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Optimizing Teleportation Cost in Distributed Quantum Circuits

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Abstract

The presented work provides a procedure for optimizing the communication cost of a distributed quantum circuit (DQC) in terms of the number of qubit teleportations. Because of technology limitations which do not allow large quantum computers to work as a single processing element, distributed quantum computation is an appropriate solution to overcome this difficulty. Previous studies have applied ad-hoc solutions to distribute a quantum system for special cases and applications. In this study, a general approach is proposed to optimize the number of teleportations for a DQC consisting of two spatially separated and long-distance quantum subsystems. To this end, different configurations of locations for executing gates whose qubits are in distinct subsystems are considered and for each of these configurations, the proposed algorithm is run to find the minimum number of required teleportations. Finally, the configuration which leads to the minimum number of teleportations is reported. The proposed method can be used as an automated procedure to find the configuration with the optimal communication cost for the DQC. This cost can be used as a basic measure of the communication cost for future works in the distributed quantum circuits.

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References

  1. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information, 10th anniversary edition. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  2. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: ACM symposium on theory of computing, pp 212–219 (1996)

  3. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Steffen, L., Fedorov, A., Oppliger, M., Salathe, Y., Kurpiers, P., et al.: Realization of deterministic quantum teleportation with solid state qubits. arXiv:1302.5621 (2013)

  5. Koashi, M., Fujii, K., Yamamoto, T., Imoto, N.: A distributed architecture for scalable quantum computation with realistically noisy devices. arXiv:1202.6588 (2012)

  6. Ying, M., Feng, Y.: An algebraic language for distributed quantum computing. IEEE Trans. Comput. 58, 728–743 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Van Meter, R., Ladd, T.D., Fowler, A.G., Yamamoto, Y.: Distributed quantum computation architecture using semiconductor nanophotonics. International Journal of Quantum Information 8(01n02), 295–323 (2010)

    Article  Google Scholar 

  8. Krojanski, H.G., Suter, D.: Scaling of decoherence in wide nmr quantum registers. Phys. Rev. Lett. 93(25), 090501 (2004)

    Article  ADS  Google Scholar 

  9. Nickerson, N.H., Li, Y., Benjamin, S.C.: Topological quantum computing with a very noisy network and local error rates approaching one percent. Nature Nat. Commun. 4, 1756 (2013)

    Article  ADS  Google Scholar 

  10. Brassard, G., Lütkenhaus, N., Mor, T., Sanders, B.C.: Limitations on practical quantum cryptography. Phys. Rev. Lett. 85, 1330 (2000)

    Article  ADS  MATH  Google Scholar 

  11. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Whitney, M., Isailovic, N., Patel, Y., Kubiatowicz, J.: Automated generation of layout and control for quantum circuits. Phys. Rev. Lett. 85(26), 1330 (2000)

    Google Scholar 

  13. Pan, J.-W., Bouwmeester, D., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)

    Article  ADS  MATH  Google Scholar 

  14. Nielsen, E., Knill, M.A., Laflamme, R.: Complete quantum teleportation using nuclear magnetic resonance. Nature 396, 52–55 (1998)

    Article  ADS  Google Scholar 

  15. Riebe, M., Häffner, H., Roos, C., Hänsel, W., Benhelm, J., et al.: Deterministic quantum teleportation with atoms. Nature 429, 734–737 (2004)

    Article  ADS  Google Scholar 

  16. Van Meter, R., Munro, W., Nemoto, K., Itoh, K.M.: Arithmetic on a distributed-memory quantum multicomputer. ACM Journal on Emerging Technologies in Computing Systems (JETC) 3, 2 (2008)

    Google Scholar 

  17. Van Meter, R.D. III: Architecture of a quantum multicomputer optimized for shor’s factoring algorithm. arXiv:quant-ph/0607065

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

    Article  ADS  MATH  Google Scholar 

  19. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76(5), 722 (1996)

    Article  ADS  Google Scholar 

  20. Pramanik, T., Majumdar, A.S.: Improving the fidelity of teleportation through noisy channels using weak measurement. Phys. Lett. A 377(44), 3209–3215 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Grover, L.K.: Quantum telecomputation. arXiv:quant-ph/9704012 (1997)

  22. Cleve, R., Buhrman, H.: Substituting quantum entanglement for communication. Phys. Rev. A 56, 1201 (1997)

    Article  ADS  Google Scholar 

  23. Cirac, J., Ekert, A., Huelga, S., Macchiavello, C.: Distributed quantum computation over noisy channels. Phys. Rev. A 59, 4249 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  24. Beals, R., Brierley, S., Gray, O., Harrow, A.W., Kutin, S., Linden, N., Shepherd, D., Stather, M.: Efficient distributed quantum computing. In: Proceedings of the Royal Society A. The Royal Society, vol. 469, p. 20120686 (2013)

  25. Yepez, J.: Type-II quantum computers. Int. J. Mod. Phys. C 12(09), 1273–1284 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  26. Kampermann, H., Streltsov, A., Brub, D.: Quantum cost for sending entanglement. Phys. Rev. Lett. 108, 250501 (2012)

    Article  Google Scholar 

  27. Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62(1), 012313 (2000)

    Article  ADS  Google Scholar 

  28. Yimsiriwattana, A., Lomonaco, S.J. Jr.: Distributed quantum computing: a distributed shor algorithm. arXiv:quant-ph/0403146 (2004)

  29. Deutsch, D.: Quantum computational networks. arXiv:quant-ph/0607065 (2006)

  30. Van Meter, R., Devitt, S.J.: The path to scalable distributed quantum computing. Computer 49(9), 31–42 (2016)

    Article  Google Scholar 

  31. Van Meter, R.: Distributed quantum computing systems: Technology to quantum circuits. In: 2017 symposium on VLSI circuits, pp. T184–T185. IEEE, Piscataway (2017)

  32. Pham, P., Svore, K.: A 2d nearest-neighbor quantum architecture for factoring in polylogarithmic depth. Quantum Inf. Comput. 13(11-12), 937–962 (2013)

    MathSciNet  Google Scholar 

  33. Houshmand, M., Hosseini-Khayat, S., Wilde, M.M.: Minimal-memory requirements for pearl-necklace encoders of quantum convolutional codes. IEEE Trans. Comput. 61(3), 299–312 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  34. Houshmand, M., Saheb Zamani, M., Sedighi, M., Arabzadeh, M.: Decomposition of diagonal Hermitian quantum gates using multiple-controlled pauli Z gates. ACM J. Emerg. Technol. Comput. Syst. 11(3), 28 (2014)

  35. Kernighan, B., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49(2), 291–307 (1970)

    Article  MATH  Google Scholar 

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Acknowledgements

This work has been partially supported by a grant from Ferdowsi University of Mashhad.

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Authors and Affiliations

  1. Department of Computer Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Mariam Zomorodi-Moghadam

  2. Department of Computer Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Mahboobeh Houshmand

  3. Department of Electrical Engineering, Imam Reza International University, Mashhad, Iran

    Monireh Houshmand

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  1. Mariam Zomorodi-Moghadam
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  2. Mahboobeh Houshmand
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  3. Monireh Houshmand
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Correspondence to Mariam Zomorodi-Moghadam.

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Zomorodi-Moghadam, M., Houshmand, M. & Houshmand, M. Optimizing Teleportation Cost in Distributed Quantum Circuits. Int J Theor Phys 57, 848–861 (2018). https://doi.org/10.1007/s10773-017-3618-x

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  • DOI: https://doi.org/10.1007/s10773-017-3618-x

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