Skip to main content
SpringerLink
Log in

Hybrid Toffoli gates with dipole-induced transparency effect in series and parallel cavity-waveguide systems

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We propose two feasible schemes for realizing hybrid Toffoli gates with dipole-induced transparency (DIT) effect in series and parallel cavity-waveguide systems. The gate operations are accomplished by encoding information on flying photon and dipole emitter evanescently coupled to the microcavity, and the spatial as well as polarization states of photon will be flipped conditional on the quantum states of dipole emitters. The schemes could be physically realized in one step and straightforwardly extended to realize the N-qubit Toffoli gate, which greatly simplifies the experimental implementation of Toffoli gate and promises a much higher fidelity compared to those based on elementary gate decomposition. Benefiting from DIT effect, the schemes can be achievable without requirement of strong coupling condition of cavity-waveguide system, and they are insensitive to experimental noises, imperfections and the phase delay of adjacent microcavities, which may be feasible with present accessible technology.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Sleator, T., Weinfurter, H.: Realizable universal quantum logic gates. Phys. Rev. Lett. 74, 4087–4090 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  2. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)

    Article  ADS  Google Scholar 

  3. Toffoli, T.: Automata languages and programming, seventh colloquium. In: de Bakker, J.W., van Leeuwen, J. (eds.) Lectures Notes in Computer Science, vol. 84. Springer, New York (1980)

    Google Scholar 

  4. Cory, D.G., Price, M.D., Maas, W., Knill, E., Laflamme, R., Zurek, W.H., Havel, T.F., Somaroo, S.S.: Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998)

    Article  ADS  Google Scholar 

  5. Aoki, T., Takahashi, G., Kajiya, T., Yoshikawa, J., Braunstein, S.L., Loock, P., Furusawa, A.: Quantum error correction beyond qubits. Nat. Phys. 5, 541–546 (2009)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  7. Lanyon, B.P., Barbieri, M., Almeida, M.P., Jennewein, T., Ralph, T.C., Resch, K.J., Pryde, G.J., O’Brien, J.L., Gilchrist, A., White, A.G.: Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys. 5, 134–140 (2009)

    Article  Google Scholar 

  8. Monz, T., Kim, K., Hansel, W., Riebe, M., Villar, A.S., Schindler, P., Chwalla, M., Hennrich, M., Blatt, R.: Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett. 102, 040501 (2009)

    Article  ADS  Google Scholar 

  9. Reed, M.D., DiCarlo, L., Nigg, S.E., Sun, L., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Realization of three-qubit quantum error correction with superconducting circuits. Nature (London) 482, 382–385 (2012)

    Article  ADS  Google Scholar 

  10. Duan, L.M., Wang, B., Kimble, H.J.: Robust quantum gates on neutral atoms with cavity-assisted photon scattering. Phys. Rev. A 72, 032333 (2005)

    Article  ADS  Google Scholar 

  11. Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565–582 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  12. Chen, C.Y., Feng, M., Gao, K.L.: Toffoli gate originating from a single resonant interaction with cavity QED. Phys. Rev. A 73, 064304 (2006)

    Article  ADS  Google Scholar 

  13. Shao, X.Q., Zhu, A.D., Zhang, S., Chung, J.S., Yeon, K.H.: Efficient scheme for implementing an N-qubit Toffoli gate by a single resonant interaction with cavity quantum electrodynamics. Phys. Rev. A 75, 034307 (2007)

    Article  ADS  Google Scholar 

  14. Chen, A.M., Cho, S.Y., Kim, M.D.: Implementation of a three-qubit Toffoli gate in a single step. Phys. Rev. A 85, 032326 (2012)

    Article  ADS  Google Scholar 

  15. Zheng, S.B.: Implementation of Toffoli gates with a single asymmetric Heisenberg XY interaction. Phys. Rev. A 87, 042318 (2013)

    Article  ADS  Google Scholar 

  16. Takano, H., Song, B.S., Asano, T., Noda, S.: Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal. Appl. Phys. Lett. 86, 241101 (2005)

    Article  ADS  Google Scholar 

  17. Takano, H., Song, B.S., Asano, T., Noda, S.: Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal. Opt. Express 14, 3491–3496 (2006)

    Article  ADS  Google Scholar 

  18. Rokhsari, H., Vahala, K.J.: Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics. Phys. Rev. Lett. 92, 253905 (2004)

    Article  ADS  Google Scholar 

  19. Shen, J.T., Fan, S.: Coherent photon transport from spontaneous emission in one-dimensional waveguides. Opt. Lett. 30, 2001–2003 (2005)

    Article  ADS  Google Scholar 

  20. Zheng, H., Gauthier, D.J., Baranger, H.U.: Waveguide-QED-based photonic quantum computation. Phys. Rev. Lett. 111, 090502 (2013)

    Article  ADS  Google Scholar 

  21. Zheng, H., Gauthier, D.J., Baranger, H.U.: Waveguide QED: many-body bound-state effects in coherent and Fock-state scattering from a two-level system. Phys. Rev. A 82, 063816 (2010)

    Article  ADS  Google Scholar 

  22. Lodahl, P., Mahmoodian, S., Stobbe, S.: Interfacing single photons and single quantum dots with photonic nanostructures. Rev. Mod. Phys. 87, 347–400 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  23. Neumann, P., Mizuochi, N., Rempp, F., Hemmer, P., Watanabe, H., Yamasaki, S., Jacques, V., Gaebel, T., Jelezko, F., Wrachtrup, J.: Multipartite entanglement among single spins in diamond. Science 320, 1326–1329 (2008)

    Article  ADS  Google Scholar 

  24. Doherty, M.W., Manson, N.B., Delaney, P., Jelezko, F., Wrachtrup, J., Hollenberg, L.C.L.: The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013)

    Article  ADS  Google Scholar 

  25. Waks, E., Vuckovic, J.: Dipole induced transparency in drop-filter cavity-waveguide systems. Phys. Rev. Lett. 96, 153601 (2006)

    Article  ADS  Google Scholar 

  26. Waks, E., Vuckovic, J.: Dispersive properties and large Kerr nonlinearities using dipole-induced transparency in a single-sided cavity. Phys. Rev. A 73, 041803 (2006)

    Article  ADS  Google Scholar 

  27. Faraon, A., Fushman, I., Englund, D., Stoltz, N., Petroff, P., Vuckovic, J.: Dipole induced transparency in waveguide coupled photonic crystal cavities. Opt. Express 16, 12154–12162 (2008)

    Article  ADS  Google Scholar 

  28. Peng, Z.H., Jia, C.X., Zhang, Y.Q., Zhu, Z.H., Liu, X.J.: Hybrid transparency effect in the drop-filter cavity-waveguide system. Opt. Commun. 427, 363–368 (2018)

    Article  ADS  Google Scholar 

  29. Chang, D.E., Sorensen, A.S., Demler, E.A., Lukin, M.D.: A single-photon transistor using nanoscale surface plasmons. Nat. Phys. 3, 807–812 (2007)

    Article  Google Scholar 

  30. Shen, J.T., Fan, S.: Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits. Phys. Rev. Lett. 95, 213001 (2005)

    Article  ADS  Google Scholar 

  31. Zhou, L., Gong, Z.R., Liu, Y.x, Sun, C.P., Nori, F.: Controllable scattering of a single photon inside a one-dimensional resonator waveguide. Phys. Rev. Lett. 101, 100501 (2008)

    Article  ADS  Google Scholar 

  32. Sun, S., Kim, H., Solomon, G.S., Waks, E.: A quantum phase switch between a single solid-state spin and a photon. Nat. Nanotech. 11, 539–544 (2016)

    Article  ADS  Google Scholar 

  33. Leuenberger, M.N., Flatte, M.E., Awschalom, D.D.: Teleportation of electronic many-qubit states encoded in the electron spin of quantum dots via single photons. Phys. Rev. Lett. 94, 107401 (2005)

    Article  ADS  Google Scholar 

  34. An, J.H., Feng, M., Oh, C.H.: Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities. Phys. Rev. A 79, 032303 (2009)

    Article  ADS  Google Scholar 

  35. Hu, C.Y., Young, A., O’Brien, J.L., Munro, W.J., Rarity, J.G.: 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 78, 085307 (2008)

