key":"118","doi-asserted-by":"publisher","unstructured":"N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Phys. Rev. A 98, 063815 (2018).","DOI":"10.1103\/PhysRevA.98.063815"},{"key":"119","doi-asserted-by":"publisher","unstructured":"F. Iemini, A. Russomanno, J. Keeling, M. Schir\u00f2, M. Dalmonte, and R. Fazio, Phys. Rev. Lett. 121, 035301 (2018).","DOI":"10.1103\/PhysRevLett.121.035301"},{"key":"120","doi-asserted-by":"publisher","unstructured":"Y. Hama, W. J. Munro, and K. Nemoto, Phys. Rev. Lett. 120, 060403 (2018).","DOI":"10.1103\/PhysRevLett.120.060403"},{"key":"121","doi-asserted-by":"publisher","unstructured":"S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, 2011).","DOI":"10.1017\/CBO9780511973765"},{"key":"122","doi-asserted-by":"publisher","unstructured":"D. Rossini and E. Vicari, Phys. Rev. B 102, 035119 (2020).","DOI":"10.1103\/PhysRevB.102.035119"},{"key":"123","doi-asserted-by":"publisher","unstructured":"K. Binder, Phys. Rev. Lett. 47, 693 (1981a).","DOI":"10.1103\/PhysRevLett.47.693"},{"key":"124","doi-asserted-by":"publisher","unstructured":"K. Binder, Zeitschrift f\u00fcr Physik B Condensed Matter 43, 119 (1981b).","DOI":"10.1007\/BF01293604"},{"key":"125","doi-asserted-by":"publisher","unstructured":"Q. Tang and W. Zhu, Phys. Rev. Research 2, 013022 (2020).","DOI":"10.1103\/PhysRevResearch.2.013022"},{"key":"126","doi-asserted-by":"publisher","unstructured":"S. Goto and I. Danshita, Phys. Rev. A 102, 033316 (2020).","DOI":"10.1103\/PhysRevA.102.033316"},{"key":"127","doi-asserted-by":"publisher","unstructured":"O. Lunt and A. Pal, Phys. Rev. Research 2, 043072 (2020).","DOI":"10.1103\/PhysRevResearch.2.043072"},{"key":"128","doi-asserted-by":"publisher","unstructured":"T.-C. Lu and T. Grover, PRX Quantum 2, 040319 (2021).","DOI":"10.1103\/PRXQuantum.2.040319"},{"key":"129","doi-asserted-by":"publisher","unstructured":"M. Szyniszewski, A. Romito, and H. Schomerus, Phys. Rev. B 100, 064204 (2019).","DOI":"10.1103\/PhysRevB.100.064204"},{"key":"130","doi-asserted-by":"publisher","unstructured":"A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrishnan, D. A. Huse, and J. H. Pixley, Phys. Rev. B 101, 060301 (2020).","DOI":"10.1103\/PhysRevB.101.060301"},{"key":"131","doi-asserted-by":"publisher","unstructured":"B. Groisman, S. Popescu, and A. Winter, Phys. Rev. A 72, 032317 (2005).","DOI":"10.1103\/PhysRevA.72.032317"},{"key":"132","doi-asserted-by":"publisher","unstructured":"R. Fan, S. Vijay, A. Vishwanath, and Y.-Z. You, Phys. Rev. B 103, 174309 (2021).","DOI":"10.1103\/PhysRevB.103.174309"},{"key":"133","doi-asserted-by":"publisher","unstructured":"P. Calabrese and J. Cardy, Journal of Physics A: Mathematical and Theoretical 42, 504005 (2009).","DOI":"10.1088\/1751-8113\/42\/50\/504005"},{"key":"134","doi-asserted-by":"publisher","unstructured":"P. Zoller, M. Marte, and D. F. Walls, Phys. Rev. A 35, 198 (1987).","DOI":"10.1103\/PhysRevA.35.198"},{"key":"135","doi-asserted-by":"publisher","unstructured":"S. Choi, Y. Bao, X.