- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Fault-tolerant interfaces for modular quantum computing on diverse qubit platforms

Frederik K. Marqversen1,2, Gefen Baranes3,4, Maxim Sirotin3,4, and Johannes Borregaard3,*

  • *Contact author: borregaard@fas.harvard.edu
PDF

Phys. Rev. Research 8, 023097 – Published 30 April, 2026

DOI: https://doi.org/10.1103/ds45-fm9n

Abstract

Modular architectures offer a scalable path toward fault-tolerant quantum computing by interconnecting smaller quantum processing units provided that high-rate, fault-tolerant interfaces can be realized across modules. We present a comprehensive analysis and comparison of known methods for establishing such interfaces, including lattice surgery, transversal gates, and grow-and-distill protocols based on code growing and logical distillation. Using the surface code, we identify optimal interface strategies across a wide range of hardware parameters, such as gate fidelities, entangling rates, and memory resources, and estimate the requirements to achieve logical error rates of 10−6 and 10−12. Our results establish when the interface becomes a bottleneck in the computation and provide guidance for experimental implementations with superconducting, atomic, and solid-state hardware.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (51)

  1. L. Egan, D. M. Debroy, C. Noel, A. Risinger, D. Zhu, D. Biswas, M. Newman, M. Li, K. R. Brown, M. Cetina, and C. Monroe, Fault-tolerant control of an error-corrected qubit, Nature (London) 598, 281 (2021).
  2. D. Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
  3. P. S. Rodriguez et al., Experimental demonstration of logical magic state distillation, Nature 645, 620 (2025).
  4. B. W. Reichardt et al., Logical computation demonstrated with a neutral atom quantum processor, arXiv:2411.11822.
  5. C. Ryan-Anderson et al., High-fidelity teleportation of a logical qubit using transversal gates and lattice surgery, Science 385, 1327 (2024).
  6. J.-S. Chen, E. Nielsen, M. Ebert, V. Inlek, K. Wright, V. Chaplin, A. Maksymov, E. Páez, A. Poudel, P. Maunz, and J. Gamble, Benchmarking a trapped-ion quantum computer with 30 qubits, Quantum 8, 1516 (2024).
  7. D. Bluvstein, A. A. Geim, S. H Li, S. J. Evered, J. Ataides, G. Baranes, A. Gu, T. Manovitz, M. Xu, M. Kalinowski, et al., Architectural mechanisms of a universal fault-tolerant quantum computer, Nature 649, 39 (2026).
  8. N. Lacroix et al., Scaling and logic in the color code on a superconducting quantum processor, Nature 645, 614 (2025).
  9. R. S. Gupta, N. Sundaresan, T. Alexander, C. J. Wood, S. T. Merkel, M. B. Healy, M. Hillenbrand, T. J.-O’Connor, J. R. Wootton, T. J. Yoder, A. W. Cross, M. Takita, and B. J. Brown, Encoding a magic state with beyond break-even fidelity, Nature (London) 625, 259 (2024).
  10. H. Putterman, K. Noh, C. T. Hann, G. S. MacCabe, S. Aghaeimeibodi, R. N. Patel, M. Lee, W. M. Jones, H. Moradinejad, R. Rodriguez, N. Mahuli, J. Rose, J. C. Owens, H. Levine, E. Rosenfeld, P. Reinhold, L. Moncelsi, J. A. Alcid, N. Alidoust, and P. Arrangoiz-Arriola, Hardware-efficient quantum error correction via concatenated bosonic qubits, Nature (London) 638, 927 (2025).
  11. Y. Alexeev, M. Amsler, M. A. Barroca, S. Bassini, T. Battelle, D. Camps, D. Casanova, Y. J. Choi, F. T. Chong, C. Chung, C. Codella, A. D. Córcoles, J. Cruise, A. D. Meglio, I. Duran, T. Eckl, S. Economou, S. Eidenbenz, B. Elmegreen, and C. Fare, Quantum-centric supercomputing for materials science: A perspective on challenges and future directions, Future Gener. Comput. Syst. 160, 666 (2024).
  12. S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys. 92, 015003 (2020).
  13. C. Gidney and M. Ekerå, How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits, Quantum 5, 433 (2021).
  14. J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, and R. Babbush, Even more efficient quantum computations of chemistry through tensor hypercontraction, PRX Quantum 2, 030305 (2021).
  15. M. E. Beverland, P. Murali, M. Troyer, K. M. Svore, T. Hoefler, V. Kliuchnikov, G. H. Low, M. Soeken, A. Sundaram, and A. Vaschillo, Assessing requirements to scale to practical quantum advantage, arXiv:2211.07629.
  16. A. M. Dalzell, S. McArdle, M. Berta, P. Bienias, C.-F. Chen, A. Gilyén, C. T. Hann, M. J. Kastoryano, E. T. Khabiboulline, A. Kubica, G. Salton, S. Wang, and F. G. S. L. Brandão, Quantum Algorithms: A Survey of Applications and End-to-End Complexities (Cambridge University Press, 2025).
  17. C. Monroe, R. Raussendorf, A. Ruthven, K. R. Brown, P. Maunz, L.-M. Duan, and J. Kim, Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects, Phys. Rev. A 89, 022317 (2014).
  18. J. Sinclair, J. Ramette, B. Grinkemeyer, D. Bluvstein, M. D. Lukin, and V. Vuletić, Fault-tolerant optical interconnects for neutral-atom arrays, Phys. Rev. Res. 7, 013313 (2025).
  19. J. Stack, M. Wang, and F. Mueller, Assessing teleportation of logical qubits in a distributed quantum architecture under error correction, arXiv:2504.05611.
  20. J. Ramette, J. Sinclair, N. P. Breuckmann, and V. Vuletić, Fault-tolerant connection of error-corrected qubits with noisy links, npj Quantum Inf. 10, 58 (2024).
  21. C. Pattison, G. Baranes, J. P. B. Ataides, M. D. Lukin, and H. Zhou, Constant-rate entanglement distillation for fast quantum interconnects, Proceedings of the 52nd Annual International Symposium on Computer Architecture, ISCA'25 (Association for Computing Machinery, New York, NY, 2025), pp. 257–270.
  22. Y. Li, A magic state’s fidelity can be superior to the operations that created it, New J. Phys. 17, 023037 (2015).
  23. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
  24. S. Majidy, C. Wilson, and R. Laflamme, Building Quantum Computers: A Practical Introduction (Cambridge University Press, 2024).
  25. R. Acharya et al., Quantum error correction below the surface code threshold, Nature (London) 638, 920 (2025).
  26. H. P. Bartling, J. Yun, K. N. Schymik, M. van Riggelen, L. A. Enthoven, H. B. van Ommen, M. Babaie, F. Sebastiano, M. Markham, D. J. Twitchen, and T. H. Taminiau, Universal high-fidelity quantum gates for spin-qubits in diamond, Phys. Rev. Appl. 23, 034052 (2025).
  27. C. M. Knaut, A. Suleymanzade, Y.-C. Wei, D. R. Assumpcao, P.-J. Stas, Y. Q. Huan, B. Machielse, E. N. Knall, M. Sutula, G. Baranes, N. Sinclair, C. De-Eknamkul, D. S. Levonian, M. K. Bhaskar, H. Park, M. Lončar, and M. D. Lukin, Entanglement of nanophotonic quantum memory nodes in a telecom network, Nature (London) 629, 573 (2024).
  28. H. Zhou, C. Zhao, M. Cain, D. Bluvstein, C. Duckering, H.-Y. Hu, S.-T. Wang, A. Kubica, and M. D. Lukin, Algorithmic fault tolerance for fast quantum computing, Nature 646, 303 (2025).
  29. M. Cain, C. Zhao, H. Zhou, N. Meister, J. P. B. Ataides, A. Jaffe, D. Bluvstein, and M. D. Lukin, Correlated decoding of logical algorithms with transversal gates, Phys. Rev. Lett. 133, 240602 (2024).
  30. H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, A tweezer array with 6100 highly coherent atomic qubits, Nature 647, 60 (2025).
  31. N.-C. Chiu, E. C. Trapp, J. Guo, M. H. Abobeih, L. M. Stewart, S. Hollerith, P. Stroganov, M. Kalinowski, A. A. Geim, S. J. Evered, et al., Continuous operation of a coherent 3,000-qubit system, Nature 646, 1075 (2025).
  32. P.-J. Stas, Y. Q. Huan, B. Machielse, E. N. Knall, A. Suleymanzade, B. Pingault, M. Sutula, S. W. Ding, C. M. Knaut, D. R. Assumpcao, et al., Robust multi-qubit quantum network node with integrated error detection, Science 378, 557 (2022).