    Article  ADS  Google Scholar 

  36. Peng, Z.H., Zou, J., Liu, X.J., Xiao, Y.J., Kuang, L.M.: Atomic and photonic entanglement concentration via photonic Faraday rotation. Phys. Rev. A 86, 034305 (2012)

    Article  ADS  Google Scholar 

  37. Peng, Z.H., Kuang, L.M., Zou, J., Liu, X.J.: Quantum controlled-not gate in the bad cavity regime. Quantum Inf. Process 14, 2833–2846 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  38. Feng, L., El-Ganainy, R., Ge, L.: Non-Hermitian photonics based on parity-time symmetry. Nat. Photon. 11, 752–762 (2017)

    Article  ADS  Google Scholar 

  39. Peng, B., Özdemir, S.K., Lei, F., Monifi, F., Gianfreda, M., Long, G.L., Fan, S., Nori, F., Bender, C.M., Yang, L.: Parity-time-symmetric whispering-gallery microcavities. Nat. Phys. 10, 394–398 (2014)

    Article  Google Scholar 

  40. Chang, L., Jiang, X., Hua, S., Yang, C., Wen, J., Jiang, L., Li, G., Wang, G., Xiao, M.: Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators. Nat. Photon. 8, 524–529 (2014)

    Article  ADS  Google Scholar 

  41. Peng, B., Özdemir, S.K., Rotter, S., Yilmaz, H., Liertzer, M., Monifi, F., Bender, C.M., Nori, F., Yang, L.: Loss-induced suppression and revival of lasing. Science 346, 328–332 (2014)

    Article  ADS  Google Scholar 

  42. Wei, H.R., Deng, F.G.: Scalable photonic quantum computing assisted by quantum-dot spin in double-sided optical microcavity. Opt. Express 21, 17671–17685 (2013)

    Article  ADS  Google Scholar 

  43. Wei, H.R., Deng, F.G.: Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities. Opt. Express 22, 593–607 (2014)

    Article  ADS  Google Scholar 

  44. Luo, M.X., Ma, S.Y., Chen, X.B., Wang, X.: Hybrid Toffoli gate on photons and quantum spins. Sci. Rep. 5, 16716 (2015)

    Article  ADS  Google Scholar 

  45. Wei, H.R., Deng, F.G., Long, G.L.: Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities. Opt. Express 24, 18619–18630 (2016)

    Article  ADS  Google Scholar 

  46. Wang, T.J., Wang, C.: Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator. Phys. Rev. A 90, 052310 (2014)

    Article  ADS  Google Scholar 

  47. Wei, H.R., Long, G.L.: Hybrid quantum gates between flying photon and diamond nitrogen-vacancy centers assisted by optical microcavities. Sci. Rep. 5, 12918 (2015)

    Article  ADS  Google Scholar 

  48. Ren, B.C., Wang, G.Y., Deng, F.G.: Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime. Phys. Rev. A 91, 032328 (2015)

    Article  ADS  Google Scholar 

  49. Walls, D.F., Milburn, G.J.: Quantum Optics, 2nd edn. Springer, New York (2008)

    Book  Google Scholar 

  50. Xiao, Y.F., Li, M., Liu, Y.C., Li, Y., Sun, X., Gong, Q.: Asymmetric Fano resonance analysis in indirectly coupled microresonators. Phys. Rev. A 82, 065804 (2010)

    Article  ADS  Google Scholar 

  51. Lu, H., Liu, X., Mao, D., Wang, G.: Plasmonic nanosensor based on Fano resonance in waveguide-coupled resonators. Opt. Lett. 37, 3780–3782 (2012)

    Article  ADS  Google Scholar 

  52. Thompson, R.J., Rempe, G., Kimble, H.J.: Observation of normal-mode splitting for an atom in an optical cavity. Phys. Rev. Lett. 68, 1132–1135 (1992)

    Article  ADS  Google Scholar 

  53. Purcell, E.M.: Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946)

    Article  Google Scholar 

  54. Xiao, Y.F., Zou, X.B., Jiang, W., Chen, Y.L., Guo, G.C.: Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems. Phys. Rev. A 75, 063833 (2007)

    Article  ADS  Google Scholar 

  55. Xiao, Y.F., Gao, J., Zou, X.B., McMillan, J.F., Yang, X., Chen, Y.L., Han, Z.F., Guo, G.C., Wong, C.W.: Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gateoperations. New J. Phys. 10, 123013 (2008)

