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Multi-Step Multi-Input One-Way Quantum Information Processing with Spatial and Temporal Modes of Light pp 1–14Cite as

Introduction

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Part of the book series: Springer Theses ((Springer Theses))

Abstract

In this chapter, we briefly review one-way quantum computation as well as the background of this thesis. A measurement-based model of quantum computation, referred to as “one-way quantum computation”, is proposed as an alternative to the standard circuit model of quantum computation. One-way quantum computation can be considered as an application of quantum teleportation to quantum computation. Once a sufficiently large entangled state called a “cluster state” is prepared in advance, an arbitrary quantum computation can be implemented by a succession of measurements on the cluster state. Recently, generation of up to six-mode cluster states and subsequent demonstrations of single-mode Gaussian operations are reported. In this thesis, we show the first successful demonstration of two-mode Gaussian operations in one-way quantum computation. As a next step for many-mode operations, we discuss how one-way quantum computation can be implemented using temporal-mode cluster states.

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Notes

  1. 1.

    To be precise, Fig. 1.4 shows the teleportation-based input coupling scheme (Sect. 5.3.3), where both measurements are homodyne measurements. A homodyne measurement has one DOF: the relative phase \(\theta \) between the signal beam and the local oscillator beam. Thus, Fig. 1.4 has two DOF. In general, we can implement a transformation with multiple DOF using an elementary one-mode one-way gate (Sect. 4.2.3) by choosing a complicated measurement. However, we usually assume that we construct a large-scale quantum computation by concatenating several kinds of elementary gates with limited DOF. Therefore, the total DOF of operations still increase as well by concatenating elementary gates.

  2. 2.

    Since both optical DV and CV systems have merits and demerits of their own, a hybrid scheme is also being studied [31], where DV gates are implemented using optical CV setups. It is thought that the imperfections of quantum states may be compensated by limiting the dimension of computational bases.

  3. 3.

    In Ref. [26], it was already mentioned that special shapes of cluster states can be generated by using beam splitter networks. However, its generalization was given in Ref. [35].

References

  1. Planck, M.: Ueber das Gesetz der Energieverteilung im Normalspectrum. Annalen der Physik 309, 553 (1901)

    Article  ADS  Google Scholar 

  2. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  MATH  ADS  Google Scholar 

  3. Deutsch, D.: Proc. Roy. Soc. London, Ser. A 400, 96 (1985)

    Google Scholar 

  4. Shor, P.W.: In: Proceedings, 35\(^{th}\) Annual Symposium on Foundations of Computer Science. IEEE Press, Los Alamitos, CA (1994)

    Google Scholar 

  5. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logorithms on a quantum computer. SIAM J. Computing 26, 1484 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Grover, L.K.: Quantum mechanics helps in searching for a needle in a Haystack. Phys. Rev. Lett. 79, 325 (1997)

    Article  ADS  Google Scholar 

  7. S. J. Lomonaco, Jr., and L. H. Kauffman, Quantum Hidden Subgroup Problems: A Mathematical Perspective, e-print arXiv:0201095 [quant-ph]

  8. Lomonaco, S.J. Jr., Kauffman, L.H.: A Continuous Variable Shor Algorithm, e-print arXiv:0210141 [quant-ph]

  9. Aspect, A., Grangier, P., Roger, G.: Experimental tests of realistic local theories via Bell’s theorem. Phys. Rev. Lett. 47, 460 (1981)

    Article  ADS  Google Scholar 

  10. Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  11. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  12. 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  MathSciNet  MATH  ADS  Google Scholar 

  13. Vaidman, L.: Teleportation of quantum states. Phys. Rev. A 49, 1473 (1994)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869 (1998)

    Article  ADS  Google Scholar 

  16. Boschi, D., Branca, S., De Martini, F., Hardy, L., Popescu, S.: Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80, 1121 (1998)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. Furusawa, A., Sørensen, J.L., Braunshtein, S.L., Fuchs, C.A., Kimble, H.J., Polzik, E.S.: Unconditional quantum teleportation. Science 282, 706 (1998)

    Article  ADS  Google Scholar 

  18. Takei, N., Yonezawa, H., Aoki, T., Furusawa, A.: High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables. Phys. Rev. Lett. 94, 220502 (2005)

    Article  ADS  Google Scholar 

  19. Yonezawa, H., Furusawa, A., van Loock, P.: Sequential quantum teleportation of optical coherent states. Phys. Rev. A 76, 032305 (2007)

    Article  ADS  Google Scholar 

  20. Yonezawa, H., Braunstein, S.L., Furusawa, A.: Experimental demonstration of quantum teleportation of broadband squeezing. Phys. Rev. Lett. 99, 110503 (2007)

    Article  ADS  Google Scholar 

  21. Yukawa, M., Benichi, H., Furusawa, A.: High-fidelity continuous-variable quantum teleportation toward multistep quantum operations. Phys. Rev. A 77, 022314 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Bartlett, S.D., Munro, W.J.: Quantum teleportation of optical quantum gates. Phys. Rev. Lett. 90, 117901 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  24. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  25. Gottesman, D., Kitaev, A., Preskill3, J.: Encoding a qubit in an oscillator. Phys. Rev. A 64, 012310 (2001)

    Google Scholar 

  26. Zhang, J., Braunstein, S.L.: Continuous-variable Gaussian analog of cluster states. Phys. Rev. A 73, 032318 (2006)

    Article  ADS  Google Scholar 

  27. Menicucci, N.C., van Loock, P., Gu, M., Weedbrook, C., Ralph, T.C., Nielsen, M.A.: Universal quantum computation with continuous-variable cluster states. Phys. Rev. Lett. 97, 110501 (2006)

    Article  ADS  Google Scholar 

  28. Nielsen, M.A.: Cluster-state quantum computation. Rep. Math. Phys. 57, 147 (2006)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  29. van Loock, P.: Examples of Gaussian cluster computation. J. Opt. Soc. Am. B 24, 340 (2007)

    Article  ADS  Google Scholar 

  30. Braunstein, S.L., Pati, A.K.: Quantum information theory with continuous variables. Kluwer, Dordrecht (2003)

    Google Scholar 

  31. Furusawa, A., van Loock, P.: Quantum teleportation and entanglement. Wiley -VCH (2011)

    Google Scholar 

  32. Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910 (2001)

    Article  ADS  Google Scholar 

  33. Walther, P., Resch, K.J., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., Zeilinger, A.: Experimental one-way quantum computing. Nature 434, 169 (2005)

    Article  ADS  Google Scholar 

  34. Prevedel, R., Walther, P., Tiefenbacher, F., Böhi, P., Kaltenbaek, R., Jennewein, T., Zeilinger, A.: High-speed linear optics quantum computing using active feed-forward. Nature 445, 65 (2007)

    Article  ADS  Google Scholar 

  35. van Loock, Peter, Weedbrook, Christian, Mile, Gu: Building Gaussian cluster states by linear optics. Phys. Rev. A 76, 032321 (2007)

    Article  ADS  Google Scholar 

  36. Filip, R., Marek, P., Andersen, U.L.: Measurement-induced continuous-variable quantum interactions. Phys. Rev. A 71, 042308 (2005)

    Article  ADS  Google Scholar 

  37. Yoshikawa, J., Miwa, Y., Huck, A., Andersen, U.L., van Loock, P., Furusawa, A.: Demonstration of a quantum nondemolition sum gate. Phys. Rev. Lett. 101, 250501 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  38. Su, X., Tan, A., Jia, X., Zhang, J., Xie, C., Peng, K.: Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables. Phys. Rev. Lett. 98, 070502 (2007)

    Article  ADS  Google Scholar 

  39. Yukawa, M., Ukai, R., van Loock, P., Furusawa, A.: Experimental generation of four-mode continuous-variable cluster states. Phys. Rev. A 78, 012301 (2008)

    Article  ADS  Google Scholar 

  40. Su, X., Zhao, Y., Hao, S., Jia, X., Xie, C., Peng, K.: Experimental preparation of eight-partite linear and two-diamond shape cluster states for photonic qumodes, arXiv:1205.0590 [quant-ph]

  41. Miwa, Y., Ukai, R., Yoshikawa, J., Filip, R., van Loock, P., Furusawa, A.: Demonstration of cluster-state shaping and quantum erasure for continuous variables. Phys. Rev. A 82, 032305 (2010)

    Article  ADS  Google Scholar 

  42. Ukai, R., Yoshikawa, J., Iwata, N., van Loock, P., Furusawa, A.: Universal linear Bogoliubov transformations through one-way quantum computation. Phys. Rev. A 81, 032315 (2010)

    Article  ADS  Google Scholar 

  43. Wang, Y., Su, X., Shen, H., Tan, A., Xie, C., Peng, K.: Toward demonstrating controlled-X operation based on continuous-variable four-partite cluster states and quantum teleporters. Phys. Rev. A 81, 022311 (2010)

    Article  ADS  Google Scholar 

  44. Ukai, R., Yokoyama, S., Yoshikawa, J., van Loock, P., Furusawa, A.: Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation. Phys. Rev. Lett. 107, 250501 (2011)

    Article  ADS  Google Scholar 

  45. Eisert, J., Jacobs, K., Papadopoulos, P., Plenio, B.: Optimal local implementation of nonlocal quantum gates. Phys. Rev. A 62, 052317 (2000)

    Article  ADS  Google Scholar 

  46. 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  ADS  Google Scholar 

  47. Gao, W.-B., Goebel, A.M., Lu, C.-Y., Dai, H.-N., Wagenknecht, C., Zhang, Q., Zhao, B., Peng, C.-Z., Chen, Z.-B., Chen, Y.-A., Pan, J.-W.: Teleportation-based realization of an optical quantum two-qubit entangling gate. In: Proceedings of the National Academy of Sciences of the United States of America vol. 107, p. 20869 (2010)

    Google Scholar 

  48. Gottesman, D.: The Heisenberg representation of quantum computers. In: Corney, S.P., Delbourgo, R., Jarvis, P.D. (eds.) Group22: Proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics, pp. 32–43. International Press, Cambridge, MA (1999), e-print arXiv:9807006 [quant-ph]

  49. Zhou, X., Leung, D.W., Chuang, I.L.: Methodology for quantum logic gate construction. Phys. Rev. A 62, 052316 (2000)

    Article  ADS  Google Scholar 

  50. Menicucci, N.C., Ma, X., Ralph, T.C.: Arbitrarily large continuous-variable cluster states from a single quantum nondemolition gate. Phys. Rev. Lett. 104, 250503 (2010)

    Article  ADS  Google Scholar 

  51. Nicolas, C.: Menicucci, temporal-mode continuous-variable cluster states using linear optics. Phys. Rev. A 83, 062314 (2011)

    Article  Google Scholar 

  52. Menicucci, N.C., Flammia, S.T., Zaidi, H., Pfister, O.: Ultracompact generation of continuous-variable cluster states. Phys. Rev. A 76, 010302(R) (2007)

    Article  MathSciNet  ADS  Google Scholar 

  53. Zaidi, H., Menicucci, N.C., Flammia, S.T., Bloomer, R., Pysher, M., Pfister, O.: Entangling the optical frequency comb: simultaneous generation of multiple 2 \(\times \)2 and 2\(\times \)3 continuous-variable cluster states in a single optical parametric oscillator. Laser Phys. 18, 659 (2008)

    Article  ADS  Google Scholar 

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  1. Applied Physics, The University of Tokyo, Tokyo, Japan

    Ryuji Ukai

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Ukai, R. (2015). Introduction. In: Multi-Step Multi-Input One-Way Quantum Information Processing with Spatial and Temporal Modes of Light. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55019-8_1

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