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

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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.

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References

  1. Cirac J.I., Zoller P.: Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091 (1995)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  6. DeMille D.: Quantum computation with trapped polar molecules. Phys. Rev. Lett. 88, 067901 (2002)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  9. Yelin S.F., Kirby K., Côté R.: Schemes for robust quantum computation with polar molecules. Phys. Rev. A 74, 050301(R) (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  15. Loss D., DiVincenzo D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)

    Article  ADS  Google Scholar 

  16. Kane B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 133 (1998)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  18. Milburn G.J.: Quantum optical Fredkin gate. Phys. Rev. Lett. 62, 2124 (1989)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  20. Knill E., Laflamme R., Milburn G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)

    Article  MATH  ADS  Google Scholar 

  21. Pittman T.B., Jacobs B.C., Franson J.D.: Probabilistic quantum logic operations using polarizing beam splitters. Phys. Rev. A 64, 062311 (2001)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  27. Nemoto K., Munro W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  30. Lloyd S., Braunstein S.L.: Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  34. Franson J.D., Jacobs B.C., Pittman T.B.: Zeno logic gates using microcavities. J. Opt. Soc. Am. B 24, 209 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  35. Leung P.M., Ralph T.C.: Improving the fidelity of optical Zeno gates via distillation. Phys. Rev. A 74, 062325 (2006)

    Article  ADS  Google Scholar 

  36. Leung P.M., Ralph T.C.: Optical zeno gate: bounds for fault tolerant operation. New J. Phys. 9, 224 (2007)

    Article  ADS  Google Scholar 

  37. Myers C.R., Gilchrist A.: Photon-loss-tolerant Zeno controlled-SIGN gate. Phys. Rev. A 75, 052339 (2007)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  41. Vahala K.J.: Optical microcavities. Nature 424, 839 (2003)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  44. Min B., Yang L., Vahala K.: Perturbative analytic theory of an ultrahigh- Q toroidal microcavity. Phys. Rev. A 76, 013823 (2007)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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. Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: In: Atom-Photon Interactions: Basic Processes and Applications. Wiley, New-York (1992)

  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. Kimble H.J.: Strong interactions of single atoms and photons in cavity QED. Phys. Scr. T 76, 127 (1998)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

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You, H., Franson, J.D. Theoretical comparison of quantum Zeno gates and logic gates based on the cross-Kerr nonlinearity. Quantum Inf Process 11, 1627–1651 (2012). https://doi.org/10.1007/s11128-011-0318-y

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  • DOI: https://doi.org/10.1007/s11128-011-0318-y

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