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Error-Corrected Fermionic Quantum Processors with Neutral Atoms

Robert Ott1,2, Daniel González-Cuadra1,2,3,4, Torsten V. Zache1,2, Peter Zoller1,2, Adam M. Kaufman5, and Hannes Pichler1,2,*

  • *Contact author: hannes.pichler@uibk.ac.at
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Phys. Rev. Lett. 135, 090601 – Published 25 August, 2025

DOI: https://doi.org/10.1103/zkpl-hh28

Abstract

Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where nonlocal fermionic statistics are guaranteed at the hardware level. Implementing quantum error correction in this setup is, however, challenging, due to the atom-number superselection present in atomic systems, that is, the impossibility of creating coherent superpositions of different particle numbers. In this Letter, we overcome this constraint and present a blueprint for an error-corrected fermionic quantum processor that can be implemented using current experimental capabilities. To achieve this, we first consider an ancillary set of fermionic modes and design a fermionic reference, which we then use to construct superpositions of different numbers of referenced fermions. This allows us to build logical fermionic modes that can be error corrected using standard atomic operations. Here, we focus on phase errors, which we expect to be a dominant source of errors in neutral-atom quantum processors. We then construct logical fermionic gates, and show their implementation for the logical particle-number conserving processes relevant for quantum simulation. Finally, our protocol is illustrated with a minimal fermionic circuit, where it leads to a quadratic suppression of the logical error rate.

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References (86)

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2010).
  2. J. Preskill, Quantum 2, 79 (2018).
  3. S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Rev. Mod. Phys. 92, 015003 (2020).
  4. E. Altman et al., PRX Quantum 2, 017003 (2021).
  5. A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Nature (London) 607, 667 (2022).
  6. A. Di Meglio et al., PRX Quantum 5, 037001 (2024).
  7. F. Verstraete and J. I. Cirac, J. Stat. Mech. (2005) P09012.
  8. E. Zohar and J. I. Cirac, Phys. Rev. B 98, 075119 (2018).
  9. C. Derby, J. Klassen, J. Bausch, and T. Cubitt, Phys. Rev. B 104, 035118 (2021).
  10. S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, arXiv:1701.08213.
  11. S. B. Bravyi and A. Y. Kitaev, Ann. Phys. (Amsterdam) 298, 210 (2002).
  12. Y.-A. Chen and Y. Xu, PRX Quantum 4, 010326 (2023).
  13. D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, J. Ye, and P. Zoller, Proc. Natl. Acad. Sci. U.S.A. 120, e2304294120 (2023).
  14. F. Gkritsis, D. Dux, J. Zhang, N. Jain, C. Gogolin, and P. M. Preiss, PRX Quantum 6, 010318 (2025).
  15. J. Argüello-Luengo, A. González-Tudela, T. Shi, P. Zoller, and J. I. Cirac, Nature (London) 574, 215 (2019).
  16. T. V. Zache, D. González-Cuadra, and P. Zoller, Quantum 7, 1140 (2023).
  17. R. Jördens, N. Strohmaier, K. Günter, H. Moritz, and T. Esslinger, Nature (London) 455, 204 (2008).
  18. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, Nature (London) 545, 462 (2017).
  19. S. Hirthe, T. Chalopin, D. Bourgund, P. Bojović, A. Bohrdt, E. Demler, F. Grusdt, I. Bloch, and T. A. Hilker, Nature (London) 613, 463 (2023).
  20. M. Xu, L. H. Kendrick, A. Kale, Y. Gang, G. Ji, R. T. Scalettar, M. Lebrat, and M. Greiner, Nature (London) 620, 971 (2023).
  21. P. T. Brown, D. Mitra, E. Guardado-Sanchez, R. Nourafkan, A. Reymbaut, C.-D. Hébert, S. Bergeron, A.-M. Tremblay, J. Kokalj, D. A. Huse et al., Science 363, 379 (2019).
  22. J. Koepsell, J. Vijayan, P. Sompet, F. Grusdt, T. A. Hilker, E. Demler, G. Salomon, I. Bloch, and C. Gross, Nature (London) 572, 358 (2019).
  23. J. Koepsell, D. Bourgund, P. Sompet, S. Hirthe, A. Bohrdt, Y. Wang, F. Grusdt, E. Demler, G. Salomon, C. Gross et al., Science 374, 82 (2021).
  24. L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, Phys. Rev. Lett. 114, 193001 (2015).
  25. L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein, Science 353, 1260 (2016).
  26. T. Hartke, B. Oreg, C. Turnbaugh, N. Jia, and M. Zwierlein, Science 381, 82 (2023).
  27. T. Hartke, B. Oreg, N. Jia, and M. Zwierlein, Nature (London) 601, 537 (2022).
  28. S. Murmann, A. Bergschneider, V. M. Klinkhamer, G. Zürn, T. Lompe, and S. Jochim, Phys. Rev. Lett. 114, 080402 (2015).
  29. Z. Z. Yan, B. M. Spar, M. L. Prichard, S. Chi, H.-T. Wei, E. Ibarra-García-Padilla, K. R. A. Hazzard, and W. S. Bakr, Phys. Rev. Lett. 129, 123201 (2022).
  30. B. M. Spar, E. Guardado-Sanchez, S. Chi, Z. Z. Yan, and W. S. Bakr, Phys. Rev. Lett. 128, 223202 (2022).
  31. J. H. Becher, E. Sindici, R. Klemt, S. Jochim, A. J. Daley, and P. M. Preiss, Phys. Rev. Lett. 125, 180402 (2020).
  32. F. Serwane, G. Zürn, T. Lompe, T. Ottenstein, A. Wenz, and S. Jochim, Science 332, 336 (2011).
  33. P. W. Shor, Phys. Rev. A 52, R2493 (1995).
  34. D. Gottesman, Stabilizer Codes and Quantum Error Correction (California Institute of Technology, California, 1997).
  35. C. Ryan-Anderson, N. Brown, C. Baldwin, J. Dreiling, C. Foltz, J. Gaebler, T. Gatterman, N. Hewitt, C. Holliman, C. Horst et al., Science 385, 1327 (2024).
  36. M. Da Silva, C. Ryan-Anderson, J. Bello-Rivas, A. Chernoguzov, J. Dreiling, C. Foltz, F. Frachon, J. Gaebler, T. Gatterman, L. Grans-Samuelsson et al., arXiv:2404.02280.
  37. L. Postler, S. Heußen, I. Pogorelov, M. Rispler, T. Feldker, M. Meth, C. D. Marciniak, R. Stricker, M. Ringbauer, R. Blatt et al., Nature (London) 605, 675 (2022).
  38. L. Postler, F. Butt, I. Pogorelov, C. D. Marciniak, S. Heußen, R. Blatt, P. Schindler, M. Rispler, M. Müller, and T. Monz, PRX Quantum 5, 030326 (2024).
  39. L. Egan, D. M. Debroy, C. Noel, A. Risinger, D. Zhu, D. Biswas, M. Newman, M. Li, K. R. Brown, M. Cetina et al., Nature (London) 598, 281 (2021).
  40. R. Acharya, D. A. Abanin, L. Aghababaie-Beni, I. Aleiner, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, N. Astrakhantsev et al., Nature (London) 638, 920 (2025).
  41. H. Putterman, K. Noh, C. T. Hann, G. S. MacCabe, S. Aghaeimeibodi, R. N. Patel, M. Lee, W. M. Jones, H. Moradinejad, R. Rodriguez et al., Nature (London) 638, 927 (2025).
  42. V. Sivak, A. Eickbusch, B. Royer, S. Singh, I. Tsioutsios, S. Ganjam, A. Miano, B. Brock, A. Ding, L. Frunzio et al., Nature (London) 616, 50 (2023).
  43. D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter et al., Nature (London) 626, 58 (2024).
  44. B. W. Reichardt, A. Paetznick, D. Aasen, I. Basov, J. M. Bello-Rivas, P. Bonderson, R. Chao, W. van Dam, M. B. Hastings, A. Paz et al., arXiv:2411.11822.
  45. M. Bedalov, M. Blakely, P. Buttler, C. Carnahan, F. T. Chong, W. C. Chung, D. C. Cole, P. Goiporia, P. Gokhale, B. Heim et al., arXiv:2412.07670.
  46. F. Iemini, L. Mazza, D. Rossini, R. Fazio, and S. Diehl, Phys. Rev. Lett. 115, 156402 (2015).
  47. F. Iemini, D. Rossini, R. Fazio, S. Diehl, and L. Mazza, Phys. Rev. B 93, 115113 (2016).
  48. N. Lang and H. P. Büchler, Phys. Rev. B 92, 041118(R) (2015).
  49. A. Bühler, N. Lang, C. V. Kraus, G. Möller, S. D. Huber, and H.-P. Büchler, Nat. Commun. 5, 4504 (2014).
  50. S. Diehl, A. Micheli, A. Kantian, B. Kraus, H. Büchler, and P. Zoller, Nat. Phys. 4, 878 (2008).
  51. S. Diehl, E. Rico, M. A. Baranov, and P. Zoller, Nat. Phys. 7, 971 (2011).
  52. L. Jiang, T. Kitagawa, J. Alicea, A. R. Akhmerov, D. Pekker, G. Refael, J. I. Cirac, E. Demler, M. D. Lukin, and P. Zoller, Phys. Rev. Lett. 106, 220402 (2011).
  53. A. Schuckert, E. Crane, A. V. Gorshkov, M. Hafezi, and M. J. Gullans, Fermion-qubit fault-tolerant quantum computing, arXiv:2411.08955.
  54. M. Holland, S. J. J. M. F. Kokkelmans, M. L. Chiofalo, and R. Walser, Phys. Rev. Lett. 87, 120406 (2001).