-L. Qi, and E. Altman, Phys. Rev. Lett. 125, 030505 (2020).","DOI":"10.1103\/PhysRevLett.125.030505"},{"key":"136","doi-asserted-by":"publisher","unstructured":"N. Mac\u00e9, F. Alet, and N. Laflorencie, Phys. Rev. Lett. 123, 180601 (2019).","DOI":"10.1103\/PhysRevLett.123.180601"},{"key":"137","doi-asserted-by":"publisher","unstructured":"A. Rodriguez, L. J. Vasquez, K. Slevin, and R. A. R\u00f6mer, Phys. Rev. Lett. 105, 046403 (2010).","DOI":"10.1103\/PhysRevLett.105.046403"},{"key":"138","doi-asserted-by":"publisher","unstructured":"W. Beugeling, A. Andreanov, and M. Haque, Journal of Statistical Mechanics: Theory and Experiment 2015, P02002 (2015).","DOI":"10.1088\/1742-5468\/2015\/02\/p02002"},{"key":"139","doi-asserted-by":"publisher","unstructured":"D. J. Luitz, I. Khaymovich, and Y. Bar Lev, SciPost Physics Core 2 (2020).","DOI":"10.21468\/SciPostPhysCore.2.2.006"},{"key":"140","doi-asserted-by":"publisher","unstructured":"T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Science 364, 260 (2019).","DOI":"10.1126\/science.aau4963"},{"key":"141","doi-asserted-by":"publisher","unstructured":"S. de L\u00e9s\u00e9leuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. B\u00fcchler, T. Lahaye, and A. Browaeys, Science 365, 775 (2019).","DOI":"10.1126\/science.aav9105"},{"key":"142","unstructured":"B. Chiaro, C. Neill, A. Bohrdt, M. Filippone, F. Arute, K. Arya, R. Babbush, D. Bacon, J. Bardin, R. Barends, S. Boixo, D. Buell, B. Burkett, Y. Chen, Z. Chen, R. Collins, A. Dunsworth, E. Farhi, A. Fowler, B. Foxen, C. Gidney, M. Giustina, M. Harrigan, T. Huang, S. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P. Klimov, A. Korotkov, F. Kostritsa, D. Landhuis, E. Lucero, J. McClean, X. Mi, A. Megrant, M. Mohseni, J. Mutus, M. McEwen, O. Naaman, M. Neeley, M. Niu, A. Petukhov, C. Quintana, N. Rubin, D. Sank, K. Satzinger, A. Vainsencher, T. White, Z. Yao, P. Yeh, A. Zalcman, V. Smelyanskiy, H. Neven, S. Gopalakrishnan, D. Abanin, M. Knap, J. Martinis, and P. Roushan, ``Direct measurement of non-local interactions in the many-body localized phase,'' (2020), arXiv:1910.06024."},{"key":"143","doi-asserted-by":"publisher","unstructured":"G. Pagano, A. Bapat, P. Becker, K. S. Collins, A. De, P. W. Hess, H. B. Kaplan, A. Kyprianidis, W. L. Tan, C. Baldwin, L. T. Brady, A. Deshpande, F. Liu, S. Jordan, A. V. Gorshkov, and C. Monroe, Proceedings of the National Academy of Sciences 117, 25396 (2020).","DOI":"10.1073\/pnas.2006373117"},{"key":"144","doi-asserted-by":"publisher","unstructured":"P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. L\u00e4uchli, and A. Browaeys, Nature 595, 233 (2021).","DOI":"10.1038\/s41586-021-03585-1"},{"key":"145","doi-asserted-by":"publisher","unstructured":"S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuleti\u0107, and M. D. Lukin, Nature 595, 227 (2021).","DOI":"10.1038\/s41586-021-03582-4"},{"key":"146","doi-asserted-by":"publisher","unstructured":"J. Zeiher, J.-y. Choi, A. Rubio-Abadal, T. Pohl, R. van Bijnen, I. Bloch, and C. Gross, Phys. Rev. X 7, 041063 (2017).","DOI":"10.1103\/PhysRevX.7.041063"},{"key":"147","doi-asserted-by":"publisher","unstructured":"C. Veit, N. Zuber, O. A. Herrera-Sancho, V. S. V. Anasuri, T. Schmid, F. Meinert, R. L\u00f6w, and T. Pfau, Phys. Rev. X 11, 011036 (2021).","DOI":"10.1103\/PhysRevX.11.011036"},{"key":"148","doi-asserted-by":"publisher","unstructured":"A. Sol\u00f3rzano, L. F. Santos, and E. J. Torres-Herrera, Phys. Rev. Research 3, L032030 (2021).","DOI":"10.1103\/PhysRevResearch.3.L032030"},{"key":"149","doi-asserted-by":"publisher","unstructured":"C. Schneider, D. Porras, and T. Schaetz, Reports