OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 4 — Apr. 1, 2014
  • pp: 697–703

One-step implementation of the genuine Fredkin gate in high-Q coupled three-cavity arrays

Xiao-Qiang Shao, Tai-Yu Zheng, Xun-Li Feng, C. H. Oh, and Shou Zhang  »View Author Affiliations


JOSA B, Vol. 31, Issue 4, pp. 697-703 (2014)
http://dx.doi.org/10.1364/JOSAB.31.000697


View Full Text Article

Enhanced HTML    Acrobat PDF (581 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present two efficient methods for implementing the Fredkin gate with atoms separately trapped in an array of three high-Q coupled cavities. The first proposal is based on the resonant dynamics, which leads to a fast resonant interaction in a certain subspace while leaving others unchanged, and the second one utilizes a dispersive interaction such that an effective long-distance dipole–dipole interaction between two distributed target qubits is achieved by a virtually excited process. Both schemes can achieve the standard form of the Fredkin gate in a single step without any subsequent single-qubit operation. The effects of decoherence on the performance of the gate are also analyzed in virtue of the master equation, and strictly numerical simulation reveals that the average fidelity of the quantum gate is high.

© 2014 Optical Society of America

OCIS Codes
(020.5580) Atomic and molecular physics : Quantum electrodynamics
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: October 30, 2013
Revised Manuscript: January 15, 2014
Manuscript Accepted: January 25, 2014
Published: March 5, 2014

Citation
Xiao-Qiang Shao, Tai-Yu Zheng, Xun-Li Feng, C. H. Oh, and Shou Zhang, "One-step implementation of the genuine Fredkin gate in high-Q coupled three-cavity arrays," J. Opt. Soc. Am. B 31, 697-703 (2014)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-31-4-697


