Skip to main content

Distributed Quantum Computation Assisted by Remote Toffoli Gate

  • Conference paper
  • First Online:
Cloud Computing and Security (ICCCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10039))

Included in the following conference series:

Abstract

Distributed quantum computation requires quantum operations to act on logical qubits over a distance. We will develop a formal model for the telegate-based distributive quantum computation. We show that a controlled-controlled-NOT (Toffoli) gate as an elementary gate of the universal quantum computation may be remotely implemented by exploring a high-level quantum system. These remote Toffoli gates cost at most two Einstein-Podolsky-Rosen (EPR) pairs, whereas four or six EPR pairs are required from the teleportation-based quantum computation or the remote CNOT gate, respectively. Thus, the previous Toffoli gate-based circuit synthesis may be used as an elementary subroutine of this distributed quantum computation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Feynman, R.: Simulating physics with computers. Int. J. Theoret. Phys. 21(6), 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  2. Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. A 400(1818), 97–117 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  3. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000). pp. 216–271

    MATH  Google Scholar 

  4. Barreiro, J.T., Langford, N.K., Peters, N.A., Kwiat, P.G.: Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005)

    Article  Google Scholar 

  5. Wang, X.L., et al.: Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518(7540), 516–519 (2015)

    Article  Google Scholar 

  6. Luo, M.X., Wang, X.: Parallel photonic quantum computation assisted by quantum dots in one-side optical microcavities. Sci. Rep. 4, 5732 (2014)

    Google Scholar 

  7. Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. A 439(1907), 553–558 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 116–123 (1997)

    Article  MathSciNet  Google Scholar 

  9. Grover, L.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)

    Article  Google Scholar 

  10. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Murphy, B., Brent, R.P.: On quadratic polynomials for the number field sieve. Aust. Comput. Sci. Commun. 20, 199–213 (1998)

    MathSciNet  MATH  Google Scholar 

  12. Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(6), 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  13. Farhi, E., et al.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292(5516), 472–475 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10, 631–633 (2014)

    Article  Google Scholar 

  15. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Berlin (2006). pp. 130–211

    MATH  Google Scholar 

  16. Gu, B., Sheng, V.S., Wang, Z., Ho, D., Osman, S., Li, S.: Incremental learning for v-support vector regression. Neural Netw. 67, 140–150 (2015)

    Article  Google Scholar 

  17. Chen, B., Shu, H., Coatrieux, G., Chen, G., Sun, X., Coatrieux, J.-L.: Color image analysis by quaternion-type moments. J. Math. Imaging Vis. 51(1), 124–144 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  18. Xia, Z., Wang, X., Sun, X., Wang, B.: Steganalysis of least significant bit matching using multi-order differences. Sec. Commun. Netw. 7(8), 1283–1291 (2014)

    Article  Google Scholar 

  19. Regev, O.: Quantum computation and lattice problems. SIAM J. Comput. 33(3), 738–760 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35(1), 170–188 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Barenco, A., et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 34–57 (1995)

    Article  Google Scholar 

  22. Nielsen, M.A., Dowling, M.R., Gu, M., Doherty, A.C.: Quantum computation as geometry. Science 311, 1133–1135 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Radhakrishnan, J., Rotteler, M., Sen, P.: Random measurement bases, quantum state distinction and applications to the hidden subgroup problem. Algorithmica 55, 490–516 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kawachi, A., Koshiba, T., Nishimura, H., Yamakami, T.: Computational indistinguishability between quantum states and its cryptographic application. J. Cryptol. 25, 528–555 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Chuang, I.L., Vandersypen, L.M.K., Zhou, X., Leung, D.W., Lloyd, S.: Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998)

    Article  Google Scholar 

  26. Jones, J.A., Mosca, M., Hansen, R.H.: Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344–346 (1998)

    Article  Google Scholar 

  27. Vandersypen, L.M.K., et al.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)

    Article  Google Scholar 

  28. Lucero, E., et al.: Computing prime factors with a Josephson phase qubit quantum processor. Nat. Phys. 8, 719–723 (2012)

    Article  Google Scholar 

  29. Feng, G., Xu, G., Long, G.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110, 190501 (2013)

    Article  Google Scholar 

  30. Tame, M.S., Bell, B.A., Di Franco, C., Wadsworth, W.J., Rarity, J.G.: Experimental realization of a one-way quantum computer algorithm solving Simon’s problem. Phys. Rev. Lett. 113, 200501 (2014)

    Article  Google Scholar 

  31. Sun, C.P., Li, Y., Liu, X.F.: Quasi-spin-wave quantum memories with a dynamical symmetry. Phys. Rev. Lett. 91, 147903 (2003)

    Article  Google Scholar 

  32. Simon, J., Haruka, T., Ghosh, S., Vuleti, V.: Single-photon bus connecting spin-wave quantum memories. Nat. Phys. 3, 765–769 (2007)

    Article  Google Scholar 

  33. Reim, K.F., et al.: Towards high-speed optical quantum memories. Nat. Photon. 4, 218–221 (2010)

    Article  Google Scholar 

  34. Diniz, I., et al.: Strongly coupling a cavity to inhomogeneous ensembles of emitters: potential for long-lived solid-state quantum memories. Phys. Rev. A 84, 063810 (2011)

    Article  Google Scholar 

  35. George, C., Dollimore, J., Kindberg, T., Blair, G.: Distributed Systems: Concepts and Design. Addison-Wesley, Reading (2011). pp. 230–312

    MATH  Google Scholar 

  36. Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)

    Article  Google Scholar 

  37. Cirac, J.I., Ekert, A., Huelga, S.F., Macchiavello, C.: Distributed quantum computation over noisy channels. Phys. Rev. A 59, 42–49 (1999)

    Article  MathSciNet  Google Scholar 

  38. Meter, R.V., Munro, W.J., Nemoto, K., Itoh, K.M.: Arithmetic on a distributed-memory quantum multicomputer. ACM J. Emerg. Tech. Comput. Syst. 3, 1–23 (2008)

    Article  Google Scholar 

  39. Spiller, T.P., et al.: Quantum computation by communication. New J. Phys. 8, 30 (2006)

    Article  Google Scholar 

  40. Danos, V., D’Hondt, E., Kashefi, E., Panangaden, P.: Distributed measurement-based quantum computation. Elect. Notes Theoret. Comput. Sci. 170, 73–94 (2007)

    Article  MATH  Google Scholar 

  41. Love, P.J., Boghosian, B.M.: Type II quantum algorithms. Phys. A 362(1), 210–214 (2006)

    Article  Google Scholar 

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

  43. Huang, Y.F., Ren, X.F., Zhang, Y.S., Duan, L.M., Guo, G.C.: Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Lett. 93, 240501 (2004)

    Article  Google Scholar 

  44. Meter, R.V., Nemoto, K., Munro, W.: Communication links for distributed quantum computation. IEEE Trans. Comput. 56(12), 1643–1653 (2007)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  46. Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Optically controlled phase gate and teleportation of a controlled-NOT gate for spin qubits in quantum dot-microcavity coupled system. Phys. Rev. A 87, 062337 (2013)

    Article  Google Scholar 

  47. Luo, M.X., Li, H.R., Wang, X.: Teleportation of a controlled-Not gate for photon and electron-spin qubits assisted by the nitrogen-vacancy center. Quantum Inf. Comput. 15(15), 1397–1419 (2015)

    MathSciNet  Google Scholar 

  48. Luo, M.X., Wang, X.: Universal remote quantum computation assisted by the cavity input-output process. Proc. R. Soc. A 471(2184), 20150274 (2015)

    Article  Google Scholar 

  49. Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  50. Toffoli, T.: Reversible computing. In: de Bakker, J., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 632–644. Springer, Berlin (2005)

    Chapter  Google Scholar 

  51. Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493(R) (1995)

    Article  Google Scholar 

  52. Calderbank, A., Rains, E., Shor, P.W., Sloane, N.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theor. 44, 1369–1387 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  53. Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)

    Article  Google Scholar 

  54. Knill, E., Laflamme, R., Martinez, R., Negrevergne, C.: Benchmarking quantum computers: the five-qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)

    Article  Google Scholar 

  55. Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  56. Shi, Y.: Both Toffoli and controlled-NOT need little help to do universal quantum computation. Quantum Inf. Comput. 3(1), 84–92 (2003)

    MathSciNet  MATH  Google Scholar 

  57. Yu, N., Duan, R., Ying, R.: Five two-qubit gates are necessary for implementing the Toffoli gate. Phys. Rev. A 88, 010304(R) (2013)

    Article  Google Scholar 

  58. Lanyon, B.P., et al.: Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys. 5, 134–140 (2008)

    Article  Google Scholar 

  59. Luo, M.X., Ma, S.Y., Chen, X.B., Wang, X.: Hybrid Toffoli gate on photons and quantum spins. Sci. Rep. 5, 16716 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 61303039), Chuying Fellowship, CSC Fund, and Open Foundation of China-USA Computer Science Research Center (Nanjing University of Information Science and Technology) (No. KJR16132).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ming-Xing Luo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Luo, MX., Li, HR. (2016). Distributed Quantum Computation Assisted by Remote Toffoli Gate. In: Sun, X., Liu, A., Chao, HC., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2016. Lecture Notes in Computer Science(), vol 10039. Springer, Cham. https://doi.org/10.1007/978-3-319-48671-0_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48671-0_42

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48670-3

  • Online ISBN: 978-3-319-48671-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics