Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Quantum Computing Using Optics

  • Gerard J. Milburn
  • Andrew G. White
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_431

Definition of the Subject

Quantum computation is a new approach to information processing based on physical devices that operate according to the quantum principles ofsuperposition and unitary evolution [5,9]. This enablesmore efficient algorithms than are available for a computer operating according to classical principles, the most significant of which is Shor'sefficient algorithm for finding the prime factors of a large integer [51]. There is no knownefficient algorithm for this task on conventional computing hardware.

Optical implementations of quantum computing have largely focused on encoding quantum information using single photon states of light. For example,a single photon could be excited to one of two carefully defined orthogonal mode functions of the field with different momentum directions. However,as optical photons do not interact with each other directly, physical devices that enable one encoded bit of information to unitarily change another arehard to implement. In...

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

Bibliography

  1. 1.
    Beckman D, Chari AN, Devabhaktuni S, Preskill J (1996) Phys RevA 54:1034MathSciNetADSGoogle Scholar
  2. 2.
    Braunstein SL et al (1999) Phys Rev Lett 83:1054MathSciNetADSGoogle Scholar
  3. 3.
    Cleve R, Ekert A, Henderson L, Macchiavello C, Mosca M (1999) On quantumalgorithms. LANL quant-ph/9903061Google Scholar
  4. 4.
    Darquie B, Jones MPA, Dingjan J, Beugnon J, Bergamini S, Sortais Y, Messin G,Browaeys A, Grangier P (2005) Science 309:454ADSGoogle Scholar
  5. 5.
    Deutsch D (1985) Quantum‐theory, the Church–Turing principle and theuniversal quantum computer. Proc R Soc Lond A 400:97–117MathSciNetADSMATHGoogle Scholar
  6. 6.
    Duan L-M, Lukin MD, Cirac JI, Zoller P (2001) Nature414:413ADSGoogle Scholar
  7. 7.
    Einstein A (1905) On a Heuristic Point of View about the Creation andConversion of Light? Ann Physik 17:132ADSMATHGoogle Scholar
  8. 8.
    Eisaman MD, Fleischhauer M, Lukin MD, Zibrov AS (2006) Toward quantum control ofsingle photons. Opt Photonics News 17:22–27ADSGoogle Scholar
  9. 9.
    Feynman RP (1982) Simulating physics with computers. Int J Theor Phys21:467MathSciNetGoogle Scholar
  10. 10.
    Gasparoni S et al (2004) Phys Rev Lett 93:020504ADSGoogle Scholar
  11. 11.
    Gilchrist A, Langford NK, Nielsen MA (2005) Distance measures to compare realand ideal quantum processes. Phys Rev A 71:062310ADSGoogle Scholar
  12. 12.
    Gottesman D, Chuang IL (1999) Demonstrating the viability of universal quantumcomputation using teleportation and single‐qubit operations. Nature 402:390–393ADSGoogle Scholar
  13. 13.
    Hennrich M, Legero T, Kuhn A, Rempe G (2004) Photon statistics ofa non‐stationary periodically driven single‐photon source. New J Phys 6:86Google Scholar
  14. 14.
    Hofmann H, Takeuchi S (2002) Phys RevA 66:024308ADSGoogle Scholar
  15. 15.
    Hong CK, Ou ZY, Mandel L (1987) Measurement of subpicosecond time intervalsbetween two photons by interference. Phys Rev Lett 59:2044ADSGoogle Scholar
