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Floquet Engineering of Interactions and Entanglement in Periodically Driven Rydberg Chains

Nazli Ugur Koyluoglu1,2,*, Nishad Maskara1, Johannes Feldmeier1, and Mikhail D. Lukin1,†

  • *Contact author: nazliugurkoyluoglu@g.harvard.edu
  • †Contact author: lukin@physics.harvard.edu

Phys. Rev. Lett. 135, 113603 – Published 11 September, 2025

DOI: https://doi.org/10.1103/5qhh-322q

Abstract

Neutral atom arrays driven into Rydberg states constitute a promising approach for realizing programmable quantum systems. Enabled by strong interactions associated with Rydberg blockade, they allow for simulation of complex spin models and quantum dynamics. We introduce a new Floquet engineering technique for systems in the blockade regime that provides control over novel forms of interactions and entanglement dynamics in such systems. Our approach is based on time-dependent control of Rydberg laser detuning and leverages perturbations around periodic many-body trajectories as resources for operator spreading. These time-evolved operators are utilized as a basis for engineering interactions in the effective Hamiltonian describing the stroboscopic evolution. As an example, we show how our method can be used to engineer strong spin exchange, consistent with the blockade, in a one-dimensional chain, enabling the exploration of gapless Luttinger liquid phases. In addition, we demonstrate that combining gapless excitations with Rydberg blockade can lead to dynamic generation of large-scale multipartite entanglement. Experimental feasibility and possible generalizations are discussed.

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References (96)

  1. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold-atom Fermi–Hubbard antiferromagnet, Nature (London) 545, 462 (2017).
  2. 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. Vuletić, and M. D. Lukin, Quantum phases of matter on a 256-atom programmable quantum simulator, Nature (London) 595, 227 (2021).
  3. G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletić, and M. D. Lukin, Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021).
  4. C. Chen, G. Bornet, M. Bintz, G. Emperauger, L. Leclerc, V. S. Liu, P. Scholl, D. Barredo, J. Hauschild, S. Chatterjee, M. Schuler, A. M. Läuchli, M. P. Zaletel, T. Lahaye, N. Y. Yao, and A. Browaeys, Continuous symmetry breaking in a two-dimensional Rydberg array, Nature (London) 616, 691 (2023).
  5. L. Feng, O. Katz, C. Haack, M. Maghrebi, A. V. Gorshkov, Z. Gong, M. Cetina, and C. Monroe, Continuous symmetry breaking in a trapped-ion spin chain, Nature (London) 623, 713 (2023).
  6. T. Langen, S. Erne, R. Geiger, B. Rauer, T. Schweigler, M. Kuhnert, W. Rohringer, I. E. Mazets, T. Gasenzer, and J. Schmiedmayer, Experimental observation of a generalized Gibbs ensemble, Science 348, 207 (2015).
  7. M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Observation of many-body localization of interacting fermions in a quasirandom optical lattice, Science 349, 842 (2015).
  8. A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, Quantum thermalization through entanglement in an isolated many-body system, Science 353, 794 (2016).
  9. J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z. X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature (London) 551, 601 (2017).
  10. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  11. J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I. D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, and C. Monroe, Observation of a discrete time crystal, Nature (London) 543, 217 (2017).
  12. D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuletić, and M. D. Lukin, Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021).
  13. G. Bornet, G. Emperauger, C. Chen, B. Ye, M. Block, M. Bintz, J. A. Boyd, D. Barredo, T. Comparin, F. Mezzacapo, T. Roscilde, T. Lahaye, N. Y. Yao, and A. Browaeys, Scalable spin squeezing in a dipolar Rydberg atom array, Nature (London) 621, 728 (2023).
  14. J. A. Hines, S. V. Rajagopal, G. L. Moreau, M. D. Wahrman, N. A. Lewis, O. Marković, and M. Schleier-Smith, Spin squeezing by Rydberg dressing in an array of atomic ensembles, Phys. Rev. Lett. 131, 063401 (2023).
  15. T. Manovitz, S. H. Li, S. Ebadi, R. Samajdar, A. A. Geim, S. J. Evered, D. Bluvstein, H. Zhou, N. U. Köylüoğlu, J. Feldmeier, P. E. Dolgirev, N. Maskara, M. Kalinowski, S. Sachdev, D. A. Huse, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum coarsening and collective dynamics on a programmable quantum simulator, Nature (London) 638, 86 (2025).
  16. T. Fukuhara, S. Hild, J. Zeiher, P. Schauß, I. Bloch, M. Endres, and C. Gross, Spatially resolved detection of a spin-entanglement wave in a Bose-Hubbard chain, Phys. Rev. Lett. 115, 035302 (2015).
  17. R. Islam, R. Ma, P. M. Preiss, M. Eric Tai, A. Lukin, M. Rispoli, and M. Greiner, Measuring entanglement entropy in a quantum many-body system, Nature (London) 528, 77 (2015).
  18. A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Generation and manipulation of Schrödinger cat states in Rydberg atom arrays, Science 365, 570 (2019).
  19. T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Probing Rényi entanglement entropy via randomized measurements, Science 364, 260 (2019).
  20. M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. V. Zache, R. Blatt, C. F. Roos, and P. Zoller, Exploring large-scale entanglement in quantum simulation, Nature (London) 624, 539 (2023).
  21. M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, States of an ensemble of two-level atoms with reduced quantum uncertainty, Phys. Rev. Lett. 104, 073604 (2010).
  22. E. Pedrozo-Peñafiel, S. Colombo, C. Shu, A. F. Adiyatullin, Z. Li, E. Mendez, B. Braverman, A. Kawasaki, D. Akamatsu, Y. Xiao, and V. Vuletić, Entanglement on an optical atomic-clock transition, Nature (London) 588, 414 (2020).
