Quantum network communication: a discrete-time quantum-walk approach

Science China Information Sciences volume 61, Article number: 042501 (2018) Cite this article

Abstract

We study the problem of quantum multi-unicast communication over the butterfly network in a quantum-walk architecture, where multiple arbitrary single-qubit states are transmitted simultaneously between multiple source-sink pairs. Here, by introducing quantum walks, we demonstrate a quantum multi-unicast communication scheme over the butterfly network and the inverted crown network, respectively, where the arbitrary single-qubit states can be efficiently transferred with both the probability and the state fidelity one. The presented result concerns only the butterfly network and the inverted crown network, but our techniques can be applied to a more general graph. It paves a way to combine quantum computation and quantum network communication.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

References

  1. 1

    Zhou Z L, Wu Q J, Huang F, et al. Fast and accurate near-duplicate image elimination for visual sensor networks. Int J Distrib Sens N, doi: 10.1177/1550147717694172

  2. 2

    Zhang Y H, Sun X M, Wang B W. Efficient algorithm for K-Barrier coverage based on integer linear programming. China Commun, 2016, 13: 16–23

    Article  Google Scholar 

  3. 3

    Pan Z Q, Lei J J, Zhang Y, et al. Fast motion estimation based on content property for low-complexity H. HEVC encoder. IEEE Trans Broadcast, 2016, 62: 675–684

    Article  Google Scholar 

  4. 4

    Pan Z Q, Jin P, Lei J J, et al. Fast reference frame selection based on content similarity for low complexity HEVC encoder. J Vis Commun Image R, 2016, 40: 516–524

    Article  Google Scholar 

  5. 5

    Zhang J, Tang J, Wang T B, et al. Energy-efficient data-gathering rendezvous algorithms with mobile sinks for wireless sensor networks. Int J Sens Netw, 2017, 23: 248–257

    Article  Google Scholar 

  6. 6

    Ahlswede R, Cai N, Li S-Y R, et al. Network information flow. IEEE Trans Inf Theory, 2000, 46: 1204–1216

    MathSciNet  Article  MATH  Google Scholar 

  7. 7

    Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802–803

    Article  MATH  Google Scholar 

  8. 8

    Hayashi M, Iwama K, Nishimura H, et al. Quantum network coding. In: Proceedings of Annual Symposium on Theoretical Aspects of Computer Science. Berlin: Springer, 2007. 4393: 610–621

    Google Scholar 

  9. 9

    Hayashi M. Prior entanglement between senders enables perfect quantum network coding with modification. Phys Rev A, 2007, 76: 040301

    MathSciNet  Article  Google Scholar 

  10. 10

    Satoh T, Le Gall F, Imai H. Quantum network coding for quantum repeaters. Phys Rev A, 2012, 86: 032331

    Article  Google Scholar 

  11. 11

    Soeda A, Kinjo Y, Turner P S, et al. Quantum computation over the butterfly network. Phys Rev A, 2011, 84: 012333

    Article  Google Scholar 

  12. 12

    Li J, Chen X B, Xu G, et al. Perfect quantum network coding independent of classical network solutions. IEEE Commun Lett, 2015, 19: 115–118

    Article  Google Scholar 

  13. 13

    Li J, Chen X B, Sun X M, et al. Quantum network coding for multi-unicast problem based on 2D and 3D cluster states. Sci China Inf Sci, 2016, 59: 042301

    Article  Google Scholar 

  14. 14

    Mahdian M, Bayramzadeh R. Perfect K-pair quantum network coding using superconducting qubits. J Supercond Nov Magn, 2015, 28: 345–348

    Article  Google Scholar 

  15. 15

    Shang T, Li J, Pei Z, et al. Quantum network coding for general repeater networks. Quantum Inf Process, 2015, 14: 3533–3552

    MathSciNet  Article  MATH  Google Scholar 

  16. 16

    Xu G, Chen X-B, Li J, et al. Network coding for quantum cooperative multicast. Quantum Inf Process, 2015, 14: 4297–4322

    MathSciNet  Article  MATH  Google Scholar 

  17. 17

    Shang T, Du G, Liu J-W. Opportunistic quantum network coding based on quantum teleportation. Quantum Inf Process, 2016, 15: 1743–1763

    MathSciNet  Article  MATH  Google Scholar 

  18. 18

    Kobayashi H, Le Gall F, Nishimura H, et al. Perfect quantum network communication protocol based on classical network coding. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Austin, 2010. 2686–2690

    Google Scholar 

  19. 19

    Kobayashi H, Le Gall F, Nishimura H, et al. Constructing quantum network coding schemes from classical nonlinear protocols. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), St. Petersburg, 2011. 109–113

    Google Scholar 

  20. 20

    Jain A, Franceschetti M, Meyer D A. On quantum network coding. J Math Phys, 2011, 52: 032201

    MathSciNet  Article  MATH  Google Scholar 

  21. 21

    Wang X-L, Chen L-K, Li W, et al. Experimental ten-photon entanglement. Phys Rev Lett, 2016, 117: 210502

    Article  Google Scholar 

  22. 22

    Leung D, Oppenheim J, Winter A. Quantum network communication: the butterfly and beyond. IEEE Trans Inf Theory, 2010, 56: 3478–3490

    MathSciNet  Article  MATH  Google Scholar 

  23. 23

    Aharonov D, Ambainis A, Kempe J, et al. Quantum walks on graphs. In: Proceedings of the 33rd ACM Symposium on Theory of Computing, Hersonissos, 2001. 50–59

    Google Scholar 

  24. 24

    Ambainis A. Quantum walk algorithm for element distinctness. SIAM J Comput, 2007, 37: 210–239

    MathSciNet  Article  MATH  Google Scholar 

  25. 25

    Magniez F, Santha M, Szegedy M. Quantum algorithms for the triangle problem. SIAM J Comput, 2007, 37: 413–424

    MathSciNet  Article  MATH  Google Scholar 

  26. 26

    Tamascelli D, Zanetti L. A quantum-walk-inspired adiabatic algorithm for solving graph isomorphism problems. J Phys A-Math Theor, 2014, 47: 325302

    MathSciNet  Article  MATH  Google Scholar 

  27. 27

    Childs A M, Ge Y M. Spatial search by continuous-time quantum walks on crystal lattices. Phys Rev A, 2014, 89: 052337

    Article  Google Scholar 

  28. 28

    Babatunde A M, Cresser J, Twamley J. Using a biased quantum random walk as a quantum lumped element router. Phys Rev A, 2014, 90: 012339

    Article  Google Scholar 

  29. 29

    Zhan X, Qin H, Bian Z-H, et al. Perfect state transfer and efficient quantum routing: a discrete-time quantum-walk approach. Phys Rev A, 2014, 90: 012331

    Article  Google Scholar 

  30. 30

    Yalçınkaya İ, Gedik Z. Qubit state transfer via discrete-time quantum walks. J Phys A-Math Theor, 2015, 48: 225302

    MathSciNet  Article  MATH  Google Scholar 

  31. 31

    Travaglione B C, Milburn G J. Implementing the quantum random walk. Phys Rev A, 2002, 65: 032310

    Article  Google Scholar 

  32. 32

    Tregenna B, Flanagan W, Maile R, et al. Controlling discrete quantum walks: coins and initial states. New J Phys, 2003, 5: 83

    Article  Google Scholar 

  33. 33

    Soeda A, Kinjo Y, Turner P S, et al. Quantum computation over the butterfly network. 2011. arXiv: 1010.4350v3

    Google Scholar 

  34. 34

    Rohde P P, Schreiber A, Stefanak M, et al. Increasing the dimensionality of quantum walks using multiple walkers. J Comput Theor Nano, 2013, 10: 1644–1652

    Article  Google Scholar 

  35. 35

    Raussendorf R, Browne D E, Briegel H J. Measurement-based quantum computation on cluster states. Phys Rev A, 2003, 68: 022312

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61572053, 61671087, U1636106, 61602019, 61472048, 61402148), Beijing Natural Science Foundation (Grant No. 4162005), and Natural Science Foundation of Hebei Province (Grant No. F2015205114).

Author information

Affiliations

  1. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Yuguang Yang, Jiajie Yang, Yihua Zhou & Weimin Shi

  2. State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences), Beijing, 100093, China

    Yuguang Yang

  3. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiubo Chen

  4. School of Computer, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Jian Li

  5. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, China

    Huijuan Zuo

Authors
  1. Yuguang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiajie Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yihua Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weimin Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiubo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Huijuan Zuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuguang Yang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Yang, J., Zhou, Y. et al. Quantum network communication: a discrete-time quantum-walk approach. Sci. China Inf. Sci. 61, 042501 (2018). https://doi.org/10.1007/s11432-017-9190-0

Download citation

Keywords

  • network coding
  • quantum network coding
  • quantum walk
  • state fidelity
  • butterfly network
  • inverted crown network