  16. 16.
    Hutchinson GD, Milburn GJ (2004) Nonlinear quantum optical computing viameasurement. J Modern Opt 51:1211–1222MathSciNetADSMATHGoogle Scholar
  17. 17.
    James DFV, Kwiat PG, Munro WJ, White AG (2001) Measurement of qubits. Phys RevA 64:052312ADSGoogle Scholar
  18. 18.
    Jiang L, Taylor JM, Khaneja N, Lukin MD (2007) Optimal approach to quantumcommunication using dynamic programming. arXiv:quant-ph/0710.5808
  19. 19.
    Keller M, Lange B, Hayasaka K, Lange W, Walther H (2003) Continuous generationof single photons with controlled waveform in an ion-trap cavity system. Nature 431:1075ADSGoogle Scholar
  20. 20.
    Kieling K, Rudolph T, Eisert J (2007) Percolation, renormalization, and quantumcomputing with nondeterministic gates. Phys Rev Lett 99:130501MathSciNetADSGoogle Scholar
  21. 21.
    Kiesel N, Schmid C, Weber U, Ursin R, Weinfurter H (2007) Phys Rev Lett99:250505Google Scholar
  22. 22.
    Knill E (2002) Phys Rev A 66:052306MathSciNetADSGoogle Scholar
  23. 23.
    Knill E (2005) Quantum computing with realistically noisy devices. Nature434:39–44ADSGoogle Scholar
  24. 24.
    Knill E, Laflamme R, Milburn GJ (2001) Efficient linear optical quantumcomputation. Nature 409:46ADSGoogle Scholar
  25. 25.
    Kok P, Lee H, Dowling JP (2002) Phys RevA 66:063814ADSGoogle Scholar
  26. 26.
    Kok P, Munro WJ, Nemoto K, Ralph TC, Dowling JP, Milburn GJ (2007) Linearoptical quantum computing. Rev Mod Phys 79:135ADSGoogle Scholar
  27. 27.
    Langford NK, Weinhold TJ, Prevedel R, Gilchrist A, O'Brien JL, Pryde GJ, WhiteAG (2005) Phys Rev Lett 95:210504ADSGoogle Scholar
  28. 28.
    Lanyon BP, Barbieri M, Almeida MP, Jennewein T, Ralph TC, Resch KJ, Pryde G,O'Brien JL, Gilchrist A, White AG (2007) Quantum computing using shortcuts through higher dimensions. appear in Nat PhysGoogle Scholar
  29. 29.
    Lanyon BP, Weinhold TJ, Langford NK, Barbieri M, James DFV, Gilchrist A, WhiteAG (2007) Phys Rev Lett 99:250505ADSGoogle Scholar
  30. 30.
    Lu C-Y, Browne DE, Yang T, Pan J-W (2007) Phys Rev Lett99:250504ADSGoogle Scholar
  31. 31.
    Lu C-Y, Zhou X-Q, Gühne O, Gao W-B, Zhang J, Yuan Z-S, Goebel A, Yang T, Pan J-W(2007) Experimental entanglement of six photons in graph states. Nature Phys 3:91Google Scholar
  32. 32.
    Menicucci NC et al (2002) Phys Rev Lett 88:167901ADSGoogle Scholar
  33. 33.
    Migdall A et al (2002) Phys RevA 66:053805ADSGoogle Scholar
  34. 34.
    Milburn GJ (1989) A quantum optical fredkin gate. Phys Rev Lett62:2124–2127ADSGoogle Scholar
  35. 35.
    Mishina OS, Kupriyanov DV, Muller JH, Polzik ES (2007) Spectral theory ofquantum memory and entanglement via Raman scattering of light by an atomic ensemble. Phys Rev A 75:042326ADSGoogle Scholar
  36. 36.
    Neergaard‐Nielsen JS, Melholt Nielsen B, Takahashi H, Vistnes AI, PolzikES (2007) High purity bright single photon source. Opt Express 15:7940Google Scholar
  37. 37.
    Nielsen MA (2004) Optical quantum computation using cluster states. Phys RevLett 93:040503ADSGoogle Scholar
  38. 38.
    O'Brien JL et al (2004) Phys Rev Lett 93:080502ADSGoogle Scholar
  39. 39.
    O'Brien JL, Pryde GJ, White AG, Ralph TC Branning D(2003) Demonstration of an all‐optical quantum controlled‐NOT gate. Nature 426:264ADSGoogle Scholar
  40. 40.
    Okamoto R, Hofmann HF, Takeuchi S, Sasaki K (2007) Phys Rev Lett99:250506Google Scholar
  41. 41.
    Pittman TB, Jacobs BC, Franson JD (2001) Probabilistic quantum logic operationsusing polarizing beam splitters. Phys Rev A 64:062311ADSGoogle Scholar
  42. 42.
    Pittman TB, Jacobs BC, Franson JD (2002) Phys Rev Lett88:257902ADSGoogle Scholar
  43. 43.
    Pittman TB, Fitch MJ, Jacobs BC, Franson JD (2003) Experimentalcontrolled‐NOT logic gate for single photons in the coincidence basis. Phys Rev A 68:032316ADSGoogle Scholar
  44. 44.
    Popescu S (2006) KLM quantum computation as a measurement basedcomputation. arXiv:quant-ph/0610025
  45. 45.
    Prevedel R et al (2007) Nature 445:65ADSGoogle Scholar
  46. 46.
    Ralph TC, White AG, Munro WJ, Milburn GJ (2001) Simple scheme for efficientlinear optics quantum gates. Phys Rev A 65:012314ADSGoogle Scholar
  47. 47.
    Ralph TC, Langford NK, Bell TB, White AG (2002) Linear opticalcontrolled‐NOT gate in the coincidence basis. Phys Rev A 65:062324ADSGoogle Scholar
  48. 48.
    Raussendorf R, Briegel HJ (2001) A one-way quantum computer. Phys Rev Lett86:5188ADSGoogle Scholar
  49. 49.
    Rhode PP, Ralph TC (2005) Phys Rev A 71:032320ADSGoogle Scholar
  50. 50.
    Sangouard N, Simon C, Minar J, Zbinden H, de Riedmatten H, Gisin N (2007)Long‐distance entanglement distribution with single‐photon sources. arXiv:quant-ph/0706.1924v1
  51. 51.
    Shor P (1994) Algorithms for quantum computation: Discrete logarithms andfactoring. Proc 35th annual symposium on foundations of computer science. See also LANL preprint quant-ph/9508027Google Scholar
  52. 52.
    Simon C et al (2007) Phys Rev Lett 98:190503ADSGoogle Scholar
  53. 53.
    Special Issue on Single photon Sources (2004) Single photon Sources51(9–10)Google Scholar
  54. 54.
    U'Ren AB, Mukamel E, Banaszek K, Walmsley IA (2003) Phil Trans Roy SocA 361:1471Google Scholar
  55. 55.
    Van Meter R, Ladd TD, Munro WJ, Nemoto K (2007) System Design fora Long-Line Quantum Repeater. arXiv:quant-ph/0705.4128v1
  56. 56.
    Vandersypen LMK et al (2001) Nature 414:883ADSGoogle Scholar
  57. 57.
    Walls DF, Milburn GJ (2008) Quantum Optics, 2nd edn. Springer, BerlinMATHGoogle Scholar
  58. 58.
    Walther P, Resch KJ, Rudolph T, Schenck E, Weinfurter H, Vedral V, Aspelmeyer M,Zeilinger A (2005) Experimental one-way quantum computing. Nature 434:169ADSGoogle Scholar
  59. 59.
    Weinhold TJ, Gilchrist A, Resch KJ, Doherty AC, O'Brien JL, Pryde GJ, White AG (2008) Understanding photonic quantum-logic gates: The road to fault tolerance. arxiv 0808.0794Google Scholar
  60. 60.
    White AG et al (2007) Measuring two-qubit gates. J Opt Soc Am B24:172–183ADSGoogle Scholar
  61. 61.
    Yamamoto Y, Kitagawa M, Igeta K (1988) Proc 3rd Asia‐Pacific phys conf779. World Scientific, SingaporeGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Gerard J. Milburn
    • 1
  • Andrew G. White
    • 1
  1. 1.Centre for Quantum Computer TechnologyThe University of QueenslandBrisbaneAustralia