    Article  ADS  Google Scholar 

  56. Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  57. Peng, Z.H., Zou, J., Liu, X.J.: Scheme for implementing efficient quantum information processing with multiqubit W-class states in cavity QED. J. Phys. B At. Mol. Opt. Phys. 41, 065505 (2008)

    Article  Google Scholar 

  58. Dicke, R.H.: Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954)

    Article  ADS  Google Scholar 

  59. Peng, Z.H., Zou, J., Liu, X.J.: Perfect quantum information processing with Dicke-class state. Eur. Phys. J. D 58, 403–407 (2010)

    Article  ADS  Google Scholar 

  60. Vahala, K.J.: Optical microcavities. Nature 424, 839–846 (2003)

    Article  ADS  Google Scholar 

  61. Hausmann, B.J.M., Shields, B., Quan, Q., Maletinsky, P., McCutcheon, M., Choy, J.T., Babinec, T.M., Kubanek, A., Yacoby, A., Lukin, M.D., Loncar, M.: Integrated diamond networks for quantum nanophotonics. Nano. Lett. 12, 1578–1582 (2012)

    Article  ADS  Google Scholar 

  62. Barclay, P.E., Fu, K.M.C., Santori, C., Beausoleil, R.G.: Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond. Appl. Phys. Lett. 95, 191115 (2009)

    Article  ADS  Google Scholar 

  63. Liu, Y.C., Xiao, Y.F., Li, B.B., Jiang, X.F., Li, Y., Gong, Q.: Coupling of a single diamond nanocrystal to a whispering-gallery microcavity: photon transport benefitting from Rayleigh scattering. Phys. Rev. A 84, 011805(R) (2011)

    Article  ADS  Google Scholar 

  64. Wolters, J., Sadzak, N., Schell, A.W., Schroder, T., Benson, O.: Measurement of the ultrafast spectral diffusion of the optical transition of nitrogen vacancy centers in nano-size diamond using correlation interferometry. Phys. Rev. Lett. 110, 027401 (2013)

    Article  ADS  Google Scholar 

  65. Chu, Y., de Leon, N.P., Shields, B.J., Hausmann, B., Evans, R., Togan, E., Burek, M.J., Markham, M., Stacey, A., Zibrov, A.S., Yacoby, A., Twitchen, D.J., Loncar, M., Park, H., Maletinsky, P., Lukin, M.D.: Coherent optical transitions in implanted nitrogen vacancy centers. Nano. Lett. 14, 1982–1986 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Z. H. Peng, C. X. Jia and X. J. Liu were supported by the National Science Foundation of China (NSFC) under Grants No. 11405052 and Photoelectric Information Technology Open Foundation Project of Hunan Applied Basic Research Base under Grants No. GD19K04. Y. Q. Zhang and Z. H. Zhu were supported by NSFC under Grants Nos. 11504104 and 11704115. J. B. Yuan and S. Q. Tang were supported by NSFC under Grants Nos. 11547258 and 11647129. L. M. Kuang was supported by NSFC under Grants Nos. 11775075 and 11434011.

Author information

Authors and Affiliations

  1. Institute of Modern Physics and Department of Physics, College of Physics and Electronic Science, Hunan University of Science and Technology, Xiangtan, 411201, China

    Zhao-Hui Peng, Chun-Xia Jia, Yu-Qing Zhang, Zhong-Hua Zhu & Xiao-Juan Liu

  2. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Chun-Xia Jia & Le-Man Kuang

  3. College of Physics and Electronic Engineering, and Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang Normal University, Hengyang, 421008, China

    Shi-Qing Tang & Ji-Bing Yuan

Authors
  1. Zhao-Hui Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chun-Xia Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu-Qing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhong-Hua Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shi-Qing Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ji-Bing Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Xiao-Juan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Le-Man Kuang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhao-Hui Peng.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Peng, ZH., Jia, CX., Zhang, YQ. et al. Hybrid Toffoli gates with dipole-induced transparency effect in series and parallel cavity-waveguide systems. Quantum Inf Process 18, 284 (2019). https://doi.org/10.1007/s11128-019-2400-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2400-9

Keywords

Search

Navigation