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Hyper CNOT and Hyper Bell-State Analysis Assisted by Quantum Dots in Double-Side Optical Microcavities

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Abstract

There are many important works about the construction of universal quantum logic gates which are key elements in quantum computation. However, most of them focus on quantum transformations on the same degree of freedom (DOF) of quantum systems. We propose a CNOT gate performed on the polarization DOF and spatial mode DOF of one photon system assisted by a quantum dot in double-side optical microcavities. This hyper CNOT gate is implemented by using spin selective photon reflection from the cavity, without auxiliary spatial modes or polarization modes. This interface can also be used to construct a hyper photonic Bell-state analyzer. The high fidelities of the hyper CNOT gates may be achieved with low side leakage and cavity loss.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–475 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing, Proc. IEEE Inter. Conf. Computers, Systems and Signal Process., Bangalore, India, 175–179 (1984)

  6. 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, 1895–1899 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Barencoa, A., Ekerta, A.K.: Concentrating partial entanglement by local operations. J. Modern Opt. 42, 1253–1259 (1995)

    Article  ADS  Google Scholar 

  8. Deutsch, D.: Quantum Theory, the Church-Turing Principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Deutsch, D.: Quantum computational networks. Proc. R. Soc. Lond. A 425, 73–90 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–4467 (1995)

    Article  ADS  Google Scholar 

  11. 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, 4714–4717 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Shende, V., Bullock, S.S., Markov, I.L.: Synthesis of quantum logic circuits. IEEE Tran. Comput. AID Design 26, 1000–1010 (2006)

    Article  Google Scholar 

  13. Luo, M.-X., Chen, X.-B., Yang, Y.-X., Wang, X.: Geometry of quantum computation with qudits. Sci. Rep. 4, 4044 (2014)

    ADS  Google Scholar 

  14. Zhang, J., Vala, J., Sastry, S., Whaley, K.B.: Exact two-qubit universal quantum circuit. Phys. Rev. Lett. 027903, 91 (2003)

    Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Niskanen, A.O., Vartiainen, J.J., Salomaa, M.M.: Optimal multiqubit operations for Josephson charge qubits. Phys. Rev. Lett. 197901, 90 (2003)

    Google Scholar 

  17. Gershenfeld, N.A., Chuang, N.A.: Bulk spin-resonance quantum computation. Science 275, 350–356 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  19. Schmidt-Kaler, F., Häffner, H., Riebe, M., Gulde, S., Lancaster, G.P.T., Deuschle, T., Becher, C., Roos, C.F., Eschner, J., Blatt, R.: Realization of the Cirac-Zoller controlled-NOT quantum gate. Nature 422, 408–411 (2003)

    Article  ADS  Google Scholar 

  20. Li, X., Wu, Y., Steel, D., Gammon, D., Stievater, T.H., Katzer, D.S., Park, D., Piermarocchi, C., Sham, L.J.: An all-optical quantum gate in a semiconductor quantum dot. Science 301, 809–811 (2003)

    Article  ADS  Google Scholar 

  21. Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)

    Article  ADS  MATH  Google Scholar 

  22. Nemoto, K., Munro, W.J.: Nearly Deterministic Linear Optical Controlled-NOT Gate. Phys. Rev. Lett. 250502, 93 (2004)

    Google Scholar 

  23. O’Brien, J.L., Pryde, G.J., White, A.G., Ralph, T.C., Branning, D.: Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264–267 (2003)

    Article  ADS  Google Scholar 

  24. Hu, C.Y., Munro, W.J., O’Brien, J.L., Rarity, J.G.: The entanglement beam splitter: a quantum-dot spin in a double-sided optical microcavity. Phys. Rev. B 205326, 80 (2009)

    Google Scholar 

  25. Auffeves-Garnier, A., Simon, C., Gerard, J.M., Poizat, J.P.: Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime. Phys. Rev. A 053823, 75 (2007)

    Google Scholar 

  26. Schmidt, H., Imamogdlu, A.: Giant Kerr nonlinearities obtained by electromagnetically induced transparency. Opt. Lett. 21, 1936–1938 (1996)

    Article  ADS  Google Scholar 

  27. Hu, C.Y., Young, A., O’Brien, J.L., Munro, W.J., Rarity, J.sG.: Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon. Phys. Rev. B 085307, 78 (2008)

    Google Scholar 

  28. Hu, C.Y., Munro, W.J., Rarity, J.G.: Deterministic photon entangler using a charged quantum dot inside a microcavity. Phys. Rev. B 125318, 78 (2008)

    Google Scholar 

  29. Bonato, C., Haupt, F., Oemrawsingh, S.S.R., Gudat, J., Ding, D., van Exter, M.P., Bouwmeester, D.: CNOT and Bell-state analysis in the weak-coupling cavity QED regime. Phys. Rev. Lett. 160503, 104 (2010)

    Google Scholar 

  30. Duan, L.-M., Kimble, H.J.: Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 127902, 92 (2004)

    Google Scholar 

  31. Stephens, A.M., Evans, Z.W.E., Devitt, S.J., Greentree, A.D., Fowler, A.G., Munro, W.J., O’Brien, J.L., Nemoto, K., Hollenberg, L.C.L.: Deterministic optical quantum computer using photonic modules. Phys. Rev. A 032318, 78 (2008)

