Adaptive routing for quantum memory failures in the quantum Internet

  • Laszlo GyongyosiEmail author
  • Sandor Imre


We define an adaptive routing method for the management of quantum memory failures in the quantum Internet. In the quantum Internet, the entangled quantum states are stored in the local quantum memories of the quantum nodes. A quantum memory failure in a particular quantum node can destroy several entangled connections in the entangled network. A quantum memory failure event makes the immediate and efficient determination of shortest replacement paths an emerging issue in a quantum Internet scenario. The replacement paths omit those nodes that are affected by the quantum memory failure to provide a seamless network transmission. In the proposed solution, the shortest paths are determined by a base-graph, which contains all information about the overlay quantum network. The method provides efficient adaptive routing in quantum memory failure scenarios of the quantum Internet. The results can be straightforwardly applied in practical quantum networks, including long-distance quantum communications.


Quantum Internet Quantum networking Quantum repeaters Quantum entanglement 



This work was partially supported by the National Research Development and Innovation Office of Hungary (Project No. 2017-1.2.1-NKP-2017-00001), by the Hungarian Scientific Research Fund—OTKA K-112125 and in part by the BME Artificial Intelligence FIKP Grant of EMMI (BME FIKP-MI/SC).

Author Contributions

LGY designed the protocol and wrote the manuscript. LGY and SI analyzed the results. All authors reviewed the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Van Meter, R.: Quantum Networking. Wiley, New Jersey (2014). ISBN 1118648927, 9781118648926Google Scholar
  2. 2.
    Lloyd, S., Shapiro, J.H., Wong, F.N.C., Kumar, P., Shahriar, S.M., Yuen, H.P.: Infrastructure for the quantum Internet. ACM SIGCOMM Comput. Commun. Rev. 34, 9–20 (2004)CrossRefGoogle Scholar
  3. 3.
    Kimble, H.J.: The quantum Internet. Nature 453, 1023–1030 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    Gyongyosi, L., Imre, S., Nguyen, H.V.: A survey on quantum channel capacities. IEEE Commun. Surv. Tutor. (2018).
  5. 5.
    Van Meter, R., Ladd, T.D., Munro, W.J., Nemoto, K.: System design for a long-line quantum repeater. IEEE/ACM Trans. Netw. 17(3), 1002–1013 (2009)CrossRefGoogle Scholar
  6. 6.
    Van Meter, R., Satoh, T., Ladd, T.D., Munro, W.J., Nemoto, K.: Path selection for quantum repeater networks. Netw. Sci. 3(1–4), 82–95 (2013)CrossRefGoogle Scholar
  7. 7.
    Van Meter, R., Devitt, S.J.: Local and distributed quantum computation. IEEE Comput. 49(9), 31–42 (2016)CrossRefGoogle Scholar
  8. 8.
    Gyongyosi, L., Imre, S.: Decentralized base-graph routing for the quantum Internet. Phys. Rev. A (2018).
  9. 9.
    Gyongyosi, L., Imre, S.: Dynamic topology resilience for quantum networks. In: Proceedings of SPIE 10547, Advances in Photonics of Quantum Computing, Memory, and Communication XI, p. 105470Z (2018).
  10. 10.
    Gyongyosi, L., Imre, S.: Topology adaption for the quantum Internet. Quantum Inf. Process. 17, 295 (2018). ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Pirandola, S., Laurenza, R., Ottaviani, C., Banchi, L.: Fundamental limits of repeaterless quantum communications. Nat. Commun. 8, 15043 (2017). ADSCrossRefGoogle Scholar
  12. 12.
    Pirandola, S., Braunstein, S.L., Laurenza, R., Ottaviani, C., Cope, T.P.W., Spedalieri, G., Banchi, L.: Theory of channel simulation and bounds for private communication. Quantum Sci. Technol. 3, 035009 (2018)ADSCrossRefGoogle Scholar
  13. 13.
    Pirandola, S.: Capacities of repeater-assisted quantum communications. arXiv:1601.00966 (2016)
  14. 14.
    Gyongyosi, L., Imre, S.: Multilayer optimization for the quantum Internet. Sci. Rep. (2018).
  15. 15.
    Gyongyosi, L., Imre, S.: Entanglement availability differentiation service for the quantum Internet. Sci. Rep. (2018).
  16. 16.
    Gyongyosi, L., Imre, S.: Entanglement-gradient routing for quantum networks. Sci. Rep. (2017).
  17. 17.
    Imre, S., Gyongyosi, L.: Advanced Quantum Communications—An Engineering Approach. Wiley-IEEE Press, New Jersey (2013)zbMATHGoogle Scholar
  18. 18.
    Caleffi, M.: End-to-end entanglement rate: toward a quantum route metric. In: 2017 IEEE Globecom (2018).
  19. 19.
    Caleffi, M.: Optimal routing for quantum networks. IEEE Access 5, 22299 (2017). CrossRefGoogle Scholar
  20. 20.
    Caleffi, M., Cacciapuoti, A.S., Bianchi, G.: Quantum Internet: from communication to distributed computing. arXiv:1805.04360 (2018)
  21. 21.
    Castelvecchi, D.: The quantum Internet has arrived, nature, news and comment. (2018). Accessed 22 Feb 2018
  22. 22.
    Cacciapuoti, A.S., Caleffi, M., Tafuri, F., Cataliotti, F.S., Gherardini, S., Bianchi, G.: Quantum Internet: networking challenges in distributed quantum computing. arXiv:1810.08421 (2018)
  23. 23.
    Kok, P., Munro, W.J., Nemoto, K., Ralph, T.C., Dowling, J.P., Milburn, G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    Petz, D.: Quantum Information Theory and Quantum Statistics. Springer, Heidelberg (2008)Google Scholar
  25. 25.
    Bacsardi, L.: On the way to quantum-based satellite communication. IEEE Commun. Mag. 51(08), 50–55 (2013)CrossRefGoogle Scholar
  26. 26.
    Biamonte, J., et al.: Quantum machine learning. Nature 549, 195–202 (2017)ADSCrossRefGoogle Scholar
  27. 27.
    Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum algorithms for supervised and unsupervised machine learning. arXiv:1307.0411 (2013)
  28. 28.
    Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10, 631 (2014)CrossRefGoogle Scholar
  29. 29.
    Lloyd, S.: Capacity of the noisy quantum channel. Phys. Rev. A 55, 1613–1622 (1997)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Lloyd, S.: The universe as quantum computer. In: Zenil, H. (ed.) A Computable Universe: Understanding and Exploring Nature as Computation. World Scientific, Singapore (2013). arXiv:1312.4455v1
  31. 31.
    Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)ADSCrossRefGoogle Scholar
  32. 32.
    Chou, C., Laurat, J., Deng, H., Choi, K.S., de Riedmatten, H., Felinto, D., Kimble, H.J.: Functional quantum nodes for entanglement distribution over scalable quantum networks. Science 316(5829), 1316–1320 (2007)ADSCrossRefGoogle Scholar
  33. 33.
    Muralidharan, S., Kim, J., Lutkenhaus, N., Lukin, M.D., Jiang, L.: Ultrafast and fault-tolerant quantum communication across long distances. Phys. Rev. Lett 112, 250501 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    Yuan, Z., Chen, Y., Zhao, B., Chen, S., Schmiedmayer, J., Pan, J.W.: Experimental demonstration of a BDCZ quantum repeater node. Nature 454, 1098–1101 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    Kobayashi, H., Le Gall, F., Nishimura, H., Rotteler, M.: General scheme for perfect quantum network coding with free classical communication. In: Lecture Notes in Computer Science (Automata, Languages and Programming SE-52), vol. 5555, pp. 622–633. Springer (2009)Google Scholar
  36. 36.
    Hayashi, M.: Prior entanglement between senders enables perfect quantum network coding with modification. Phys. Rev. A 76, 040301(R) (2007)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Hayashi, M., Iwama, K., Nishimura, H., Raymond, R., Yamashita, S.: Quantum network coding. In: Thomas, W., Weil, P. (eds.) Lecture Notes in Computer Science (STACS 2007 SE52), vol. 4393. Springer, Berlin (2007)Google Scholar
  38. 38.
    Chen, L., Hayashi, M.: Multicopy and stochastic transformation of multipartite pure states. Phys. Rev. A 83(2), 022331 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    Schoute, E., Mancinska, L., Islam, T., Kerenidis, I., Wehner, S.: Shortcuts to quantum network routing. arXiv:1610.05238 (2016)
  40. 40.
    Lloyd, S., Weedbrook, C.: Quantum generative adversarial learning. Phys. Rev. Lett. 121. arXiv:1804.09139 (2018)
  41. 41.
    Gisin, N., Thew, R.: Quantum communication. Nat. Photonics 1, 165–171 (2007)ADSCrossRefGoogle Scholar
  42. 42.
