Abstract

Here we investigate a physical implementation of the universal quantum controlled phase (CPHASE) gate operation on photonic qubits by using nitrogen vacancy (N-V) centers and microcavity resonators. The quantum CPHASE gate can be achieved by sending the photons through the microcavity and interacting with the N-V center. The proposed scheme can be further used for scalable quantum computation. We show that this technique provides us a deterministic source of cluster state generation on photonic qubits. In this scheme, only single photons and single N-V center are required and the proposed schemes are feasible with the current experimental technology.

© 2013 OSA

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    [CrossRef] [PubMed]
  4. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett.104, 010503 (2010).
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    [CrossRef] [PubMed]
  10. Q. Chen, W. L. Yang, M. Fang, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
    [CrossRef]
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  25. Z. R. Lin, G. P. Guo, T. Tu, F. Y. Zhu, and G. C. Guo, “Generation of quantum-dot cluster states with a superconducting transmission line resonator,” Phys. Rev. Lett.101, 230501 (2008).
    [CrossRef] [PubMed]
  26. J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, “Efficient one-step generation of large cluster states with solid-state circuits,” Phys. Rev. A75, 052319 (2007).
    [CrossRef]
  27. Y. X. Liu, L. F. Wei, J. S. Tsai, and F. Nori, “Controllable coupling between flux qubits,” Phys. Rev. Lett.96, 067003 (2006).
    [CrossRef] [PubMed]
  28. P. E. Barclay, K. -M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers,” Opt. Express17, 9588–9601 (2009).
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  29. P. E. Barclay, C. Santori, K.-M. Fu, R. G. Beausoleil, and O. Painter, “Coherent interference effects in a nano-assembled diamond NV center cavity-QED system,” Opt. Express17, 8081–8097 (2009).
    [CrossRef] [PubMed]
  30. P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
    [CrossRef] [PubMed]
  31. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
    [CrossRef] [PubMed]

2012 (1)

C. Wang, Y. Zhang, G. S. Jin, and R. Zhang, “Efficient entanglement purification of separate nitrogen-vacancy centers via coupling to microtoroidal resonators,” J. Opt. Soc. Ame. B29(12), 3349–3354 (2012).
[CrossRef]

2011 (4)

Q. Chen, W. L. Yang, M. Fang, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
[CrossRef]

K. Lemr, A. Cernoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dusek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett.106, 013602 (2011).
[CrossRef] [PubMed]

R. Ukai, S. Yokoyama, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett.107, 250501 (2011).
[CrossRef]

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A84, 010301(R)(2011).
[CrossRef]

2010 (4)

W. L. Yang, Z. Y. Xu, M. Feng, and J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys.12, 113039 (2010).
[CrossRef]

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett.104, 010503 (2010).
[CrossRef]

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A82, 022331 (2010).
[CrossRef]

2009 (5)

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A, 79, 022301 (2009).
[CrossRef]

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

P. E. Barclay, C. Santori, K.-M. Fu, R. G. Beausoleil, and O. Painter, “Coherent interference effects in a nano-assembled diamond NV center cavity-QED system,” Opt. Express17, 8081–8097 (2009).
[CrossRef] [PubMed]

P. E. Barclay, K. -M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers,” Opt. Express17, 9588–9601 (2009).
[CrossRef] [PubMed]

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A79, 032303 (2009).
[CrossRef]

2008 (4)

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef] [PubMed]

Y. F. Xiao, J. Gao, X. B. Zou, J. F. McMillan, X. Yang, Y. L. Chen, Z. F. Han, G. C. Guo, and C. W. Wong, “Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations,” New J. Phys.10, 123013 (2008).
[CrossRef]

Z. R. Lin, G. P. Guo, T. Tu, F. Y. Zhu, and G. C. Guo, “Generation of quantum-dot cluster states with a superconducting transmission line resonator,” Phys. Rev. Lett.101, 230501 (2008).
[CrossRef] [PubMed]

2007 (3)

J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, “Efficient one-step generation of large cluster states with solid-state circuits,” Phys. Rev. A75, 052319 (2007).
[CrossRef]

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A75, 042323 (2007).
[CrossRef]

X. B. Zou, S.L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A75, 034302 (2007).
[CrossRef]

2006 (2)