  33. Y.-C. Wei, P.-J. Stas, A. Suleymanzade, G. Baranes, F. Machado, Y. Q. Huan, C. M. Knaut, S. W. Ding, M. Merz, E. N. Knall, U. Yazlar, M. Sirotin, I. W. Wang, B. Machielse, S. F. Yelin, J. Borregaard, H. Park, M. Lončar, and M. D. Lukin, Universal distributed blind quantum computing with solid-state qubits, Science 388, 509 (2025).
  34. G. Baranes, I. W. Wang, F. Machado, A. Suleymanzade, P.-J. Stas, Y.-C. Wei, S. F. Yelin, J. Borregaard, and M. D. Lukin, Designing fault-tolerant blind quantum computation, arXiv:2505.21621.
  35. R. Acharya et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  36. S. Storz et al., Loophole-free Bell inequality violation with superconducting circuits, Nature (London) 617, 265 (2023).
  37. G. Baranes, M. Cain, J. Ataides, D. Bluvstein, J. Sinclair, V. Vuletic, H. Zhou, and M. D. Lukin, Leveraging atom loss errors in fault tolerant quantum algorithms, Phys. Rev. X 16, 011002 (2026).
  38. J. P. B. Ataides, H. Zhou, Q. Xu, G. Baranes, B. Li, M. D. Lukin, and L. Jiang, Constant-overhead fault-tolerant Bell-pair distillation using high-rate codes Phys. Rev. Lett. 135, 130804 (2025).
  39. T. J. Yoder, E. Schoute, P. Rall, E. Pritchett, J. M. Gambetta, A. W. Cross, M. Carroll, and M. E. Beverland, Tour de gross: A modular quantum computer based on bivariate bicycle codes, arXiv:2506.03094.
  40. F. K. Marqversen, quantum_computations, GitHub (2025), https://github.com/frederik-kofoed-marqversen/quantum_computations.
  41. M. Sirotin, Growing_simulation, GitHub (2025), https://github.com/MaximSirotin/BellPairsCode.
  42. L. Lao and B. Criger, Magic state injection on the rotated surface code, in Proceedings of the 19th ACM International Conference on Computing Frontiers (ACM, Turin, Italy, 2022), pp. 113–120.
  43. C. Gidney, Stim: A fast stabilizer circuit simulator, Quantum 5, 497 (2021).
  44. Y. Q. Huan, A. Suleymanzade, P.-J. Stas, Y.-C. Wei, E. N. Knall, F. A. Arias, E. Kniazev, B. Machielse, U. Yazlar, G. Baranes, et al., Towards Quantum Repeater Nodes with Weakly-Coupled Nuclear Spins in Diamond, Quantum 2.0 (Optica Publishing Group, 2025), pp. QW4A–3.
  45. S. Krastanov, H. Raniwala, J. Holzgrafe, K. Jacobs, M. Lončar, M. J. Reagor, and D. R. Englund, Optically heralded entanglement of superconducting systems in quantum networks, Phys. Rev. Lett. 127, 040503 (2021).
  46. M. Cain, D. Bluvstein, C. Zhao, S. Gu, N. Maskara, M. Kalinowski, A. A. Geim, A. Kubica, M. D. Lukin, and H. Zhou, Fast correlated decoding of transversal logical algorithms, arXiv:2505.13587.
  47. Y. P. Zhong, H.-S. Chang, K. J. Satzinger, M.-H. Chou, A. Bienfait, C. R. Conner, É. Dumur, J. Grebel, G. A. Peairs, R. G. Povey, et al., Violating Bell’s inequality with remotely connected superconducting qubits, Nat. Phys. 15, 741 (2019).
  48. J. P. Covey, H. Weinfurter, and H. Bernien, Quantum networks with neutral atom processing nodes, npj Quantum Inf. 9, 90 (2023).
  49. S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V. Vuletić, and M. D. Lukin, High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature (London) 622, 268 (2023).
  50. S. Ritter, C. Nölleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mücke, E. Figueroa, J. Bochmann, and G. Rempe, An elementary quantum network of single atoms in optical cavities, Nature (London) 484, 195 (2012).
  51. Y. Li and J. D. Thompson, High-rate and high-fidelity modular interconnects between neutral atom quantum processors, PRX Quantum 5, 020363 (2024).

Outline

Information

Phys. Rev. Research 8, 023097– Published 30 April, 2026
  • Received 24 October 2025
  • Accepted 18 March 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation