- 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

Network requirements for distributed quantum computation

Hugo Jacinto1,2,*, Élie Gouzien1, and Nicolas Sangouard2

  • *Contact author: hugo.jacinto@alice-bob.com
PDF

Phys. Rev. Research 8, 013205 – Published 23 February, 2026

DOI: https://doi.org/10.1103/v9ln-c4v2

Abstract

Physical constraints and engineering challenges, including wafer dimensions, classical control cabling, and refrigeration volumes, impose significant limitations on the scalability of quantum computing units. As a result, a modular quantum computing architecture, comprising small processors interconnected by quantum links, is emerging as a promising approach to fault-tolerant quantum computing. However, the requirements that the network must fulfill to enable distributed quantum computation remain largely unexplored. We consider an architecture tailored for qubits with nearest-neighbor physical connectivity, leveraging the surface code for error correction and enabling fault-tolerant operations through lattice surgery and magic state distillation. We propose measurement teleportation as a tool to extend lattice surgery techniques to qubits located on different computing units interconnected via Bell pairs. Through memory simulations, we build an error model for logical operations and deduce an end-to-end resource estimation of Shor’s algorithm over a minimalist distributed architecture. Concretely, for a characteristic physical gate error rate of 10−3, a processor cycle time of 1 µs, factoring a 2048-bit RSA integer is shown to be possible with 379 computing processors, each made with 89 781 qubits, with negligible space and time overhead with respect to a monolithic approach without parallelization, if 70 Bell pairs are available per cycle time between each processor with a fidelity exceeding 98.1%.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (61)

  1. 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.
  2. 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).
  3. T. L. Scholten, C. J. Williams, D. Moody, M. Mosca, W. Hurley, W. J. Zeng, M. Troyer, and J. M. Gambetta, Assessing the benefits and risks of quantum computers, arXiv:2401.16317.
  4. S. A. Moses, et al., A race-track trapped-ion quantum processor, Phys. Rev. X 13, 041052 (2023).
  5. R. Acharya, et al., Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
  6. Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, Evidence for the utility of quantum computing before fault tolerance, Nature (London) 618, 500 (2023).
  7. E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature (London) 549, 172 (2017).
  8. D. Litinski, A game of surface codes: Large-scale quantum computing with lattice surgery, Quantum 3, 128 (2019).
  9. C. Gidney and M. Ekerå, How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits, Quantum 5, 433 (2021).
  10. S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault-tolerant quantum memory, Nature (London) 627, 778 (2024).
  11. S. Gu, Y. Vaknin, A. Retzker, and A. Kubica, Optimizing quantum error correction protocols with erasure qubits, PRX Quantum 6, 040354 (2025).
  12. C. Gidney, M. Newman, P. Brooks, and C. Jones, Yoked surface codes, Nat Commun 16, 4498 (2025).
  13. A. C. Vazquez, C. Tornow, D. Ristè, S. Woerner, M. Takita, and D. J. Egger, Combining quantum processors with real-time classical communication, Nature (London) 636, 75 (2024).
  14. M. Jing, C. Zhu, and X. Wang, Circuit knitting faces exponential sampling overhead scaling bounded by entanglement cost, Phys. Rev. A 111, 012433 (2025).
  15. C. Piveteau and D. Sutter, Circuit knitting with classical communication, IEEE Trans. Inf. Theory 70, 2734 (2024).
  16. K. Heya, T. Phung, M. Malekakhlagh, R. Steiner, M. Turchetti, W. Shanks, J. Mamin, W.-S. Lu, Y. P. Kandel, N. Sundaresan, and J. Orcutt, Randomized benchmarking of a high-fidelity remote CNOT gate over a meter-scale microwave interconnect, Phys. Rev. Lett. 135, 200801 (2025).
  17. S. Storz, J. Schär, A. Kulikov, P. Magnard, P. Kurpiers, J. Lütolf, T. Walter, A. Copetudo, K. Reuer, A. Akin, et al., Loophole-free Bell inequality violation with superconducting circuits, Nature (London) 617, 265 (2023).
  18. H. Yan, Y. Zhong, H.-S. Chang, A. Bienfait, M.-H. Chou, C. R. Conner, E. Dumur, J. Grebel, R. G. Povey, and A. N. Cleland, Entanglement purification and protection in a superconducting quantum network, Phys. Rev. Lett. 128, 080504 (2022).
  19. S. Storz, A. Kulikov, J. D. Schär, V. Barizien, X. Valcarce, F. Berterottière, N. Sangouard, J.-D. Bancal, and A. Wallraff, Complete self-testing of a system of remote superconducting qubits, Phys. Rev. Lett. 135, 030801 (2025).
  20. M. Caleffi, M. Amoretti, D. Ferrari, J. Illiano, A. Manzalini, and A. S. Cacciapuoti, Distributed quantum computing: A survey, Comput. Networks 254, 110672 (2024).
  21. Q. Xu, A. Seif, H. Yan, N. Mannucci, B. O. Sane, R. Van Meter, A. N. Cleland, and L. Jiang, Distributed quantum error correction for chip-level catastrophic errors, Phys. Rev. Lett. 129, 240502 (2022).
  22. W. Dür and H.-J. Briegel, Entanglement purification for quantum computation, Phys. Rev. Lett. 90, 067901 (2003).
  23. E. T. Campbell, Distributed quantum-information processing with minimal local resources, Phys. Rev. A 76, 040302(R) (2007).
  24. S. Krastanov, V. V. Albert, and L. Jiang, Optimized entanglement purification, Quantum 3, 123 (2019).
  25. L. Jiang, J. M. Taylor, A. S. Sørensen, and M. D. Lukin, Distributed quantum computation based on small quantum registers, Phys. Rev. A 76, 062323 (2007).
  26. K. Fujii, T. Yamamoto, M. Koashi, and N. Imoto, A distributed architecture for scalable quantum computation with realistically noisy devices, arXiv:1202.6588.
  27. N. Nickerson, Y. Li, and S. Benjamin, Topological quantum computing with a very noisy network and local error rates approaching one percent, Nat. Commun. 4, 1756 (2013).
  28. N. H. Nickerson, J. F. Fitzsimons, and S. C. Benjamin, Freely scalable quantum technologies using cells of 5-to-50 qubits with very lossy and noisy photonic links, Phys. Rev. X 4, 041041 (2014).
  29. 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).
  30. J. Sinclair, J. Ramette, B. Grinkemeyer, D. Bluvstein, M. Lukin, and V. Vuletić, Fault-tolerant optical interconnects for neutral-atom arrays, arXiv:2408.08955.
  31. A. G. Fowler and C. Gidney, Low overhead quantum computation using lattice surgery, arXiv:1808.06709.
  32. A. R. O’Rourke and S. Devitt, Compare the pair: Rotated vs. unrotated surface codes at equal logical error rates, Phys. Rev. Res. 7, 033074 (2025).
  33. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, J. Math. Phys. 43, 4452 (2002).
  34. 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).
  35. Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/v9ln-c4v2 for all the Appendixes mentioned in the main text, which cites additionally [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54].
  37. C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5, 497 (2021).
  38. A. M. Stephens, Fault-tolerant thresholds for quantum error correction with the surface code, Phys. Rev. A 89, 022321 (2014).
  39. M. Newville, T. Stensitzki, D. B. Allen, and A. Ingargiola, Lmfit: Non-linear least-square minimization and curve-fitting for python, Astrophysics Source Code Library (2014), doi:10.5281/zenodo.12785036.
  40. C. Guinn, S. Stein, E. Tureci, G. Avis, C. Liu, S. Krastanov, A. A. Houck, and A. Li, Co-designed superconducting architecture for lattice surgery of surface codes with quantum interface routing card, arXiv:2312.01246 [quant-ph].
  41. C. Gidney and A. G. Fowler, Flexible layout of surface code computations using autoccz states, arXiv:1905.08916 [quant-ph].
  42. D. B. Tan, M. Y. Niu, and C. Gidney, A sat scalpel for lattice surgery: Representation and synthesis of subroutines for surface-code fault-tolerant quantum computing, in 2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA) (IEEE, New York, 2024), pp. 325–339.
  43. C. Chamberland and E. T. Campbell, Universal quantum computing with twist-free and temporally encoded lattice surgery, PRX Quantum 3, 010331 (2022).
  44. C. Chamberland and E. T. Campbell, Circuit-level protocol and analysis for twist-based lattice surgery, Phys. Rev. Res. 4, 023090 (2022).
  45. D. Litinski and F. von Oppen, Lattice surgery with a twist: Simplifying clifford gates of surface codes, Quantum 2, 62 (2018).
  46. C. Gidney, Inplace access to the surface code y basis, Quantum 8, 1310 (2024).
  47. E. Gouzien, D. Ruiz, F.-M. Le Régent, J. Guillaud, and N. Sangouard, Performance analysis of a repetition cat code architecture: Computing 256-bit elliptic curve logarithm in 9 hours with 126 133 cat qubits, Phys. Rev. Lett. 131, 040602 (2023).
  48. R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. Mc- Clean, A. Paler, A. Fowler, and H. Neven, Encoding electronic spectra in quantum circuits with linear t com8 plexity, Phys. Rev. X 8, 041015 (2018).
  49. B. Domokos, Áron Márton, and J. K. Asbóth, Characterization of errors in a cnot between surface code patches, arXiv:2405.05337 [quant-ph].
  50. C. Gidney, Stability experiments: The overlooked dual of memory experiments, Quantum 6, 786 (2022).
  51. S. Bravyi and A. Kitaev, Universal quantum computation with ideal clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
  52. G. P. Gehér, C. McLauchlan, E. T. Campbell, A. E. Moylett, and O. Crawford, Error-corrected hadamard gate simulated at the circuit level, Quantum 8, 1394 (2024).
  53. C. Gidney, Windowed quantum arithmetic, arXiv:1905.07682 [quant-ph].
  54. C. Gidney, Approximate encoded permutations and piecewise quantum adders, arXiv:1905.08488 [quant-ph].
  55. O. Higgott, and C. Gidney, Sparse {B}lossom: correcting a million errors per core second with minimum-weight matching, Quantum 9, 1600 (2025).
  56. M. A. Shalby, R. Wang, D. Sedov, and L. P. Pryadko, Optimized noise-resilient surface code teleportation interfaces, Phys. Rev. A 112, L020403 (2025).
  57. D. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
  58. M. Ekerå and J. Håstad, Quantum algorithms for computing short discrete logarithms and factoring RSA integers, in Post-Quantum Cryptography, Lecture Notes in Computer Science (Springer International Publishing, Cham, 2017), Vol. 10346, p. 347.
  59. P. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science (1994), pp. 124–134.
  60. D. Litinski, Magic state distillation: Not as costly as you think, Quantum 3, 205 (2019).
  61. https://github.com/HugoJ1/shor_multi_chip.

Outline

Information

Phys. Rev. Research 8, 013205– Published 23 February, 2026
  • Received 15 April 2025
  • Accepted 9 January 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