Quantum Information Processing

, Volume 11, Issue 6, pp 1627–1651 | Cite as

Theoretical comparison of quantum Zeno gates and logic gates based on the cross-Kerr nonlinearity

Article

Abstract

Quantum logic operations can be implemented using nonlinear phase shifts (the Kerr effect) or the quantum Zeno effect based on strong two-photon absorption. Both approaches utilize three-level atoms, where the upper level is tuned on resonance for the Zeno gates and off-resonance for the nonlinear phase gates. The performance of nonlinear phase gates and Zeno gates are compared under conditions where the parameters of the resonant cavities and three-level atoms are the same in both cases. It is found that the expected performance is comparable for the two approaches despite the fundamental differences between the Zeno and Kerr effects.

Keywords

Zeno effect Quantum computing Quantum logic gates Zeno gates 

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References

  1. 1.
    Cirac J.I., Zoller P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091 (1995)ADSCrossRefGoogle Scholar
  2. 2.
    Monroe C., Meekhof D.M., King B.E., Itano W.M., Wineland D.J.: Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714 (1995)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Monz T., Kim K., Villar A.S., Schindler P., Chwalla M., Riebe M., Roos C.F., Häffner H., Hänsel W., Hennrich M., Blatt R.: Realization of universal ion-trap quantum computation with decoherence-free qubits. Phys. Rev. Lett. 103, 200503 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    Jaksch D., Briegel H.-J., Cirac J.I., Gardiner C.W., Zoller P.: Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    Isenhower L., Urban E., Zhang X.L., Gill A.T., Henage T., Johnson T.A., Walker T.G., Saffman M.: Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett. 104, 010503 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    DeMille D.: Quantum computation with trapped polar molecules. Phys. Rev. Lett. 88, 067901 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    André A., DeMille D., Doyle J.M., Lukin M.D., Maxwell S.E., Rabl P., Schoelkopf R.J., Zoller P.: A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators. Nat. Phys. 2, 636 (2006)CrossRefGoogle Scholar
  8. 8.
    Rabl P., DeMille D., Doyle J.M., Lukin M.D., Schoelkopf R.J., Zoller P.: Hybrid quantum processors: molecular ensembles as quantum memory for solid state circuits. Phys. Rev. Lett. 97, 033003 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    Yelin S.F., Kirby K., Côté R.: Schemes for robust quantum computation with polar molecules. Phys. Rev. A 74, 050301(R) (2006)ADSCrossRefGoogle Scholar
  10. 10.
    Yamamoto T., Pashkin Yu.A., Astafiev O., Nakamura Y., Tsai J.S.: Demonstration of conditional gate operation using superconducting charge qubits. Nature 425, 941 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    Plantenberg J.H., de Groot P.C., Harmans C.J.P.M., Mooij J.E.: Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits. Nature 447, 836 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    Niskanen A.O., Harrabi K., Yoshihara F., Nakamura Y., Lloyd S., Tsai J.S.: Quantum coherent tunable coupling of superconducting qubits. Science 316, 723 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    Lucero E., Hofheinz M., Ansmann M., Bialczak R.C., Katz N., Neeley Matthew, O’Connell A.D., Wang H., Cleland A.N., Martinis J.M.: High-fidelity gates in a Josephson qubit. Phys. Rev. Lett. 100, 247001 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    DiCarlo L., Chow J.M., Gambetta J.M., Bishop L.S., Johnson B.R., Schuster D.I., Majer J., Blais A., Frunzio L., Girvin S.M., Schoelkopf R.J.: Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    Loss D., DiVincenzo D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    Kane B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 133 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    Xu K.J., Huang Y.P., Moore M.G., Piermarocchi C.: Two-qubit conditional phase gate in laser-excited semiconductor quantum dots using the quantum Zeno effect. Phys. Rev. Lett. 103, 037401 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    Milburn G.J.: Quantum optical Fredkin gate. Phys. Rev. Lett. 62, 2124 (1989)ADSCrossRefGoogle Scholar
  19. 19.
    Turchette Q.A., Hood C.J., Lange W., Mabuchi H., Kimble H.J.: Measurement of conditional phase shifts for quantum logic. Phys. Rev. Lett. 75, 4710 (1995)MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Knill E., Laflamme R., Milburn G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)ADSCrossRefGoogle Scholar
  21. 21.
    Pittman T.B., Jacobs B.C., Franson J.D.: Probabilistic quantum logic operations using polarizing beam splitters. Phys. Rev. A 64, 062311 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    Pittman T.B., Jacobs B.C., Franson J.D.: Demonstration of nondeterministic quantum logic operations using linear optical elements. Phys. Rev. Lett 88, 257902 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    Franson J.D., Donegan M.M., Fitch M.J., Jacobs B.C., Pittman T.B.: High-fidelity quantum logic operations using linear optical elements. Phys. Rev. Lett 89, 137901 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    Pittman T.B., Fitch M.J., Jacobs B.C., Franson J.D.: Experimental controlled-NOT logic gate for single photons in the coincidence basis. Phys. Rev. A 68, 032316 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    O’Brein J.L., Pryde G.J., White A.G., Ralph T.C., Branning D.: Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    Prevedal R., Walther P., Tiefenbacher F., Bohi P., Kaltenbaek R., Jennewein T., Zeilinger A.: High-speed linear optics quantum computing using active feed-forward. Nature 445, 65 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    Nemoto K., Munro W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)ADSCrossRefGoogle Scholar
  28. 28.
    Spiller T.P., Nemoto K., Braunstein S.L., Munro W.J., Van Loock P., Milburn G.J.: Quantum computation by communication. New J. Phys. 8, 30 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    Birnbaum K.M., Boca A., Miller R., Boozer A.D., Northup T.E., Kimble H.J.: Photon blockade in an optical cavity with one trapped atom. Nature 436, 87 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    Lloyd S., Braunstein S.L.: Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784 (1999)MathSciNetADSMATHCrossRefGoogle Scholar
  31. 31.
    Menicucci Nicolas 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)ADSCrossRefGoogle Scholar
  32. 32.
    Gu M., Weedbrook C., Menicucci N.C., Ralph T.C., van Loock P.: Quantum computing with continuous-variable clusters. Phys. Rev. A 79, 062318 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    Franson J.D., Jacobs B.C., Pittman T.B.: Quantum computing using single photons and the Zeno effect. Phys. Rev. A 70, 062302 (2004)MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    Franson J.D., Jacobs B.C., Pittman T.B.: Zeno logic gates using microcavities. J. Opt. Soc. Am. B 24, 209 (2007)MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    Leung P.M., Ralph T.C.: Improving the fidelity of optical Zeno gates via distillation. Phys. Rev. A 74, 062325 (2006)MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    Leung P.M., Ralph T.C.: Optical zeno gate: bounds for fault tolerant operation. New J. Phys. 9, 224 (2007)ADSCrossRefGoogle Scholar
  37. 37.
    Myers C.R., Gilchrist A.: Photon-loss-tolerant Zeno controlled-SIGN gate. Phys. Rev. A 75, 052339 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    Huang Y.P., Moore M.G.: Interaction- and measurement-free quantum Zeno gates for universal computation with single-atom and single-photon qubits. Phys. Rev. A 77, 062332 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    You H., Hendrickson S.M., Franson J.D.: Enhanced two-photon absorption using entangled states and small mode volumes. Phys. Rev. A 80, 043823 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    Armani D.K., Kippenberg T.J., Spillane S.M., Vahala K.J.: Ultra-high-Q toroid microcavity on a chip. Nature 421, 925 (2003)ADSCrossRefGoogle Scholar
  41. 41.
    Vahala K.J.: Optical microcavities. Nature 424, 839 (2003)ADSCrossRefGoogle Scholar
  42. 42.
    Kippenberg T.J., Spillane S.M., Armani D.K., Vahala K.J.: Fabrication and coupling to planar high-Q silica disk microcavities. Appl. Phys. Lett. 83(4), 797 (2003)ADSCrossRefGoogle Scholar
  43. 43.
    Spillane S.M., Kippenberg T.J., Vahala K.J., Goh K.W., Wilcut E., Kimble H.J.: Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005)ADSCrossRefGoogle Scholar
  44. 44.
    Min B., Yang L., Vahala K.: Perturbative analytic theory of an ultrahigh- Q toroidal microcavity. Phys. Rev. A 76, 013823 (2007)ADSCrossRefGoogle Scholar
  45. 45.
    You H., Hendrickson S.M., Franson J.D.: Analysis of enhanced two-photon absorption in tapered optical fibers. Phys. Rev. A 78, 053803 (2008)ADSCrossRefGoogle Scholar
  46. 46.
    Cohen-Tannoudji C.: Optical pumping and interactions of atoms with the electromagnetic field. In: Levy, M. (ed) Cargese Lectures in Physics, vol. 2, pp. 347–393. Gordon and Breach, New York (1968)Google Scholar
  47. 47.
    Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: In: Atom-Photon Interactions: Basic Processes and Applications. Wiley, New-York (1992)Google Scholar
  48. 48.
    Bloembergen N., Levenson M.D.: Doppler-free two-photon absorption spectroscopy. In: Shimoda, K. (eds) Topics in Applied Physics, vol. 13, pp. 329. Springer, Berlin (1976)Google Scholar
  49. 49.
    Kimble H.J.: Strong interactions of single atoms and photons in cavity QED. Phys. Scr. T 76, 127 (1998)ADSCrossRefGoogle Scholar
  50. 50.
    Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  51. 51.
    Jacobs B.C., Franson J.D.: All-optical switching using the quantum Zeno effect and two-photon absorption. Phys. Rev. A 79, 063830 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of MarylandBaltimore County, BaltimoreUSA

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