on Progress in Physics 75, 024401 (2012).","DOI":"10.1088\/0034-4885\/75\/2\/024401"},{"key":"150","doi-asserted-by":"publisher","unstructured":"P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Phys. Rev. Lett. 119, 080501 (2017).","DOI":"10.1103\/PhysRevLett.119.080501"},{"key":"151","doi-asserted-by":"publisher","unstructured":"H. B. Kaplan, L. Guo, W. L. Tan, A. De, F. Marquardt, G. Pagano, and C. Monroe, Phys. Rev. Lett. 125, 120605 (2020).","DOI":"10.1103\/PhysRevLett.125.120605"},{"key":"152","unstructured":"M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, and C. F. Roos, ``Observing emergent hydrodynamics in a long-range quantum magnet,'' (2021), arXiv:2107.00033."},{"key":"153","doi-asserted-by":"publisher","unstructured":"P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, Nature 511, 198 (2014).","DOI":"10.1038\/nature13450"},{"key":"154","doi-asserted-by":"publisher","unstructured":"R. Islam, C. Senko, W. C. Campbell, S. Korenblit, J. Smith, A. Lee, E. E. Edwards, C.-C. J. Wang, J. K. Freericks, and C. Monroe, Science 340, 583 (2013).","DOI":"10.1126\/science.1232296"},{"key":"155","doi-asserted-by":"publisher","unstructured":"C.-Y. Shih, S. Motlakunta, N. Kotibhaskar, M. Sajjan, R. Habl\u00fctzel, and R. Islam, npj Quantum Information 7, 57 (2021).","DOI":"10.1038\/s41534-021-00396-0"},{"key":"156","doi-asserted-by":"publisher","unstructured":"T. Mendes-Santos, X. Turkeshi, M. Dalmonte, and A. Rodriguez, Phys. Rev. X 11, 011040 (2021a).","DOI":"10.1103\/PhysRevX.11.011040"},{"key":"157","doi-asserted-by":"publisher","unstructured":"T. Mendes-Santos, A. Angelone, A. Rodriguez, R. Fazio, and M. Dalmonte, PRX Quantum 2, 030332 (2021b).","DOI":"10.1103\/PRXQuantum.2.030332"},{"key":"158","unstructured":"X. Turkeshi, ``Measurement-induced criticality as a data-structure transition,'' (2021), arXiv:2101.06245."},{"key":"159","doi-asserted-by":"publisher","unstructured":"E. Facco, M. d'Errico, A. Rodriguez, and A. Laio, Scientific Reports 7, 12140 (2017).","DOI":"10.1038\/s41598-017-11873-y"},{"key":"160","doi-asserted-by":"publisher","unstructured":"A. J. Daley, H. Pichler, J. Schachenmayer, and P. Zoller, Phys. Rev. Lett. 109, 020505 (2012).","DOI":"10.1103\/PhysRevLett.109.020505"},{"key":"161","doi-asserted-by":"publisher","unstructured":"D. A. Abanin and E. Demler, Phys. Rev. Lett. 109, 020504 (2012).","DOI":"10.1103\/PhysRevLett.109.020504"},{"key":"162","doi-asserted-by":"publisher","unstructured":"S. J. van Enk and C. W. J. Beenakker, Phys. Rev. Lett. 108, 110503 (2012).","DOI":"10.1103\/PhysRevLett.108.110503"},{"key":"163","doi-asserted-by":"publisher","unstructured":"A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 120, 050406 (2018).","DOI":"10.1103\/PhysRevLett.120.050406"},{"key":"164","doi-asserted-by":"publisher","unstructured":"H.-Y. Huang, R. Kueng, and J. Preskill, Nature Physics 16, 1050 (2020).","DOI":"10.1038\/s41567-020-0932-7"},{"key":"165","doi-asserted-by":"publisher","unstructured":"R. Noek, G. Vrijsen, D. Gaultney, E. Mount, T. Kim, P. Maunz, and J. Kim, Opt. Lett. 38, 4735 (2013b).","DOI":"10.1364\/OL.38.004735"},{"key":"166","doi-asserted-by":"publisher","unstructured":"M. Schacht, J. R. Danielson, S. Rahaman, J. R. Torgerson, J. Zhang, and M. M. Schauer, Journal of Physics B: Atomic, Molecular and Optical Physics 48, 065003 (2015).","DOI":"10.1088\/0953-4075\/48\/6\/065003"},{"key":"167","doi-asserted-by":"publisher","unstructured":"A. Mohanty, E. A. Dijck, M. N. Portela, N. Valappol, A. T. Grier, T. Meijknecht, L. Willmann, and K. Jungmann, Hyperfine Interactions 233, 113 (2015).","DOI":"10.1007\/s10751-015-1161-9"},{"key":"168","doi-asserted-by":"publisher","unstructured":"M. Roberts, P. Taylor, G. P. Barwood, P. Gill, H. A. Klein, and W. R. C. Rowley, Phys. Rev. Lett. 78, 1876 (1997).","DOI":"10.1103\/PhysRevLett.78.1876"},{"key":"169","unstructured":"H. X. Yang, J. Y. Ma, Y. K. Wu, Y. Wang, M. M. Cao, W. X. Guo, Y. Y. Huang, L. Feng, Z. C. Zhou, and L. M. Duan, ``Realizing coherently convertible dual-type qubits with the same ion species,'' (2021), arXiv:2106.14906."},{"key":"170","doi-asserted-by":"publisher","unstructured":"A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Stadler, V. Negnevitsky, M. Ringbauer, P. Schindler, H. J. Briegel, R. Blatt, N. Friis, and T. Monz, Nature 589, 220 (2021).","DOI":"10.1038\/s41586-020-03079-6"},{"key":"171","doi-asserted-by":"publisher","unstructured":"S. Debnath, N. M. Linke, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, Nature 536, 63 (2016).","DOI":"10.1038\/nature18648"},{"key":"172","doi-asserted-by":"publisher","unstructured":"N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).","DOI":"10.1103\/PhysRevLett.17.1133"},{"key":"173","doi-asserted-by":"publisher","unstructured":"P. C. Hohenberg, Phys. Rev. 158, 383 (1967).","DOI":"10.1103\/PhysRev.158.383"},{"key":"174","doi-asserted-by":"publisher","unstructured":"F. J. Dyson, Communications in Mathematical Physics 12, 91 (1969).","DOI":"10.1007\/BF01645907"},{"key":"175","doi-asserted-by":"publisher","unstructured":"R. D. Averitt and A. J. Taylor, Journal of Physics: Condensed Matter 14, R1357 (2002).","DOI":"10.1088\/0953-8984\/14\/50\/203"},{"key":"176","doi-asserted-by":"publisher","unstructured":"D. N. Basov, R. D. Averitt, D. van der Marel, M. Dressel, and K. Haule, Rev. Mod. Phys. 83, 471 (2011).","DOI":"10.1103\/RevModPhys.83.471"},{"key":"177","doi-asserted-by":"publisher","unstructured":"A. Lavasani, Y. Alavirad, and M. Barkeshli, Nature Physics 17, 342 (2021).","DOI":"10.1038\/s41567-020-01112-z"},{"key":"178","doi-asserted-by":"publisher","unstructured":"S. Bravyi, M. B. Hastings, and F. Verstraete, Phys. Rev. Lett. 97, 050401 (2006).","DOI":"10.1103\/PhysRevLett.97.050401"},{"key":"179","doi-asserted-by":"publisher","unstructured":"S. Czischek, G. Torlai, S. Ray, R. Islam, and R. G. Melko, Phys. Rev. A 104, 062405 (2021).","DOI":"10.1103\/PhysRevA.104.062405"},{"key":"180","unstructured":"C. Noel, P. Niroula, D. Zhu, A. Risinger, L. Egan, D. Biswas, M. Cetina, A. V. Gorshkov, M. J. Gullans, D. A. Huse, and C. Monroe, ``Observation of measurement-induced quantum phases in a trapped-ion quantum computer,'' (2021), arXiv:2106.05881."}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-02-02-638\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T15:47:14Z","timestamp":1674661634000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-02-02-638\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,2]]},"references-count":181,"URL":"https:\/\/doi.org\/10.22331\/q-2022-02-02-638","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,2]]},"article-number":"638"}}