    Xiao, Y.F., Gong, Q.: Optical microcavity: from fundamental physics to functional photonics devices. Sci. Bull. 61, 185–186 (2016)CrossRefGoogle Scholar
  43. 43.
    Zhang, W., et al.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118, 220501 (2017)ADSCrossRefGoogle Scholar
  44. 44.
    Enk, S.J., Cirac, J.I., Zoller, P.: Photonic channels for quantum communication. Science 279, 205–208 (1998)ADSCrossRefGoogle Scholar
  45. 45.
    Briegel, H.J., Dur, W., Cirac, J.I., Zoller, P.: Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998)ADSCrossRefGoogle Scholar
  46. 46.
    Dur, W., Briegel, H.J., Cirac, J.I., Zoller, P.: Quantum repeaters based on entanglement purification. Phys. Rev. A 59, 169–181 (1999)ADSCrossRefGoogle Scholar
  47. 47.
    Duan, L.M., Lukin, M.D., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001)ADSCrossRefGoogle Scholar
  48. 48.
    Van Loock, P., Ladd, T.D., Sanaka, K., Yamaguchi, F., Nemoto, K., Munro, W.J., Yamamoto, Y.: Hybrid quantum repeater using bright coherent light. Phys. Rev. Lett. 96, 240501 (2006)CrossRefGoogle Scholar
  49. 49.
    Zhao, B., Chen, Z.B., Chen, Y.A., Schmiedmayer, J., Pan, J.W.: Robust creation of entanglement between remote memory qubits. Phys. Rev. Lett. 98, 240502 (2007)ADSCrossRefGoogle Scholar
  50. 50.
    Goebel, A.M., Wagenknecht, G., Zhang, Q., Chen, Y., Chen, K., Schmiedmayer, J., Pan, J.W.: Multistage entanglement swapping. Phys. Rev. Lett. 101, 080403 (2008)ADSCrossRefGoogle Scholar
  51. 51.
    Simon, C., de Riedmatten, H., Afzelius, M., Sangouard, N., Zbinden, H., Gisin, N.: Quantum repeaters with photon pair sources and multimode memories. Phys. Rev. Lett. 98, 190503 (2007)ADSCrossRefGoogle Scholar
  52. 52.
    Tittel, W., Afzelius, M., Chaneliere, T., Cone, R.L., Kroll, S., Moiseev, S.A., Sellars, M.: Photon-echo quantum memory in solid state systems. Laser Photonics Rev. 4, 244–267 (2009)ADSCrossRefGoogle Scholar
  53. 53.
    Sangouard, N., Dubessy, R., Simon, C.: Quantum repeaters based on single trapped ions. Phys. Rev. A 79, 042340 (2009)ADSCrossRefGoogle Scholar
  54. 54.
    Dur, W., Briegel, H.J.: Entanglement purification and quantum error correction. Rep. Prog. Phys. 70, 1381–1424 (2007)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    Sheng, Y.B., Zhou, L.: Distributed secure quantum machine learning. Sci. Bull. 62, 1025–1029 (2017)CrossRefGoogle Scholar
  56. 56.
    Leung, D., Oppenheim, J., Winter, A.: Quantum network communication; the butterfly and beyond. IEEE Trans. Inf. Theory 56, 3478–3490 (2010)MathSciNetCrossRefGoogle Scholar
  57. 57.
    Kobayashi, H., Le Gall, F., Nishimura, H., Rotteler, M.: Perfect quantum network communication protocol based on classical network coding. In: Proceedings of 2010 IEEE International Symposium on Information Theory (ISIT), pp. 2686–2690 (2010)Google Scholar
  58. 58.
    Laurenza, R., Pirandola, S.: General bounds for sender–receiver capacities in multipoint quantum communications. Phys. Rev. A 96, 032318 (2017)ADSCrossRefGoogle Scholar
  59. 59.
    Leepila, R., Oki, E., Kishi, N.: Scheme to find k disjoint paths in multi-cost networks. In: IEEE ICC 2011 (2011)Google Scholar
  60. 60.
    Leepila, R.: Routing Schemes for Survivable and Energy-Efficient Networks. PhD Thesis, Department of Information and Communication Engineering, The University of Electro-Communications (2014)Google Scholar
  61. 61.
    Rak, J.: k-penalty: a novel approach to find k-disjoint paths with differentiated path costs. IEEE Commun. Lett. 14(4), 354–356 (2010)CrossRefGoogle Scholar
  62. 62.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1(1), 269–271 (1959)MathSciNetCrossRefGoogle Scholar
  63. 63.
    Rak, J.: Resilient Routing in Communication Networks. Springer, Berlin (2015)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Electronics and Computer ScienceUniversity of SouthamptonSouthamptonUK
  2. 2.Department of Networked Systems and ServicesBudapest University of Technology and EconomicsBudapestHungary
  3. 3.MTA-BME Information Systems Research GroupHungarian Academy of SciencesBudapestHungary

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