  23. S. Colombo, E. Pedrozo-Peñafiel, A. F. Adiyatullin, Z. Li, E. Mendez, C. Shu, and V. Vuletić, Time-reversal-based quantum metrology with many-body entangled states, Nat. Phys. 18, 925 (2022).
  24. W. J. Eckner, N. Darkwah Oppong, A. Cao, A. W. Young, W. R. Milner, J. M. Robinson, J. Ye, and A. M. Kaufman, Realizing spin squeezing with Rydberg interactions in an optical clock, Nature (London) 621, 734 (2023).
  25. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  26. H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models, Nature (London) 534, 667 (2016).
  27. M. Morgado and S. Whitlock, Quantum simulation and computing with Rydberg-interacting qubits, AVS Quantum Sci. 3, 023501 (2021).
  28. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  29. R. Verresen, M. D. Lukin, and A. Vishwanath, Prediction of toric code topological order from Rydberg blockade, Phys. Rev. X 11, 031005 (2021).
  30. R. Verresen and A. Vishwanath, Unifying Kitaev magnets, Kagomé Dimer models, and Ruby Rydberg spin liquids, Phys. Rev. X 12, 041029 (2022).
  31. P. S. Tarabunga, F. M. Surace, R. Andreoni, A. Angelone, and M. Dalmonte, Gauge-theoretic origin of Rydberg quantum spin liquids, Phys. Rev. Lett. 129, 195301 (2022).
  32. F. M. Surace, P. P. Mazza, G. Giudici, A. Lerose, A. Gambassi, and M. Dalmonte, Lattice gauge theories and string dynamics in Rydberg atom quantum simulators, Phys. Rev. X 10, 021041 (2020).
  33. R. Samajdar, W. W. Ho, H. Pichler, M. D. Lukin, and S. Sachdev, Quantum phases of Rydberg atoms on a Kagome lattice, Proc. Natl. Acad. Sci. U.S.A. 118, e2015785118 (2021).
  34. R. Samajdar, D. G. Joshi, Y. Teng, and S. Sachdev, Emergent Z2 gauge theories and topological excitations in Rydberg atom arrays, Phys. Rev. Lett. 130, 043601 (2023).
  35. A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Emerging two-dimensional gauge theories in Rydberg configurable arrays, Phys. Rev. X 10, 021057 (2020).
  36. L. Homeier, A. Bohrdt, S. Linsel, E. Demler, J. C. Halimeh, and F. Grusdt, Realistic scheme for quantum simulation of Z2 lattice gauge theories with dynamical matter in (2+1)D, Commun. Phys. 6, 127 (2023).
  37. M. Demirplak and S. A. Rice, Adiabatic population transfer with control fields, J. Phys. Chem. A 107, 9937 (2003).
  38. D. Sels and A. Polkovnikov, Minimizing irreversible losses in quantum systems by local counterdiabatic driving, Proc. Natl. Acad. Sci. U.S.A. 114, E3909 (2017).
  39. M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, Optimal steering of matrix product states and quantum many-body scars, PRX Quantum 3, 030343 (2022).
  40. H. Pichler, S.-T. Wang, L. Zhou, S. Choi, and M. D. Lukin, Quantum optimization for maximum independent set using Rydberg atom arrays, arXiv:1808.10816.
  41. M. Cain, S. Chattopadhyay, J.-G. Liu, R. Samajdar, H. Pichler, and M. D. Lukin, Quantum speedup for combinatorial optimization with flat energy landscapes, arXiv:2306.13123.
  42. M.-T. Nguyen, J.-G. Liu, J. Wurtz, M. D. Lukin, S.-T. Wang, and H. Pichler, Quantum optimization with arbitrary connectivity using Rydberg atom arrays, PRX Quantum 4, 010316 (2023).
  43. J.-Y. Desaules, F. Pietracaprina, Z. Papić, J. Goold, and S. Pappalardi, Extensive multipartite entanglement from su(2) quantum many-body scars, Phys. Rev. Lett. 129, 020601 (2022).
  44. S. Dooley, S. Pappalardi, and J. Goold, Entanglement enhanced metrology with quantum many-body scars, Phys. Rev. B 107, 035123 (2023).
  45. N. Goldman and J. Dalibard, Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields, Phys. Rev. X 4, 031027 (2014).
  46. L. D. Marin Bukov and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems: From dynamical stabilization to Floquet engineering, Adv. Phys. 64, 139 (2015).
  47. A. Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89, 011004 (2017).
  48. M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices, Phys. Rev. Lett. 111, 185301 (2013).
  49. H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices, Phys. Rev. Lett. 111, 185302 (2013).
  50. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature (London) 515, 237 (2014).
  51. N. Fläschner, B. S. Rem, M. Tarnowski, D. Vogel, D.-S. Lühmann, K. Sengstock, and C. Weitenberg, Experimental reconstruction of the Berry curvature in a Floquet Bloch band, Science 352, 1091 (2016).
  52. F. Meinert, M. J. Mark, K. Lauber, A. J. Daley, and H.-C. Nägerl, Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms, Phys. Rev. Lett. 116, 205301 (2016).
  53. S. Geier, N. Thaicharoen, C. Hainaut, T. Franz, A. Salzinger, A. Tebben, D. Grimshandl, G. Zürn, and M. Weidemüller, Floquet Hamiltonian engineering of an isolated many-body spin system, Science 374, 1149 (2021).
  54. P. Scholl, H. J. Williams, G. Bornet, F. Wallner, D. Barredo, L. Henriet, A. Signoles, C. Hainaut, T. Franz, S. Geier, A. Tebben, A. Salzinger, G. Zürn, T. Lahaye, M. Weidemüller, and A. Browaeys, Microwave engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms, PRX Quantum 3, 020303 (2022).
  55. J. S. Waugh, L. M. Huber, and U. Haeberlen, Approach to high-resolution nmr in solids, Phys. Rev. Lett. 20, 180 (1968).
  56. K. X. Wei, C. Ramanathan, and P. Cappellaro, Exploring localization in nuclear spin chains, Phys. Rev. Lett. 120, 070501 (2018).
  57. J. Choi, H. Zhou, H. S. Knowles, R. Landig, S. Choi, and M. D. Lukin, Robust dynamic Hamiltonian engineering of many-body spin systems, Phys. Rev. X 10, 031002 (2020).
  58. H. Zhou, J. Choi, S. Choi, R. Landig, A. M. Douglas, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, P. Cappellaro, H. S. Knowles, H. Park, and M. D. Lukin, Quantum metrology with strongly interacting spin systems, Phys. Rev. X 10, 031003 (2020).
  59. H. Zhou, L. S. Martin, M. Tyler, O. Makarova, N. Leitao, H. Park, and M. D. Lukin, Robust higher-order Hamiltonian engineering for quantum sensing with strongly interacting systems, Phys. Rev. Lett. 131, 220803 (2023).
  60. S. Geier, A. Braemer, E. Braun, M. Müllenbach, T. Franz, M. Gärttner, G. Zürn, and M. Weidemüller, Time-reversal in a dipolar quantum many-body spin system, Phys. Rev. Res. 6, 033197 (2024).
  61. N. Maskara, S. Ostermann, J. Shee, M. Kalinowski, A. M. Gomez, R. A. Bravo, D. S. Wang, A. I. Krylov, N. Y. Yao, M. Head-Gordon, M. D. Lukin, and S. F. Yelin, Programmable simulations of molecules and materials with reconfigurable quantum processors, arXiv:2312.02265.
  62. N. Maskara, A. A. Michailidis, W. W. Ho, D. Bluvstein, S. Choi, M. D. Lukin, and M. Serbyn, Discrete time-crystalline order enabled by quantum many-body scars: Entanglement steering via periodic driving, Phys. Rev. Lett. 127, 090602 (2021).
  63. A. Hudomal, J.-Y. Desaules, B. Mukherjee, G.-X. Su, J. C. Halimeh, and Z. Papić, Driving quantum many-body scars in the PXP model, Phys. Rev. B 106, 104302 (2022).
  64. R. Verresen, A. Vishwanath, and F. Pollmann, Stable Luttinger liquids and emergent U(1) symmetry in constrained quantum chains, arXiv:1903.09179.
  65. See Supplemental Material at http://link.aps.org/supplemental/10.1103/5qhh-322q, which includes Refs. [66–73], for additional details.
  66. D. V. Else, W. W. Ho, and P. T. Dumitrescu, Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically driven systems, Phys. Rev. X 10, 021032 (2020).
  67. M. Karabach, G. Müller, H. Gould, and J. Tobochnik, Introduction to the Bethe Ansatz I, Comput. Phys. 11, 36 (1997).
  68. F. Franchini, An Introduction to Integrable Techniques for One-Dimensional Quantum Systems (Springer International Publishing, New York, 2017), 10.1007/978-3-319-48487-7.
  69. A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys. Usp. 44, 131 (2001).
  70. H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nat. Phys. 16, 1050 (2020).
  71. A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The randomized measurement toolbox, Nat. Rev. Phys. 5, 9 (2023).
  72. S. Notarnicola, A. Elben, T. Lahaye, A. Browaeys, S. Montangero, and B. Vermersch, A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator, New J. Phys. 25, 103006 (2023).
  73. H.-Y. Hu, A. Gu, S. Majumder, H. Ren, Y. Zhang, D. S. Wang, Y.-Z. You, Z. Minev, S. F. Yelin, and A. Seif, Demonstration of robust and efficient quantum property learning with shallow shadows, Nat. Commun. 16, 2943 (2025).
  74. D. A. Abanin, W. De Roeck, W. W. Ho, and F. Huveneers, Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems, Phys. Rev. B 95, 014112 (2017).
  75. D. Abanin, W. De Roeck, W. W. Ho, and F. Huveneers, A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems, Commun. Math. Phys. 354, 809 (2017).
  76. D. V. Else, B. Bauer, and C. Nayak, Prethermal phases of matter protected by time-translation symmetry, Phys. Rev. X 7, 011026 (2017).
  77. T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. Hänsel, M. Hennrich, and R. Blatt, 14-Qubit entanglement: Creation and coherence, Phys. Rev. Lett. 106, 130506 (2011).
  78. P. Fendley, K. Sengupta, and S. Sachdev, Competing density-wave orders in a one-dimensional hard-boson model, Phys. Rev. B 69, 075106 (2004).
  79. P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, and A. Smerzi, Fisher information and multiparticle entanglement, Phys. Rev. A 85, 022321 (2012).
  80. G. Tóth, Multipartite entanglement and high-precision metrology, Phys. Rev. A 85, 022322 (2012).
  81. F. C. Alcaraz and R. Z. Bariev, An exactly solvable constrained XXZ chain, arXiv:cond-mat/9904042.
  82. S. A. Weidinger, Non-Equilibrium Field Theory of Condensed Matter Systems—Periodic Driving and Quantum Quenches, Ph.D. thesis, Technischen Universität München, 2018, https://mediatum.ub.tum.de/doc/1455522/document.pdf#page76.
  83. M. Knap, A. Kantian, T. Giamarchi, I. Bloch, M. D. Lukin, and E. Demler, Probing real-space and time-resolved correlation functions with many-body Ramsey interferometry, Phys. Rev. Lett. 111, 147205 (2013).
  84. J. Feldmeier, N. Maskara, N. U. Köylüoğlu, and M. D. Lukin, Quantum simulation of dynamical gauge theories in periodically driven Rydberg atom arrays, arXiv:2408.02733.
  85. N. Nishad, A. Keselman, T. Lahaye, A. Browaeys, and S. Tsesses, Quantum simulation of generic spin-exchange models in Floquet-engineered Rydberg-atom arrays, Phys. Rev. A 108, 053318 (2023).
  86. M. Demirplak and S. A. Rice, Adiabatic population transfer with control fields, J. Phys. Chem. A 107, 9937 (2003).
  87. I. Cepaitė, A. Polkovnikov, A. J. Daley, and C. W. Duncan, Counterdiabatic optimized local driving, PRX Quantum 4, 010312 (2023).
  88. P. M. Schindler and M. Bukov, Counterdiabatic driving for periodically driven systems, Phys. Rev. Lett. 133, 123402 (2024).
  89. M. Gärttner, J. G. Bohnet, A. Safavi-Naini, M. L. Wall, J. J. Bollinger, and A. M. Rey, Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet, Nat. Phys. 13, 781 (2017).
  90. K. A. Gilmore, M. Affolter, R. J. Lewis-Swan, D. Barberena, E. Jordan, A. M. Rey, and J. J. Bollinger, Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals, Science 373, 673 (2021).
  91. D. Linnemann, H. Strobel, W. Muessel, J. Schulz, R. J. Lewis-Swan, K. V. Kheruntsyan, and M. K. Oberthaler, Quantum-enhanced sensing based on time reversal of nonlinear dynamics, Phys. Rev. Lett. 117, 013001 (2016).
  92. S. Colombo, E. Pedrozo-Peñafiel, A. F. Adiyatullin, Z. Li, E. Mendez, C. Shu, and V. Vuletić, Time-reversal-based quantum metrology with many-body entangled states, Nat. Phys. 18, 925 (2022).
  93. M. S. Blok, V. V. Ramasesh, T. Schuster, K. O’Brien, J. M. Kreikebaum, D. Dahlen, A. Morvan, B. Yoshida, N. Y. Yao, and I. Siddiqi, Quantum information scrambling on a superconducting Qutrit processor, Phys. Rev. X 11, 021010 (2021).
  94. X. Mi et al., Time-crystalline eigenstate order on a quantum processor, Nature (London) 601, 531 (2022).
  95. J. Braumüller, A. H. Karamlou, Y. Yanay, B. Kannan, D. Kim, M. Kjaergaard, A. Melville, B. M. Niedzielski, Y. Sung, A. Vepsäläinen, R. Winik, J. L. Yoder, T. P. Orlando, S. Gustavsson, C. Tahan, and W. D. Oliver, Probing quantum information propagation with out-of-time-ordered correlators, Nat. Phys. 18, 172 (2022).
  96. J. Hauschild and F. Pollmann, Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy), SciPost Phys. Lect. Notes 5 (2018), https://scipost.org/SciPostPhysLectNotes.5.

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