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Path selection for quantum repeater networks

Abstract

Quantum networks will support long-distance quantum key distribution (QKD) and distributed quantum computation, and are an active area of both experimental and theoretical research. Here, we present an analysis of topologically complex networks of quantum repeaters composed of heterogeneous links. Quantum networks have fundamental behavioral differences from classical networks; the delicacy of quantum states makes a practical path selection algorithm imperative, but classical notions of resource utilization are not directly applicable, rendering known path selection mechanisms inadequate. To adapt Dijkstra’s algorithm for quantum repeater networks that generate entangled Bell pairs, we quantify the key differences and define a link cost metric, seconds per Bell pair of a particular fidelity, where a single Bell pair is the resource consumed to perform one quantum teleportation. Simulations that include both the physical interactions and the extensive classical messaging confirm that Dijkstra’s algorithm works well in a quantum context. Simulating about three hundred heterogeneous paths, comparing our path cost and the total work along the path gives a coefficient of determination of 0.88 or better.

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References

  1. E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269–271, Dec. 1959.

    Article  MATH  MathSciNet  Google Scholar 

  2. C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science, vol. 316, no. 5829, pp. 1316–1320, Jun. 2007.

    Article  Google Scholar 

  3. H. J. Kimble, “The quantum Internet,” Nature, vol. 453, no. 7198, pp. 1023–1030, Jun. 2008.

    Article  Google Scholar 

  4. R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature, vol. 443, no. 7113, pp. 838–841, Aug. 2006.

    Article  Google Scholar 

  5. T. Tashima, T. Kitano, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Demonstration of local expansion toward large-scale entangled webs,” Phys. Rev. Lett., vol. 105, no. 21, pp. 210503, Nov. 2010.

    Article  Google Scholar 

  6. Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, and J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett., vol. 90, no. 20, pp. 207901, May 2003.

    Article  Google Scholar 

  7. C. H. Bennett, G. Brassard, C. Crépeau, R. Josza, A. Peres, and W. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett., vol. 70, no. 13, pp. 1895–1899, Mar. 1993.

    Article  MATH  MathSciNet  Google Scholar 

  8. H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett., vol. 81, no. 26, pp. 5932–5935, Dec. 1998.

    Article  Google Scholar 

  9. S. Lloyd, J. H. Shapiro, F. N. C. Wong, P. Kumar, S. M. Shahriar, and H. P. Yuen, “Infrastructure for the quantum Internet,” ACM SIGCOMM Comput. Commun. Rev., vol. 34, no. 5, pp. 9–20, Oct. 2004.

    Article  Google Scholar 

  10. C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. IEEE Int. Conf. Computers, Systems, and Signal Processing, Bangalore, India, 1984, pp. 175–179.

    Google Scholar 

  11. D. Dodson, M. Fujiwara, P. Grangier, M. Hayashi, K. Imafuku, K. Kitayama, P. Kumar, C. Kurtsiefer, G. Lenhart, N. Luetkenhaus, et al. (2009). Updating Quantum Cryptography Report ver. 1. [Online]. Available: http://arxiv.org/abs/0905.4325.

    Google Scholar 

  12. H.-K. Lo and Y. Zhao, “Quantum cryptography,” in Encyclopedia of Complexity and System Science. New York: Springer, 2009, vol. 8, pp. 7265–7289.

    Chapter  Google Scholar 

  13. C. Elliott, D. Pearson, and G. Troxel, “Quantum cryptography in practice,” in Proc. Conf. Applications, Technologies, Architectures, and Protocols for Computer Communications (SIGCOMM). New York: ACM, 2003, pp. 227–238.

    Google Scholar 

  14. A. Mink, S. Frankel, and R. Perlner, “Quantum key distribution (QKD) and commodity security protocols: Introduction and integration,” Int. J. Netw. Secur. Appl., vol. 1, no. 2, pp. 101–112, Jul. 2009.

    Google Scholar 

  15. S. Nagayama and R. Van Meter, “IKE for IPsec with QKD,” Internet Draft, draft-nagayama-ipsecme-ipsec-with-qkd-00; Oct. 2009, expired Apr. 22, 2010.

    Google Scholar 

  16. M Peev, C. Pacher, R. Alléaume, C. Barreiro, J. Bouda, W. Boxleitner, T. Debuisschert, E. Diamanti, M. Dianati, J. F. Dynes, et al. “The SECOQC quantum key distribution network in Vienna,” New J. Phys., vol. 11, no. 7, pp. 075001, Jul. 2009.

    Article  Google Scholar 

  17. T.-Y. Chen, J. Wang, H. Liang, W.-Y. Liu, Y. Liu, X. Jiang, Y. Wang, X. Wan, W.-Q. Cai, L. Ju, et al. “Metropolitan all-pass and inter-city quantum communication network,” Opt Express, vol. 18, no. 26, pp. 27217–27225, Dec. 2010.

    Article  Google Scholar 

  18. R. Alléaume, F. Roueff, E. Diamanti, and N. Lütkenhaus, “Topological optimization of quantum key distribution networks,” New J. Phys., vol. 11, no. 7, pp. 075002, Jul. 2009.

    Article  Google Scholar 

  19. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett., vol. 67, no. 6, pp. 661–663, Aug. 1991.

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Ben-Or and A. Hassidim, “Fast quantum Byzantine agreement,” in Proc. 37th Annu. ACM Symp. Theory Computing. New York: ACM, 2005, pp. 481–485.

    Google Scholar 

  21. H. Buhrman and H. Röhrig, “Distributed quantum computing,” in Mathematical Foundations of Computer Science 2003, B. Rovan, P. Vojtáš, Eds. Berlin: Springer, 2003, pp. 1–20.

    Chapter  Google Scholar 

  22. E. D’Hondt, “Distributed quantum computation: A measurement-based approach,” Ph.D. thesis, Vrije Universiteit Brussel, Belgium, 2005.

    Google Scholar 

  23. S. Tani, H. Kobayashi, and K. Matsumoto, “Exact quantum algorithms for the leader election problem,” in Proc. 22nd Annu. Symp. Theoretical Aspects Computer Science (STACS). Berlin: Springer, 2005, pp. 581–592.

    Google Scholar 

  24. W. Dür and H. J. Briegel, “Entanglement purification and quantum error correction,” Rep. Prog. Phys., vol. 70, no. 8, pp. 1381–1424, Aug. 2007.

    Article  Google Scholar 

  25. 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., vol. 104, no. 18, pp. 180503, May 2010.

    Article  Google Scholar 

  26. L. Jiang, J. M. Taylor, K. Nemoto, W. J. Munro, R. Van Meter, and M. D. Lukin, “Quantum repeater with encoding,” Phys. Rev. A, vol. 79, no. 3, pp. 032325, Mar. 2009.

    Article  Google Scholar 

  27. W. J. Munro, K. A. Harrison, A. M. Stephens, S. J. Devitt, and K. Nemoto, “From quantum multiplexing to high-performance quantum networking,” Nat. Photonics, vol. 4, no. 11, pp. 792–796, Nov. 2010.

    Article  Google Scholar 

  28. S. Bratzik, S. Abruzzo, H. Kampermann, and D. Bruß, “Quantum repeaters and quantum key distribution: The impact of entanglement distillation on the secret key rate,” Phys. Rev. A, vol. 87, no. 6, pp. 062335, Jun. 2013.

    Article  Google Scholar 

  29. A. Basu and J. Riecke, “Stability issues in OSPF routing,” ACM SIGCOMM Comput. Commun. Rev., vol. 31, no. 4, pp. 225–236, Oct. 2001.

    Article  Google Scholar 

  30. R. Govindan and P. Radoslavov, “An analysis of the internal structure of large autonomous systems,” Technical Report 02-777, University of Southern California, USA, 2002.

    Google Scholar 

  31. J. Moy, “RFC 2178: OSPF version 2,” IETF, Jul. 1997.

    Google Scholar 

  32. C. Di Franco and D. Ballester, “Optimal path for a quantum teleportation protocol in entangled networks,” Phys. Rev. A, vol. 85, no. 1, pp. 010303, Jan. 2012.

    Article  Google Scholar 

  33. W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,” Nature, vol. 299, no. 5886, p. 802, Oct. 1982.

    Article  Google Scholar 

  34. A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, “Highfidelity transmission of entanglement over a high-loss free-space channel,” Nat. Phys., vol. 5, no. 6, pp. 389–392, Jun. 2009.

    Article  Google Scholar 

  35. T. Scheidl, R. Ursin, A. Fedrizzi, S. Ramelow, X. S. Ma, T. Herbst, R. Prevedel, L. Ratschbacher, J. Kofler, T. Jennewein, and A. Zeilinger, “Feasibility of 300 km quantum key distribution with entangled states,” New J. Phys., vol. 11, no. 8, pp. 085002, Aug. 2009.

    Article  Google Scholar 

  36. P. Villoresi, T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, “Experimental verification of the feasibility of a quantum channel between Space and Earth,” New J. Phys., vol. 10, no. 3, pp. 033038, Mar. 2008.

    Article  Google Scholar 

  37. R. Van Meter, T. D. Ladd, W. J. Munro, and K. Nemoto, “System design for a long-line quantum repeater,” IEEE/ACM Trans. Netw., vol. 17, no. 3, pp. 1002–1013, Jun. 2009.

    Article  Google Scholar 

  38. J. D. Touch, Y. S. Wang, and V. Pingali, “A recursive network architecture,” ISI Technical Report ISI-TR-2006-626, Information Sciences Institute, The University of Southern California, USA, 2006.

    Google Scholar 

  39. D. Copsey, M. Oskin, T. Metodiev, F. T. Chong, I. Chuang, and J. Kubiatowicz, “The effect of communication costs in solid-state quantum computing architectures,” in Proc. 15th Annu. ACM Symp. Parallel Algorithms and Architectures. New York: ACM, 2003, pp. 65–74.

    Google Scholar 

  40. N. Isailovic, Y. Patel, M. Whitney, and J. Kubiatowicz, “Interconnection networks for scalable quantum computers,” in Proc. 33rd Annu. Int. Symp. Computer Architecture. Washington DC: IEEE, 2006, pp. 366–377.

    Google Scholar 

  41. T. S. Metodi, D. D. Thaker, A. W. Cross, I. L. Chuang, and F. T. Chong, “High-level interconnect model for the quantum logic array architecture,” ACM J. Emerg. Technol. Comput. Syst., vol. 4, no. 1, pp. 1–28, Mar. 2008.

    Article  Google Scholar 

  42. M. Oskin, F. T. Chong, I. L. Chuang, and J. Kubiatowicz, “Building quantum wires: The long and short of it,” in Proc. 30th Annu. Int. Symp. Computer Architecture. New York: ACM, 2003, pp. 374–387.

    Google Scholar 

  43. R. Van Meter, T. D. Ladd, A. G. Fowler, and Y. Yamamoto, “Distributed quantum computation architecture using semicon ductor nanophotonics,” Int. J. Quantum Inf., vol. 8, nos. 1–2, pp. 295–323, Feb.&Mar. 2010.

    Article  Google Scholar 

  44. A. Medina, N. Taft, K. Salamatian, S. Bhattacharyya, and C. Diot, “Traffic matrix estimation: Existing techniques and new directions,” ACM SIGCOMM Comput. Commun. Rev., vol. 32, no. 4, pp. 161–174, Oct. 2002.

    Article  Google Scholar 

  45. T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interaction between matter qubits and bright coherent light,” New J. Phys., vol. 8, no. 9, pp. 184, Sept. 2006.

    Article  Google Scholar 

  46. P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett., vol. 96, no. 24, pp. 240501, Jun. 2006.

    Article  Google Scholar 

  47. L. Childress, J. M. Taylor, A. S. Sørensen, and M. D. Lukin, “Faulttolerant quantum communication based on solid-state photon emitters,” Phys. Rev. Lett., vol. 96, no. 7, pp. 070504, Feb. 2006.

    Article  Google Scholar 

  48. W. J. Munro, R. Van Meter, S. G. R. Louis, and K. Nemoto, “High-bandwidth hybrid quantum repeater,” Phys. Rev. Lett., vol. 101, no. 4, pp. 040502, Jul. 2008.

    Article  Google Scholar 

  49. J. Dehaene, M. Van den Nest, B. DeMoor, and F. Verstraete, “Local permutations of products of Bell states and entanglement distillation,” Phys. Rev. A, vol. 67, no. 2, pp. 022310, Feb. 2003.

    Article  Google Scholar 

  50. L. Jiang, J. M. Taylor, and M. D. Lukin, “Fast and robust approach to long-distance quantum communication with atomic ensembles,” Phys. Rev. A, vol. 76, no. 1, pp. 012301, Jul. 2007.

    Article  Google Scholar 

  51. L. Hartmann, B. Kraus, H.-J. Briegel, and W. Dür, “On the role of memory errors in quantum repeaters,” Phys. Rev. A, vol. 75, no. 3, pp. 032310, Mar. 2007.

    Article  Google Scholar 

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Correspondence to Rodney Van Meter.

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Van Meter, R., Satoh, T., Ladd, T.D. et al. Path selection for quantum repeater networks. Netw.Sci. 3, 82–95 (2013). https://doi.org/10.1007/s13119-013-0026-2

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  • DOI: https://doi.org/10.1007/s13119-013-0026-2

Keywords

  • quantum communication
  • quantum repeater
  • Dijkstra
  • path selection