  55. In fact, our construction generalizes a subtle discussion of optical coherence [56] to fermionic system.

  56. K. Mølmer, Phys. Rev. A 55, 3195 (1997).
  57. C. Gross and I. Bloch, Science 357, 995 (2017).
  58. D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner et al., Nature (London) 604, 451 (2022).
  59. A. M. Kaufman and K.-K. Ni, Nat. Phys. 17, 1324 (2021).
  60. A. M. Kaufman, B. J. Lester, C. M. Reynolds, M. L. Wall, M. Foss-Feig, K. R. A. Hazzard, A. M. Rey, and C. A. Regal, Science 345, 306 (2014).
  61. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler et al., Phys. Rev. Lett. 123, 170503 (2019).
  62. S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara et al., Nature (London) 622, 268 (2023).
  63. I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, Nat. Phys. 16, 857 (2020).
  64. S. Ma, G. Liu, P. Peng, B. Zhang, S. Jandura, J. Claes, A. P. Burgers, G. Pupillo, S. Puri, and J. D. Thompson, Nature (London) 622, 279 (2023).
  65. T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, Phys. Rev. Lett. 104, 010502 (2010).
  66. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, Phys. Rev. Lett. 104, 010503 (2010).
  67. A. W. Young, W. J. Eckner, N. Schine, A. M. Childs, and A. M. Kaufman, Science 377, 885 (2022).
  68. R. Tao, M. Ammenwerth, F. Gyger, I. Bloch, and J. Zeiher, Phys. Rev. Lett. 133, 013401 (2024).
  69. A. Impertro, S. Karch, J. F. Wienand, S. J. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Phys. Rev. Lett. 133, 063401 (2024).
  70. Z. Zhu, Y. Kiefer, S. Jele, M. Gächter, G. Bisson, K. Viebahn, and T. Esslinger, arXiv:2409.02984.
  71. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zkpl-hh28 for additional details on the presented numerical and analytical findings.

  72. For simplicity we assume Mr>N>Ms, but discuss generalizations in SM [71].

  73. We note that the entire construction here is employed for fermions, but can be applied to bosons as well.

  74. We define the boundary term in (1) via η0=1, ηMr+1=0.

  75. This particular set of reference states is related to the choice of R. It is perfectly possible to generalize this and choose different reference states and correspondingly R.

  76. A. Y. Kitaev, Phys. Usp. 44, 131 (2001).

  77. Our construction can interpreted as encoding multiple logical modes in a single code block, evading the no-go theorem of Ref. [53].

  78. In the fixed number sector HNLC, our scheme can be implemented with Ms=3ML system modes, 2ML reference modes and in total 2ML+NL fermionic atoms..

  79. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).

  80. We assume that these ancilla qubits are error-free as they can in principle be encoded and error corrected using standard techniques [34].

  81. In the SM we illustrate this on the example of a fermionic Steane code.

  82. N. Maskara, S. Ostermann, J. Shee, M. Kalinowski, A. McClain Gomez, R. Araiza Bravo, D. S. Wang, A. I. Krylov, N. Y. Yao, M. Head-Gordon et al., Nat. Phys. 21, 289 (2025).
  83. L. Bayha, M. Holten, R. Klemt, K. Subramanian, J. Bjerlin, S. M. Reimann, G. M. Bruun, P. M. Preiss, and S. Jochim, Nature (London) 587, 583 (2020).
  84. T. Hensgens, T. Fujita, L. Janssen, X. Li, C. Van Diepen, C. Reichl, W. Wegscheider, S. Das Sarma, and L. M. Vandersypen, Nature (London) 548, 70 (2017).
  85. T. Dvir, G. Wang, N. van Loo, C.-X. Liu, G. P. Mazur, A. Bordin, S. L. Ten Haaf, J.-Y. Wang, D. van Driel, F. Zatelli et al., Nature (London) 614, 445 (2023).
  86. R. Ott et al., Error-corrected fermionic quantum processors with neutral atoms, 10.5281/zenodo.15805349.

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Phys. Rev. Lett. 135, 090601– Published 25 August, 2025
  • Received 20 December 2024
  • Accepted 13 June 2025
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