- Open Access
Logical entanglement distribution between distant two-dimensional array qubits
Phys. Rev. Research 8, 013282 – Published 12 March, 2026
DOI: https://doi.org/10.1103/m9gc-n3dl
Abstract
Sharing logical entangled pairs between distant quantum nodes is a key process to achieve fault-tolerant quantum computation and communication. However, there is a gap between current experimental specifications and theoretical requirements for sharing logical entangled states while improving experimental techniques. Here, we propose an efficient logical entanglement distribution protocol based on surface codes for two distant two-dimensional qubit array with nearest-neighbor interaction. A notable feature of our protocol is that it allows postselection according to error estimations, which provides the tunability between the infidelity of logical entanglements and the success probability of the protocol. With this feature, the fidelity of encoded logical entangled states can be improved by sacrificing success rates. We numerically evaluated the performance of our protocol and the trade-off relationship, and found that our protocol enables us to prepare logical entangled states while improving fidelity in feasible experimental parameters. We also discuss a possible physical implementation using neutral atom arrays to show the feasibility of our protocol.
Physics Subject Headings (PhySH)
Article Text
References (51)
- Google Quantum AI, Suppressing quantum errors by scaling a surface code logical qubit, Nature (London) 614, 676 (2023).
- D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, et al., A quantum processor based on coherent transport of entangled atom arrays, Nature (London) 604, 451 (2022).
- 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., Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
- L. Hartung, M. Seubert, S. Welte, E. Distante, and G. Rempe, A quantum-network register assembled with optical tweezers in an optical cavity, Science 385, 179 (2024).
- D. Rosenberg, D. Kim, R. Das, D. Yost, S. Gustavsson, D. Hover, P. Krantz, A. Melville, L. Racz, G. Samach, et al., 3D integrated superconducting qubits, npj Quantum Inf. 3, 42 (2017).
- A. Gold, J. Paquette, A. Stockklauser, M. J. Reagor, M. S. Alam, A. Bestwick, N. Didier, A. Nersisyan, F. Oruc, A. Razavi, et al., Entanglement across separate silicon dies in a modular superconducting qubit device, npj Quantum Inf. 7, 142 (2021).
- D. Cuomo, M. Caleffi, and A. S. Cacciapuoti, Towards a distributed quantum computing ecosystem, IET Quantum Commun. 1, 3 (2020).
- A. G. Fowler, D. S. Wang, C. D. Hill, T. D. Ladd, R. Van Meter, and L. C. L. Hollenberg, Surface code quantum communication, Phys. Rev. Lett. 104, 180503 (2010).
- V. Giovannetti, L. Maccone, T. Morimae, and T. G. Rudolph, Efficient universal blind quantum computation, Phys. Rev. Lett. 111, 230501 (2013).
- B. A. Bell, D. Markham, D. A. Herrera-Martí, A. Marin, W. J. Wadsworth, J. G. Rarity, and M. S. Tame, Experimental demonstration of graph-state quantum secret sharing, Nat. Commun. 5, 5480 (2014).
- V. Galetsky, N. Vyas, A. Comin, and J. Nötzel, Feasibility of logical bell state generation in memory assisted quantum networks, Phys. Rev. Res. 7, 033090 (2025).
- 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).
- Y. Li, A magic state's fidelity can be superior to the operations that created it, New J. Phys. 17, 023037 (2015).
- C. Pattison, G. Baranes, J. P. Bonilla Ataides, M. D. Lukin, and H. Zhou, Constant-rate entanglement distillation for fast quantum interconnects, in Proceedings of the 52nd Annual International Symposium on Computer Architecture, Tokyo, Japan (ACM, New York, NY, 2025), pp. 257–270.
- L. Li, X. Hu, Z. Jia, W. Huie, W. K. C. Sun, Aakash, Y. Dong, N. Hiri-O-Tuppa, and J. P. Covey, Parallelized telecom quantum networking with an ytterbium-171 atom array, Nat. Phys. 21, 1826 (2025).
- A. L. Shaw, A. Soper, D. Shadmany, A. Kumar, L. Palm, D.-Y. Koh, V. Kaxiras, L. Taneja, M. Jaffe, D. I. Schuster, and J. Simon, A cavity-array microscope for parallel single-atom interfacing, Nature (London) 650, 320 (2026).
- Y. Maeda, T. Kobayashi, T. Ueno, K. Shibata, S. Takenaka, K. Ito, Y. Fujiwara, S. Miki, H. Terai, T. Kodama, et al., Waveguide-array-based multiplexed photonic interface for atom array, arXiv:2512.21533.
- R. Matsumoto, Conversion of a general quantum stabilizer code to an entanglement distillation protocol, J. Phys. A: Math. Gen. 36, 8113 (2003).
- C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54, 3824 (1996).
- N. Yoshioka, T. Okubo, Y. Suzuki, Y. Koizumi, and W. Mizukami, Hunting for quantum-classical crossover in condensed matter problems, npj Quant. Inf. 10, 45 (2024).
- Q. Xu, J. P. Bonilla Ataides, C. A. Pattison, N. Raveendran, D. Bluvstein, J. Wurtz, B. Vasić, M. D. Lukin, L. Jiang, and H. Zhou, Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays, Nat. Phys. 20, 1084 (2024).
- 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).
- N. P. Breuckmann and J. N. Eberhardt, Quantum low-density parity-check codes, PRX Quantum 2, 040101 (2021).
- C. B. Young, A. Safari, P. Huft, J. Zhang, E. Oh, R. Chinnarasu, and M. Saffman, An architecture for quantum networking of neutral atom processors, Appl. Phys. B 128, 151 (2022).
- G.-Z. Xu, W.-J. Zhang, L.-X. You, J.-M. Xiong, X.-Q. Sun, H. Huang, X. Ou, Y.-M. Pan, C.-L. Lv, H. Li, et al., Superconducting microstrip single-photon detector with system detection efficiency over 90% at 1550 nm, Photonics Res. 9, 958 (2021).
- D. V. Reddy, R. R. Nerem, S. W. Nam, R. P. Mirin, and V. B. Verma, Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm, Optica 7, 1649 (2020).
- T. van Leent, M. Bock, R. Garthoff, K. Redeker, W. Zhang, T. Bauer, W. Rosenfeld, C. Becher, and H. Weinfurter, Long-distance distribution of atom-photon entanglement at telecom wavelength, Phys. Rev. Lett. 124, 010510 (2020).
- T. van Leent, M. Bock, F. Fertig, R. Garthoff, S. Eppelt, Y. Zhou, P. Malik, M. Seubert, T. Bauer, W. Rosenfeld, W. Zhang, C. Becher, and H. Weinfurter, Entangling single atoms over 33 km telecom fibre, Nature (London) 607, 69 (2022).
- D. Niemietz, P. Farrera, S. Langenfeld, and G. Rempe, Nondestructive detection of photonic qubits, Nature (London) 591, 570 (2021).
- T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, Nanophotonic quantum phase switch with a single atom, Nature (London) 508, 241 (2014).
- M. Grassl, Bounds on the minimum distance of linear codes and quantum codes (2007), http://www.codetables.de, accessed 27 November 2024.
- A. E. Brouwer, Bounds on the size of linear codes, in Handbook of Coding Theory, edited by V. S. Pless and W. Huffman (Elsevier, Amsterdam, 1998), Chap. 4, pp. 295–461.
- J. Bochmann, M. Mücke, C. Guhl, S. Ritter, G. Rempe, and D. L. Moehring, Lossless state detection of single neutral atoms, Phys. Rev. Lett. 104, 203601 (2010).
- C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76, 722 (1996).
- W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller, Quantum repeaters based on entanglement purification, Phys. Rev. A 59, 169 (1999).
- E. Knill, Scalable quantum computing in the presence of large detected-error rates, Phys. Rev. A 71, 042322 (2005).
- H. Yamasaki and M. Koashi, Time-efficient constant-space-overhead fault-tolerant quantum computation, Nat. Phys. 20, 247 (2024).
- A. Gu, L. Leone, K. Goodenough, and S. Khatri, Constant overhead entanglement distillation via scrambling, arXiv:2502.09483.
- 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).
- H. Leone, T. Le, S. Srikara, and S. Devitt, Resource overheads and attainable rates for trapped-ion lattice surgery, Phys. Rev. Res. 7, 023088 (2025).
- D. Horsman, A. G. Fowler, S. Devitt, and R. Van Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
- 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).
- C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, et al., On-demand quantum state transfer and entanglement between remote microwave cavity memories, Nat. Phys. 14, 705 (2018).
- P. Magnard, S. Storz, P. Kurpiers, J. Schär, F. Marxer, J. Lütolf, T. Walter, J.-C. Besse, M. Gabureac, K. Reuer, et al., Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems, Phys. Rev. Lett. 125, 260502 (2020).
- C. Gidney, Stim: A fast stabilizer circuit simulator, Quantum 5, 497 (2021).
- M. Saffman, Quantum computing with atomic qubit arrays: Confronting the cost of connectivity, arXiv:2505.11218.
- D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays, Science 354, 1021 (2016).
- R. Lin, H.-S. Zhong, Y. Li, Z.-R. Zhao, L.-T. Zheng, T.-R. Hu, H.-M. Wu, Z. Wu, W.-J. Ma, Y. Gao, et al., Ai-enabled parallel assembly of thousands of defect-free neutral atom arrays, Phys. Rev. Lett. 135, 060602 (2025).
- H. Bombín, M. Pant, S. Roberts, and K. I. Seetharam, Fault-tolerant postselection for low-overhead magic state preparation, PRX Quantum 5, 010302 (2024).
- C. Gidney, M. Newman, P. Brooks, and C. Jones, Yoked surface codes, Nat. Commun. 16, 4498 (2025).
- Y. Maeda, Logical entanglement distribution between distant 2D array qubits (2026), https://doi.org/10.17605/OSF.IO/CTD6V.