Skip to main content
Log in

Compact implementation of the \(\hbox {(SWAP)}^a\) gate on diamond nitrogen-vacancy centers coupled to resonators

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

A compact quantum circuit for implementing the \(\hbox {(SWAP)}^a\) gate for \(0<a\le 1\) on two diamond nitrogen-vacancy centers (NV) is designed by using some input–output processes of a single photon. Our proposal is interesting because the \(\hbox {(SWAP)}^a\) gate is universal for quantum computing, and the diamond NV center has a long coherence time. Our scheme is compact, and additional electronic qubits are not employed, which beats its synthesis procedure in terms of controlled-not gates and single-qubit rotations largely. Moreover, our scheme is feasible with current experiment technology.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Fan, H., Roychowdhury, V., Szkopek, T.: Optimal two-qubit quantum circuits using exchange interactions. Phys. Rev. A 72, 052323 (2005)

    Article  ADS  Google Scholar 

  3. Roberto, J.G.: Effect of the Dzyaloshinski-Moriya term in the quantum \(\text{ SWAP }^\alpha \) gate produced with exchange coupling. Phys. Rev. A 77, 012331 (2008)

    Article  Google Scholar 

  4. Balakrishnan, S., Sankaranarayanan, R.: Entangling characterization of \(\text{ SWAP }^{1/m}\) and controlled unitary gates. Phys. Rev. A 78, 052305 (2008)

    Article  ADS  Google Scholar 

  5. Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Ren, B.C., Wei, H.R., Deng, F.G.: Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity. Laser Phys. Lett. 10, 095202 (2013)

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. 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  Google Scholar 

  14. Xu, G.F., Zhang, J., Tong, D.M., Sjöqvist, E., Kwek, L.C.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces. Phys. Rev. Lett. 109, 170501 (2012)

    Article  ADS  Google Scholar 

  15. Long, G.L., Xiao, L.: Parallel quantum computing in a single ensemble quantum computer. Phys. Rev. A 69, 052303 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  16. Hua, M., Tao, M.J., Deng, F.G.: Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics. Phys. Rev. A 90, 012328 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Beenakker, C.W.J., DiVincenzo, D.P., Emary, C., Kindermann, M.: Charge detection enables free-electron quantum computation. Phys. Rev. Lett. 93, 020501 (2004)

    Article  ADS  Google Scholar 

  19. Lin, Q., Li, J.: Quantum control gates with weak cross-Kerr nonlinearity. Phys. Rev. A 79, 022301 (2009)

    Article  ADS  Google Scholar 

  20. Lin, Q., He, B.: Single-photon logic gates using minimal resources. Phys. Rev. A 80, 042310 (2009)

    Article  ADS  Google Scholar 

  21. 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 

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

    Article  ADS  Google Scholar 

  23. 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. 104, 160503 (2010)

    Article  ADS  Google Scholar 

  24. Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Optically controlled phase gate and teleportation of a controlled-NOT gate for spin qubits in a quantum-dot-microcavity coupled system. Phys. Rev. A 87, 062337 (2013)

    Article  ADS  Google Scholar 

  25. Wang, H.F., Zhu, A.D., Zhang, S.: One-step implementation of multiqubit phase gate with one control qubit and multiple target qubits in coupled cavities. Opt. Lett. 39, 1489–1492 (2014)

    Article  ADS  Google Scholar 

  26. Wang, H.F., Zhu, A.D., Zhang, S.: Physical optimization of quantum error correction circuits with spatially separated quantum dot spins. Opt. Express 21, 12484–12494 (2013)

    Article  ADS  Google Scholar 

  27. Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Deterministic CNOT gate and entanglement swapping for photonic qubits using a quantum-dot spin in a double-sided optical microcavity. Phys. Lett. A. 377, 2870–2876 (2013)

    Article  ADS  MATH  Google Scholar 

  28. Burkard, G.: A cavity-mediated quantum CPHASE gate between NV spin qubits in diamond. arXiv:1402.6351v1

  29. Balasubramanian, G., Neumann, P., Twitchen, D., Markham, M., Kolesov, R., Mizuochi, N., Isoya, J., Achard, J., Beck, J., Tissler, J., Jacques, V., Hemmer, P.R., Jelezko, F., Wrachtrup, J.: Ultralong spin coherence time in isotopically engineered diamond. Nat. Mater. 8, 383–387 (2009)

    Article  ADS  Google Scholar 

  30. Jelezko, F., Gaebel, T., Popa, I., Gruber, A., Wrachtrup, J.: Observation of coherent oscillations in a single electron spin. Phys. Rev. Lett. 92, 076401 (2004)

    Article  ADS  Google Scholar 

  31. Fuchs, G.D., Dobrovitski, V.V., Toyli, D.M., Heremans, F.J., Awschalom, D.D.: Gigahertz dynamics of a strongly driven single quantum spin. Science 326, 1520–1522 (2009)

    Article  ADS  Google Scholar 

  32. Buckley, B.B., Fuchs, G.D., Bassett, L.C., Awschalom, D.D.: Spin-light coherence for single-spin measurement and control in diamond. Science 330, 1212–1215 (2010)

    Article  ADS  Google Scholar 

  33. Robledo, L., Childress, L., Bernien, H., Hensen, B., Alkemade, P.F.A., Hanson, R.: High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011)

    Article  ADS  Google Scholar 

  34. Yang, W.L., Yin, Z.Q., Xu, Z.Y., Feng, M., Du, J.F.: 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)

    Article  ADS  Google Scholar 

  35. Wei, H.R., Deng, F.G.: Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities. Phys. Rev. A 88, 042323 (2013)

    Article  ADS  Google Scholar 

  36. Zhang, S., Shao, X.Q., Chen, L., Zhao, Y.F., Yeon, K.H.: Robust \(\sqrt{\text{ SWAP }}\) gate on nitrogen-vacancy centres via quantum Zeno dynamics. J. Phys. B At. Mol. Opt. Phys. 44, 075505 (2011)

    Article  ADS  Google Scholar 

  37. Jelezko, F., Gaebel, T., Popa, I., Domhan, M., Gruber, A., Wrachtrup, J.: Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501 (2004)

    Article  ADS  Google Scholar 

  38. van der Sar, T., Wang, Z.H., Blok, M.S., Bernien, H., Taminiau, T.H., Toyli, D.M., Lidar, D.A., Awschalom, D.D., Hanson, R., Dobrovitski, V.V.: Decoherence-protected quantum gates for a hybrid solid-state spin register. Nature 484, 82–86 (2012)

    Article  ADS  Google Scholar 

  39. Wang, C., Zhang, Y., Jiao, R.Z., Jin, G.S.: Universal quantum controlled phase gates on photonic qubits based on nitrogen vacancy centers and microcavity resonators. Opt. Express 21, 19252–19260 (2013)

    Article  ADS  Google Scholar 

  40. Ren, B.C., Deng, F.G.: Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities. Laser Phys. Lett. 10, 115201 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Hu, C.Y., Rarity, J.G.: Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity. Phys. Rev. B 83, 115303 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. Cheng, L.Y., Wang, H.F., Zhang, S., Yeon, K.H.: Quantum state engineering with nitrogen-vacancy centers coupled to low-\(Q\) microresonator. Opt. Express 21, 5988–5997 (2013)

    Article  ADS  Google Scholar 

  45. Zheng, A.S., Li, J.H., Yu, R., Lu, X.Y., Wu, Y.: Generation of Greenberger-Horne-Zeilinger state of distant diamond nitrogen-vacancy centers via nanocavity input-output process. Opt. Express 20, 16902 (2012)

    Article  ADS  Google Scholar 

  46. Chen, Q., Feng, M.: Quantum gating on neutral atoms in low-\(Q\) cavities by a single-photon input-output process. Phys. Rev. A 79, 064304 (2009)

    Article  ADS  Google Scholar 

  47. Wang, T.J., Song, S.Y., Long, G.L.: Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities. Phys. Rev. A 85, 062311 (2012)

    Article  ADS  Google Scholar 

  48. 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 86, 042337 (2012)

    Article  ADS  Google Scholar 

  49. Wang, C.: Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system. Phys. Rev. A 86, 012323 (2012)

    Article  ADS  Google Scholar 

  50. Wang, C., Zhang, Y., Jin, G.S.: Entanglement purification and concentration of electron-spin entangled states using quantum dot spinsin optical microcavities. Phy. Rev. A 84, 032307 (2011)

    Article  ADS  Google Scholar 

  51. Luxmoore, I.J., Ahmadi, E.D., Luxmoore, B.J., Wasley, N.A., Tartakovskii, A.I., Hugues, M., Skolnick, M.S., Fox, A.M.: Restoring mode degeneracy in H1 photonic crystal cavities by uniaxial strain tuning. Appl. Phys. Lett. 100, 121116 (2012)