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” in Proceedings of the 35th Symposium on Foundations of Computer Science, Santa Fe, S. Goldwasser, ed. (IEEE, 1994), pp. 124–134.
  2. P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput. 26, 1484–1509 (1997). [CrossRef]
  3. L. K. Grover, “Quantum computers can search rapidly by using almost any transformation,” Phys. Rev. Lett. 80, 4329–4332 (1998). [CrossRef]
  4. D. P. DiVincenzo, “Two-bit gates are universal for quantum computation,” Phys. Rev. A 51, 1015–1022 (1995). [CrossRef]
  5. C. P. Yang and S. Han, “n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator,” Phys. Rev. A 72, 032311 (2005). [CrossRef]
  6. C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006). [CrossRef]
  7. T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009). [CrossRef]
  8. G. W. Lin, X. B. Zou, X. M. Lin, and G. C. Guo, “Robust and fast geometric quantum computation with multiqubit gates in cavity QED,” Phys. Rev. A 79, 064303 (2009). [CrossRef]
  9. X. Q. Shao, H. F. Wang, L. Chen, S. Zhang, and K. H. Yeon, “One-step implementation of the Toffoli gate via quantum Zeno dynamics,” Phys. Lett. A 374, 28–33 (2009). [CrossRef]
  10. X. Q. Shao, T. Y. Zheng, and S. Zhang, “Robust Toffoli gate originating from Stark shifts,” J. Opt. Soc. Am. B 29, 1203–1207 (2012). [CrossRef]
  11. W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and J. F. Du, “One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” Appl. Phys. Lett. 96, 241113 (2010). [CrossRef]
  12. C. P. Yang, Y. X. Liu, and F. Nori, “Phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 81, 062323 (2010). [CrossRef]
  13. C. P. Yang, S. B. Zheng, and F. Nori, “Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 82, 062326 (2010). [CrossRef]
  14. V. M. Stojanović, A. Fedorov, A. Wallraff, and C. Bruder, “Quantum-control approach to realizing a Toffoli gate in circuit QED,” Phys. Rev. B 85, 054504 (2012).
  15. A. M. Chen, S. Y. Cho, and M. D. Kim, “Implementation of a three-qubit Toffoli gate in a single step,” Phys. Rev. A 85, 032326 (2012). [CrossRef]
  16. C. Jones, “Composite Toffoli gate with two-round error detection,” Phys. Rev. A 87, 052334 (2013). [CrossRef]
  17. E. Fredkin and T. Toffoli, “Conservative logic,” Int. J. Theor. Phys. 21, 219–253 (1982). [CrossRef]
  18. A. Barenco, A. Berthiaume, D. Deutsch, A. Ekert, R. Jozsa, and C. Macchiavello, “Stabilisation of quantum computations by symmetrisation,” SIAM J. Comput. 26, 1541–1557 (1997). [CrossRef]
  19. I. L. Chuang and Y. Yamamoto, “Simple quantum computer,” Phys. Rev. A 52, 3489–3496 (1995). [CrossRef]
  20. G. J. Milburn, “Quantum optical Fredkin gate,” Phys. Rev. Lett. 62, 2124–2127 (1989). [CrossRef]
  21. J. Fiurášek, “Linear-optics quantum Toffoli and Fredkin gates,” Phys. Rev. A 73, 062313 (2006). [CrossRef]
  22. J. Fiurášek, “Linear optical Fredkin gate based on partial-SWAP gate,” Phys. Rev. A 78, 032317 (2008). [CrossRef]
  23. Y. X. Gong, G. C. Guo, and T. C. Ralph, “Methods for a linear optical quantum Fredkin gate,” Phys. Rev. A 78, 012305 (2008). [CrossRef]
  24. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009). [CrossRef]
  25. Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009). [CrossRef]
  26. X. B. Zou, J. Kim, and H. W. Lee, “Generation of two-mode nonclassical motional states and a Fredkin gate operation in a two-dimensional ion trap,” Phys. Rev. A 63, 065801 (2001). [CrossRef]
  27. B. Wang and L. M. Duan, “Implementation scheme of controlled SWAP gates for quantum fingerprinting and photonic quantum computation,” Phys. Rev. A 75, 050304(R) (2007). [CrossRef]
  28. J. Song, Y. Xia, and H. S. Song, “Quantum gate operations using atomic qubits through cavity input-output process,” Europhys. Lett. 87, 50005 (2009). [CrossRef]
  29. S. B. Zheng, “Implementation of Toffoli gates with a single asymmetric Heisenberg XY interaction,” Phys. Rev. A 87, 042318 (2013). [CrossRef]
  30. X. Q. Shao, T. Y. Zheng, and S. Zhang, “Fast synthesis of the Fredkin gate via quantum Zeno dynamics,” Quant. Info. Proc. 11, 1797–1808 (2012).
  31. D. G. Angelakis, M. F. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 031805(R) (2007). [CrossRef]
  32. E. K. Irish, C. D. Ogden, and M. S. Kim, “Polaritonic characteristics of insulator and superfluid states in a coupled-cavity array,” Phys. Rev. A 77, 033801 (2008). [CrossRef]
  33. J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum Hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008). [CrossRef]
  34. T. C. H. Liew and V. Savona, “Multimode entanglement in coupled cavity arrays,” New J. Phys. 15, 025015 (2013). [CrossRef]
  35. M. J. Hartmann, F. G. S. Brandão, and M. B. Plenio, “Quantum many-body phenomena in coupled cavity arrays,” Laser Photonics Rev. 2, 527–556 (2008), and reference therein. [CrossRef]
  36. A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006). [CrossRef]
  37. Z. Q. Yin and F. L. Li, “Multiatom and resonant interaction scheme for quantum state transfer and logical gates between two remote cavities via an optical fiber,” Phys. Rev. A 75, 012324 (2007). [CrossRef]
  38. Z. B. Yang, H. Z. Wu, W. J. Su, and S. B. Zheng, “Quantum phase gates for two atoms trapped in separate cavities within the null- and single-excitation subspaces,” Phys. Rev. A 80, 012305 (2009). [CrossRef]
  39. Z. B. Yang, Y. Xia, and S. B. Zheng, “Resonant scheme for realizing quantum phase gates for two separate atoms via coupled cavities,” Opt. Commun. 283, 3052–3057 (2010). [CrossRef]
  40. P. Facchi and S. Pascazio, “Quantum Zeno dynamics of a field in a cavity,” Phys. Rev. Lett. 89, 080401 (2002). [CrossRef]
  41. A. Beige, H. Cable, C. Marr, and P. L. Knight, “Speeding up gate operations through dissipation,” Laser Phys. 15, 162–169 (2005).
  42. A. G. White, A. Gilchrist, G. J. Pryde, J. L. O’Brien, M. J. Bremner, and N. K. Langford, “Measuring two-qubit gates,” J. Opt. Soc. Am. B 24, 172–183 (2007). [CrossRef]
  43. M. A. Nielsen, “A simple formula for the average gate fidelity of a quantum dynamical operation,” Phys. Lett. A 303, 249–252 (2002). [CrossRef]
  44. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
  45. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003). [CrossRef]
  46. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005). [CrossRef]
  47. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005). [CrossRef]
  48. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007). [CrossRef]
  49. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2, 741–747 (2008). [CrossRef]
  50. J. Preskill, Lecture Notes on Quantum Computation, see http://www.theory.caltech.edu/people/preskill/ph229 .

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited