Advertisement

Enhancing distributed functional monitoring with quantum protocols

  • Michele AmorettiEmail author
  • Mattia Pizzoni
  • Stefano Carretta
Article

Abstract

In distributed functional monitoring (DFM), N players located at different sites; each observes a stream of items and communicates with one coordinator, whose goal is to compute a function of the union of the streams. In threshold monitoring, a special case of DFM, the coordinator wants to know whether \(f(v(t)) > T\), where v(t) is a binary vector that represents the state of the stream as an average of local states at the sites. In this paper, we enhance the classical geometric monitoring (GM) method with quantum communication and entanglement. The proposed quantum geometric monitoring (QGM) protocol can be further specialized by defining specific network topologies. In QGM-Flat, the coordinator is connected to all N players. When N becomes too large, the performance of QGM-Flat deteriorates. For a scalable implementation, we propose to organize the players in a tree structure, with the QGM-Tree protocol. We have implemented both QGM-Flat and QGM-Tree with SimulaQron, a novel Python library for the development and simulation of quantum networking applications. We analyze the proposed quantum protocols, showing that they outperform their classical counterparts in terms of reduced communication cost, while showing the same accuracy.

Keywords

Distributed functional monitoring Quantum networks Quantum protocols 

Notes

Acknowledgements

We would like to thank Axel Dahlberg and Stephanie Wehner for their support during our software development and debugging activities, and for adding features to SimulaQron that allowed us to implement fully working QGM protocols.

References

  1. 1.
    Afzelius, M., Simon, C., de Riedmatten, H., Gisin, N.: Multimode quantum memory based on atomic frequency combs. Phys. Rev. A 79, 052329 (2009).  https://doi.org/10.1103/PhysRevA.79.052329 ADSCrossRefGoogle Scholar
  2. 2.
    Amoretti, M.: Entanglement evaluation protocols, Python code. https://github.com/qis-unipr/entanglement-verification. Accessed 25 Jun 2019
  3. 3.
    Amoretti, M., Pizzoni, M.: QGM source code. https://github.com/qis-unipr/qgm (2019)
  4. 4.
    Babcock, B., Olston, C.: Distributed top-k monitoring. In: Proceedings of the 2003 ACM SIGMOD International Conference on Management of Data, SIGMOD ’03, pp. 28–39. ACM (2003)Google Scholar
  5. 5.
    Bahera, B., Seth, S., Das, A., Panigrahi, P.K.: Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer. Quantum Inf. Process. 18, 108 (2019)ADSCrossRefGoogle Scholar
  6. 6.
    Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., William, K.: Purification of noisy entanglement, and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)ADSCrossRefGoogle Scholar
  7. 7.
    Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on einstein-podolsky-rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Bussieres, F., Sangouard, N., Afzelius, M., de Riedmatten, H., Simon, C., Tittel, W.: Prospective applications of optical quantum memories. J. Mod. Opt. 60(18), 1519–1537 (2013)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Caleffi, M., Cacciapuoti, A.S., Bianchi, G.: Quantum internet: From communication to distributed computing! In: Proceedings of the 5th ACM International Conference on Nanoscale Computing and Communication, NANOCOM ’18, pp. 3:1–3:4. ACM, New York, NY, USA (2018).  https://doi.org/10.1145/3233188.3233224
  10. 10.
    Cormode, G.: The continuous distributed monitoring model. SIGMOD Rec. 42(1), 5–14 (2013)CrossRefGoogle Scholar
  11. 11.
    Cormode, G., Garofalakis, M.: Join sizes, frequency moments, and applications. In: Garofalakis, M., Gehrke, J., Rastogi, R. (eds.) Data Stream Management, pp. 87–102. Springer, Berlin (2016) CrossRefGoogle Scholar
  12. 12.
    Cormode, G., Muthukrishnan, S., Yi, K.: Algorithms for distributed functional monitoring. ACM Trans. Algorithms 7(2), 21 (2011) MathSciNetCrossRefGoogle Scholar
  13. 13.
    Dahlberg, A., Wehner, S.: Simulaqron—A simulator for developing quantum internet software. Quantum Sci. Technol. 4, 015001 (2019)ADSCrossRefGoogle Scholar
  14. 14.
    van Dam, S.B., Humphreys, P.C., Rozpedek, F., Wehner, S., Hanson, R.: Multiplexed entanglement generation over quantum networks using multi-qubit nodes. Quantum Sci. Technol. 2(3), 034002 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    Dilman, M., Raz, D.: Efficient reactive monitoring. In: Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213), vol. 2, pp. 1012–1019 (2001)Google Scholar
  16. 16.
    Fiorentino, M., Voss, P.L., Sharping, J.E., Kumar, P.: All-fiber photon-pair source for quantum communications. IEEE Photonics Technol. Lett. 14(7), 983–985 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    Giatrakos, N., Deligiannakis, A., Garofalakis, M.: Scalable approximate query tracking over highly distributed data streams. In: ACM SIGMOD ’16. ACM (2016)Google Scholar
  18. 18.
    Greve, K.D., Yu, L., McMahon, P.L., Pelc, J.S., Natarajan, C.M., Kim, N.Y., Abe, E., Maier, S., Schneider, C., Kamp, M., Höfling, S., Hadfield, R.H., Forchel, A., Fejer, M.M., Yamamoto, Y.: Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength. Nature 491, 421–425 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    Gundogan, M., Ledingham, P.M., Kutluer, K., Mazzera, M., de Riedmatten, H.: Solid state spin-wave quantum memory for time-bin qubits. Phys. Rev. Lett. 114, 230501 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    Hammerer, K., Sørensen, A.S., Polzik, E.S.: Quantum interface between light and atomic ensembles. Rev. Mod. Phys. 82, 1041–1093 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum communication channel. Probl. Inform. Transm. 9(3), 177–183 (1973)Google Scholar
  22. 22.
    Huang, L., Nguyen, X., Garofalakis, M., Hellerstein, J.M., Jordan, M.I., Joseph, A.D., Taft, N.: Communication-efficient online detection of network-wide anomalies. In: IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications, pp. 134–142 (2007)Google Scholar
  23. 23.
    Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)CrossRefGoogle Scholar
  24. 24.
    Humphreys, P.: Deterministic delivery of remote entanglement on a quantum network. Nature 558, (2018) Google Scholar
  25. 25.
    Hushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)Google Scholar
  26. 26.
    Jobez, P., Usmani, I., Timoney, N., Laplane, C., Gisin, N., Afzelius, M.: Cavity-enhanced storage in an optical spin-wave memory. New J. Phys. 16(8), 083005 (2014)ADSCrossRefGoogle Scholar
  27. 27.
    Keralapura, R., Cormode, G., Ramamirtham, J.: Communication-efficient distributed monitoring of thresholded counts. In: Proceedings of the 2006 ACM SIGMOD International Conference on Management of Data, SIGMOD ’06, pp. 289–300. ACM (2006)Google Scholar
  28. 28.
    Kompella, K., Aelmans, M., Wehner, S., Sirbu, C.: Advertising entanglement capabilities in quantum networks. Internet-Draft draft-kaws-qirg-advent-00, IETF Secretariat (2018). http://www.ietf.org/internet-drafts/draft-kaws-qirg-advent-00.txt
  29. 29.
    Krastanov, S., Albert, V.V., Jiang, L.: Optimized entanglement purification. Quantum J. 3, 123–141 (2019)CrossRefGoogle Scholar
  30. 30.
    Kurtsiefer, C., Oberparleiter, M., Weinfurter, H.: Generation of correlated photon pairs in type-ii parametric down conversion-revisited. J. Mod. Opt. 48(13), 1997–2007 (2001)ADSGoogle Scholar
  31. 31.
    Li, M., Liu, Y.: Underground coal mine monitoring with wireless sensor networks. ACM Trans. Sen. Netw. 5(2), 10:1–10:29 (2009)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Montanaro, A.: The quantum complexity of approximating the frequency moments. Quantum Inf. Comput. 16, 13–14 (2016)MathSciNetGoogle Scholar
  33. 33.
    Nagy, M., Akl, S.G.: Entanglement verification with application to key distribution protocols. Par. Proc. Lett. 20(3), 227–237 (2010)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Pan, J.W., Simon, C., Brukner, C., Zeilinger, A.: Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001)ADSCrossRefGoogle Scholar
  35. 35.
    Panigrahi, P.K., Gupta, M., Pathak, A., Srikanth, R.: Circuits for distributing quantum measurement. In: AIP Conference Proceedings, vol. 864 (2006)Google Scholar
  36. 36.
    Rozpedek, F., Schiet, T., Thinh, L., Elkouss, D., Doherty, A., Wehner, S.: Optimizing practical entanglement distillation. Phys. Rev. A 97, 062333 (2018)ADSCrossRefGoogle Scholar
  37. 37.
    Sharfman, I., Schuster, A., Keren, D.: A geometric approach to monitoring threshold functions over distributed data streams. In: ACM SIGMOD ’06. ACM (2006)Google Scholar
  38. 38.
    Steiger, D., Häner, T., Troyer, M.: Projectq: an open source software framework for quantum computing. Quantum 2(49), 10 (2018) Google Scholar
  39. 39.
    van Enk, S.J., Lütkenhaus, N., Kimble, H.J.: Experimental procedures for entanglement verification. Phys. Rev. A 75(5), 052318 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    Van Meter, Rodney: Quantum Networking. Wiley, London (2014)CrossRefGoogle Scholar
  41. 41.
    Wehner, S., Elkouss, D., Hanson, R.: Quantum internet: A vision for the road ahead. Science 362(6412), 1–9 (2018).  https://doi.org/10.1126/science.aam9288 MathSciNetCrossRefGoogle Scholar
  42. 42.
    Zhong, M., Hedges, M., Ahlefeldt, R., Bartholomew, J., Beavan, S., Wittig, S., Longdell, J., Sellars, M.: Optically addressable nuclear spins in a solid with a six-hour coherence time. Nature 517(8), 177–180 (2015)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Engineering and ArchitectureUniversity of ParmaParmaItaly
  2. 2.Quantum Information Science @ University of ParmaParmaItaly
  3. 3.Department of Mathematical, Physical and Computer SciencesUniversity of ParmaParmaItaly

Personalised recommendations