    Article  ADS  Google Scholar 

  52. Bonato, C., Ding, D., Gudat, J., Thon, S., Kim, H., Petroff, P.M., van Exter, M.P., Bouwmeester, D.: Tuning micropillar cavity birefringence by laser induced surface defects. Appl. Phys. Lett. 95, 251104 (2009)

    Article  ADS  Google Scholar 

  53. Gudat, J., Bonato, C., van Nieuwenburg, E., Thon, S., Kim, H., Petroff, P.M., van Exter, M.P., Bouwmeester, D.: Permanent tuning of quantum dot transitions to degenerate microcavity resonances. Appl. Phys. Lett. 98, 121111 (2011)

    Article  ADS  Google Scholar 

  54. Bonato, C., van Nieuwenburg, E., Gudat, J., Thon, S., Kim, H., van Exter, M.P., Bouwmeester, D.: Strain tuning of quantum dot optical transitions via laser-induced surface defects. Phys. Rev. B 84, 075306 (2011)

    Article  ADS  Google Scholar 

  55. Albrecht, R., Bommer, A., Deutsch, C., Reichel, J., Becher, C.: Coupling of a single nitrogen-vacancy center in diamond to a fiber-based microcavity. Phys. Rev. Lett. 110, 243602 (2013)

    Article  ADS  Google Scholar 

  56. Manson, N.B., Harrison, J.P., Sellars, M.J.: Nitrogen-vacancy center in diamond: model of the electronic structure and associated dynamics. Phys. Rev. B 74, 104303 (2006)

    Article  ADS  Google Scholar 

  57. Togan, E., Chu, Y., Trifonov, A.S., Jiang, L., Maze, J., Childress, L., Dutt, M.V.G.: Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010)

    Article  ADS  Google Scholar 

  58. Walls, D.F., Milburn, G.J.: Quantum Optics. Springer, Berlin (1994)

    Book  MATH  Google Scholar 

  59. 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 

  60. Chen, Q., Yang, W.L., Feng, M., Du, J.F.: Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators. Phys. Rev. A 83, 054305 (2011)

    Article  ADS  Google Scholar 

  61. Shende, V.V., Bullock, S.S., Markov, I.L.: Recongnizing small-circuit structure in two-qubit operations. Phys. Rev. A 70, 012310 (2004)

    Article  ADS  Google Scholar 

  62. Vatan, F., Williams, C.: Optimal quantum circuits for general two-qubit gates. Phys. Rev. A 69, 032315 (2004)

    Article  ADS  Google Scholar 

  63. Zhang, Y.S., Ye, M.Y., Guo, G.C.: Conditions for optimal construction of two-qubit nonlocal gates. Phys. Rev. A 71, 062331 (2005)

    Article  ADS  Google Scholar 

  64. 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 

  65. Larsson, M., Dinyari, K.N., Wang, H.: Composite optical microcavity of diamond nanopillar and silica microsphere. Nano Lett. 9, 1447–1450 (2009)

    Article  ADS  Google Scholar 

  66. Barclay, P.E., Fu, K.M., Santori, C., Beausoleil, R.G.: Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers. Opt. Express 17, 9588–9601 (2009)

    Article  ADS  Google Scholar 

  67. Bernien, H., Hensen, B., Pfaff, W., Koolstra, G., Blok, M.S., Robledo, L., Taminiau, T.H., Markham, M., Twitchen, D.J., Childress, L., Hanson, R.: Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86 (2013)

    Article  ADS  Google Scholar 

  68. Liang, L.M., Li, C.Z.: Realization of quantum SWAP gate between flying and stationary qubits. Phys. Rev. A 72, 024303 (2005)

    Article  ADS  Google Scholar 

  69. Koshino, K., Ishizaka, S., Nakamura, Y.: Deterministic photon-photon \(\sqrt{\text{ SWAP }}\) gate using a \(\Lambda \) system. Phys. Rev. A 82, 010301 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 11174039 and NECT-11-0031.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fu-Guo Deng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, HR., Deng, FG. Compact implementation of the \(\hbox {(SWAP)}^a\) gate on diamond nitrogen-vacancy centers coupled to resonators. Quantum Inf Process 14, 465–477 (2015). https://doi.org/10.1007/s11128-014-0868-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-014-0868-x

Keywords

Navigation