    Google Scholar 

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

    ADS  Google Scholar 

  33. Luo, M. X., Ma, S.-Y., Chen, X.-B., Wang, X.: Hybrid quantum states joining and splitting assisted by quantum dots in one-side optical microcavities. Phys. Rev. A 042326, 91 (2015)

    Google Scholar 

  34. Ren, B.C., Deng, F.G.: Hyper-parallel photonic quantum computing with coupled quantum dots. Sci. Rep. 4, 4623 (2014)

    ADS  Google Scholar 

  35. Wei, H.R., Deng, F.G.: Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities. Phys. Rev. A 022305, 87 (2013)

    Google Scholar 

  36. Wang, T.J., Zhang, Y., Wang, C.: Universal hybrid hyper-controlled quantum gates assisted by quantum dots in optical double-sided microcavities. Laser Phys. Lett. 025203, 11 (2014)

    Google Scholar 

  37. Ren, B.C., Wei, H.R., Hua, M., Li, T., Deng, F.G.: Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities. Opt. Express 20, 24664–24677 (2012)

    Article  ADS  Google Scholar 

  38. Wang, T.J., Lu, Y., Long, G.L.: Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities. Phys. Rev. A 042337, 86 (2012)

    Google Scholar 

  39. Young, A.B., Oulton, R., Hu, C.Y., Thijssen, A.C.T., Schneider, C., Reitzenstein, S., Kamp, M., Höfling, S., Worschech, L., Forchel, A., Rarity, J.G.: Quantum-dot-induced phase shift in a pillar microcavity. Phys. Rev. A 011803, 84 (2011)

    Google Scholar 

  40. Petta, J.R., Johnson, A.C., Taylor, J.M., Laird, E.A., Yacoby, A., Lukin, M.D., Marcus, C.M., Hanson, M.P., Gossard, A.C.: Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180 (2005)

    Article  ADS  Google Scholar 

  41. Brunner, D., Gerardot, B.D., Dalgarno, P.A., Wüst, G., Karrai, K., Stoltz, N.G., Petroff, P.M., Warburton, R.J.: A coherent single-hole spin in a semiconductor. Science 325, 70–72 (2009)

    Article  ADS  Google Scholar 

  42. Reithmaier, J.P., Sçk, G., Löffler, A., Hofmann, C., Kuhn, S., Reitzenstein, S., Keldysh, L.V., Kulakovskii, V.D., Reinecke, T.L., Forchel, A.: Strong coupling in a single quantum dot-semiconductor microcavity system. Nature 432, 197–200 (2004)

    Article  ADS  Google Scholar 

  43. Yoshie, T., Scherer, A., Hendrickson, J., Khitrova, G., Gibbs, H.M., Rupper, G., Ell, C., Shchekin, O.B., Deppe, D.G.: Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity. Nature 432, 200–203 (2004)

    Article  ADS  Google Scholar 

  44. Warburton, R.J., Dür, C.S., Karrai, K., Kotthaus, J.P., Medeiros-Ribeiro, G., Petroff, P.M.: Charged excitons in Self-Assembled semiconductor quantum dots. Phys. Rev. Lett. 79, 5282 (1997)

    Article  ADS  Google Scholar 

  45. Hu, C.Y., Ossau, W., Yakovlev, D.R., Landwehr, G., Wojtowicz, T., Karczewski, G., Kossut, J.: Optically detected magnetic resonance of excess electrons in type-I quantum wells with a low-density electron gas. Phys. Rev. B 58, R1766-R1769 (1998)

    Article  ADS  Google Scholar 

  46. Loo, V., Lanco, L., Lemaitre, A., Sagnes, I., Krebs, O., Voisin, P., Senellart, P.: Quantum dot-cavity strong-coupling regime measured through coherent reflection spectroscopy in a very high-Q micropillar. Appl. Phys. Lett. 241110, 96 (2010)

    Google Scholar 

  47. Reiserer, A., Kalb, N., Rempe, G., Ritter, S.: A quantum gate between a flying optical photon and a single trapped atom. Nature 237-240, 508 (2014)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Physics, Chongqing University of Science & Technology, Chongqing, 401331, China

    Yong He

  2. School of Computer Science, Sichuan University of Science & Engineering, Zigong, 643000, China

    Yun Deng

  3. Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, 610031, China

    Hui-Ran Li & Ming-Xing Luo

Authors
  1. Yong He
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  2. Yun Deng
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  3. Hui-Ran Li
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  4. Ming-Xing Luo
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Correspondence to Yun Deng.

Additional information

This work is supported by the National Natural Science Foundation of China (Nos. 61303039, 61201253) and Fundamental Research Funds for the Central Universities (No. 2682014CX095).

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He, Y., Deng, Y., Li, HR. et al. Hyper CNOT and Hyper Bell-State Analysis Assisted by Quantum Dots in Double-Side Optical Microcavities. Int J Theor Phys 55, 1526–1535 (2016). https://doi.org/10.1007/s10773-015-2790-0

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