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

Y. X. Liu, L. F. Wei, J. S. Tsai, and F. Nori, “Controllable coupling between flux qubits,” Phys. Rev. Lett.96, 067003 (2006).
[CrossRef] [PubMed]

2005 (3)

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature434, 169–176 (2005)
[CrossRef] [PubMed]

N.K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett.95, 210504 (2005).
[CrossRef] [PubMed]

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

2004 (1)

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett.93, 040503 (2004).
[CrossRef] [PubMed]

2003 (2)

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

X. Q. Li, Y. W. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science301, 809–811 (2003).
[CrossRef]

2001 (1)

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett.86, 5188–5191 (2001)
[CrossRef] [PubMed]

Achard, J.

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

An, J. H.

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A79, 032303 (2009).
[CrossRef]

Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature434, 169–176 (2005)
[CrossRef] [PubMed]

Awschalom, D. D.

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

Balasubramanian, G.

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

Barclay, P. E.

Beausoleil, R. G.

Becher, C.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Beck, J.

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

Blatt, R.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Briegel, H. J.

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett.86, 5188–5191 (2001)
[CrossRef] [PubMed]

Cernoch, A.

K. Lemr, A. Cernoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dusek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett.106, 013602 (2011).
[CrossRef] [PubMed]

Chen, Q.

Q. Chen, W. L. Yang, M. Fang, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
[CrossRef]

Chen, Y. A.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

Chen, Y. L.

Y. F. Xiao, J. Gao, X. B. Zou, J. F. McMillan, X. Yang, Y. L. Chen, Z. F. Han, G. C. Guo, and C. W. Wong, “Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations,” New J. Phys.10, 123013 (2008).
[CrossRef]

Childress, L.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

Chu, Y.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

Dayan, B.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

Deuschle, T.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Du, J. F.

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A84, 010301(R)(2011).
[CrossRef]

Q. Chen, W. L. Yang, M. Fang, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
[CrossRef]

W. L. Yang, Z. Y. Xu, M. Feng, and J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys.12, 113039 (2010).
[CrossRef]

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

Dusek, M.

K. Lemr, A. Cernoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dusek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett.106, 013602 (2011).
[CrossRef] [PubMed]

Dutt, M.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

Eisert, J.

K. Lemr, A. Cernoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dusek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett.106, 013602 (2011).
[CrossRef] [PubMed]

Epstein, R. J.

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

Eschner, J.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Fang, M.

Q. Chen, W. L. Yang, M. Fang, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
[CrossRef]

Feng, M.

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A84, 010301(R)(2011).
[CrossRef]

W. L. Yang, Z. Y. Xu, M. Feng, and J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys.12, 113039 (2010).
[CrossRef]

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[CrossRef]

Sorensen, A. S.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

Soubusta, J.

K. Lemr, A. Cernoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dusek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett.106, 013602 (2011).
[CrossRef] [PubMed]

Spiller, T. P.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A75, 042323 (2007).
[CrossRef]

Steel, D.

X. Q. Li, Y. W. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science301, 809–811 (2003).
[CrossRef]

Stievater, T. H.

X. Q. Li, Y. W. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science301, 809–811 (2003).
[CrossRef]

Tanamoto, T.

J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, “Efficient one-step generation of large cluster states with solid-state circuits,” Phys. Rev. A75, 052319 (2007).
[CrossRef]

Taylor, J. M.

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

Tissler, J.

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

Togan, E.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

Trifonov, A. S.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

Tsai, J. S.

Y. X. Liu, L. F. Wei, J. S. Tsai, and F. Nori, “Controllable coupling between flux qubits,” Phys. Rev. Lett.96, 067003 (2006).
[CrossRef] [PubMed]

Tu, T.

Z. R. Lin, G. P. Guo, T. Tu, F. Y. Zhu, and G. C. Guo, “Generation of quantum-dot cluster states with a superconducting transmission line resonator,” Phys. Rev. Lett.101, 230501 (2008).
[CrossRef] [PubMed]

Twitchen, D.

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

Ukai, R.

R. Ukai, S. Yokoyama, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett.107, 250501 (2011).
[CrossRef]

Urban, E.

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett.104, 010503 (2010).
[CrossRef]

Vahala, K. J.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

van Loock, P.

R. Ukai, S. Yokoyama, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett.107, 250501 (2011).
[CrossRef]

Vedral, V.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature434, 169–176 (2005)
[CrossRef] [PubMed]

Walker, T. G.

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett.104, 010503 (2010).
[CrossRef]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin Heidelberg, 1994).

Walther, P.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature434, 169–176 (2005)
[CrossRef] [PubMed]

Wang, C.

C. Wang, Y. Zhang, G. S. Jin, and R. Zhang, “Efficient entanglement purification of separate nitrogen-vacancy centers via coupling to microtoroidal resonators,” J. Opt. Soc. Ame. B29(12), 3349–3354 (2012).
[CrossRef]

Wang, X. B.

J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, “Efficient one-step generation of large cluster states with solid-state circuits,” Phys. Rev. A75, 052319 (2007).
[CrossRef]

Watanabe, H.

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef] [PubMed]

Wei, L. F.

Y. X. Liu, L. F. Wei, J. S. Tsai, and F. Nori, “Controllable coupling between flux qubits,” Phys. Rev. Lett.96, 067003 (2006).
[CrossRef] [PubMed]

Weinfurter, H.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature434, 169–176 (2005)
[CrossRef] [PubMed]

Weinhold, T. J.

N.K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett.95, 210504 (2005).
[CrossRef] [PubMed]

White, A. G.

N.K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett.95, 210504 (2005).
[CrossRef] [PubMed]

Wong, C. W.

Y. F. Xiao, J. Gao, X. B. Zou, J. F. McMillan, X. Yang, Y. L. Chen, Z. F. Han, G. C. Guo, and C. W. Wong, “Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations,” New J. Phys.10, 123013 (2008).
[CrossRef]

Wrachtrup, J.

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

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef] [PubMed]

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

Wu, Y. W.

X. Q. Li, Y. W. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science301, 809–811 (2003).
[CrossRef]

Xiao, Y. F.

Y. F. Xiao, J. Gao, X. B. Zou, J. F. McMillan, X. Yang, Y. L. Chen, Z. F. Han, G. C. Guo, and C. W. Wong, “Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations,” New J. Phys.10, 123013 (2008).
[CrossRef]

Xu, Z. Y.

W. L. Yang, Z. Y. Xu, M. Feng, and J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys.12, 113039 (2010).
[CrossRef]

Yamasaki, S.

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef] [PubMed]

Yang, T.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

Yang, W. L.

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A84, 010301(R)(2011).
[CrossRef]

Q. Chen, W. L. Yang, M. Fang, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
[CrossRef]

W. L. Yang, Z. Y. Xu, M. Feng, and J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys.12, 113039 (2010).
[CrossRef]

Yang, X.

Y. F. Xiao, J. Gao, X. B. Zou, J. F. McMillan, X. Yang, Y. L. Chen, Z. F. Han, G. C. Guo, and C. W. Wong, “Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations,” New J. Phys.10, 123013 (2008).
[CrossRef]

Yin, Z. Q.

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A84, 010301(R)(2011).
[CrossRef]

Yokoyama, S.

R. Ukai, S. Yokoyama, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett.107, 250501 (2011).
[CrossRef]

Yoshikawa, J.

R. Ukai, S. Yokoyama, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett.107, 250501 (2011).
[CrossRef]

You, J. Q.

J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, “Efficient one-step generation of large cluster states with solid-state circuits,” Phys. Rev. A75, 052319 (2007).
[CrossRef]

Zeilinger, A.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature434, 169–176 (2005)
[CrossRef] [PubMed]

Zhang, A. N.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

Zhang, H.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

Zhang, R.

C. Wang, Y. Zhang, G. S. Jin, and R. Zhang, “Efficient entanglement purification of separate nitrogen-vacancy centers via coupling to microtoroidal resonators,” J. Opt. Soc. Ame. B29(12), 3349–3354 (2012).
[CrossRef]

Zhang, S.L.

X. B. Zou, S.L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A75, 034302 (2007).
[CrossRef]

Zhang, X. L.

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett.104, 010503 (2010).
[CrossRef]

Zhang, Y.

C. Wang, Y. Zhang, G. S. Jin, and R. Zhang, “Efficient entanglement purification of separate nitrogen-vacancy centers via coupling to microtoroidal resonators,” J. Opt. Soc. Ame. B29(12), 3349–3354 (2012).
[CrossRef]

Zhao, Z.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

Zhu, F. Y.

Z. R. Lin, G. P. Guo, T. Tu, F. Y. Zhu, and G. C. Guo, “Generation of quantum-dot cluster states with a superconducting transmission line resonator,” Phys. Rev. Lett.101, 230501 (2008).
[CrossRef] [PubMed]

Zibrov, A. S.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

Zou, X. B.

Y. F. Xiao, J. Gao, X. B. Zou, J. F. McMillan, X. Yang, Y. L. Chen, Z. F. Han, G. C. Guo, and C. W. Wong, “Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations,” New J. Phys.10, 123013 (2008).
[CrossRef]

X. B. Zou, S.L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A75, 034302 (2007).
[CrossRef]

J. Opt. Soc. Ame. B (1)

C. Wang, Y. Zhang, G. S. Jin, and R. Zhang, “Efficient entanglement purification of separate nitrogen-vacancy centers via coupling to microtoroidal resonators,” J. Opt. Soc. Ame. B29(12), 3349–3354 (2012).
[CrossRef]

Nat. Mater. (1)

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

Nature (3)

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. Dutt, A. S. Sorensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, Quantum entanglement between an optical photon and a solid-state spin qubit, Nature466, 730–734 (2010).
[CrossRef] [PubMed]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature434, 169–176 (2005)
[CrossRef] [PubMed]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

New J. Phys. (2)

W. L. Yang, Z. Y. Xu, M. Feng, and J. F. Du, “Entanglement of separate nitrogen-vacancy centers coupled to a whispering-gallery mode cavity,” New J. Phys.12, 113039 (2010).
[CrossRef]

Y. F. Xiao, J. Gao, X. B. Zou, J. F. McMillan, X. Yang, Y. L. Chen, Z. F. Han, G. C. Guo, and C. W. Wong, “Coupled quantum electrodynamics in photonic crystal cavities towards controlled phase gate operations,” New J. Phys.10, 123013 (2008).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (8)

J. Q. You, X. B. Wang, T. Tanamoto, and F. Nori, “Efficient one-step generation of large cluster states with solid-state circuits,” Phys. Rev. A75, 052319 (2007).
[CrossRef]

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A75, 042323 (2007).
[CrossRef]

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A82, 022331 (2010).
[CrossRef]

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A, 79, 022301 (2009).
[CrossRef]

W. L. Yang, Z. Q. Yin, Y. Hu, M. Feng, and J. F. Du, “High-fidelity quantum memory using nitrogen-vacancy center ensemble for hybrid quantum computation,” Phys. Rev. A84, 010301(R)(2011).
[CrossRef]

X. B. Zou, S.L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A75, 034302 (2007).
[CrossRef]

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A79, 032303 (2009).
[CrossRef]

Q. Chen, W. L. Yang, M. Fang, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
[CrossRef]

Phys. Rev. Lett. (10)

R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett.97, 087601 (2006);;L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science314, 281–285 (2006).
[CrossRef] [PubMed]

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett.86, 5188–5191 (2001)
[CrossRef] [PubMed]

N.K. Langford, T. J. Weinhold, R. Prevedel, K. J. Resch, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett.95, 210504 (2005).
[CrossRef] [PubMed]

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett.94, 030501 (2005).
[CrossRef] [PubMed]

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett.104, 010503 (2010).
[CrossRef]

K. Lemr, A. Cernoch, J. Soubusta, K. Kieling, J. Eisert, and M. Dusek, “Experimental implementation of the optimal linear-optical controlled phase gate,” Phys. Rev. Lett.106, 013602 (2011).
[CrossRef] [PubMed]

R. Ukai, S. Yokoyama, J. Yoshikawa, P. van Loock, and A. Furusawa, “Demonstration of a controlled-phase gate for continuous-variable one-way quantum computation,” Phys. Rev. Lett.107, 250501 (2011).
[CrossRef]

Z. R. Lin, G. P. Guo, T. Tu, F. Y. Zhu, and G. C. Guo, “Generation of quantum-dot cluster states with a superconducting transmission line resonator,” Phys. Rev. Lett.101, 230501 (2008).
[CrossRef] [PubMed]

M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett.93, 040503 (2004).
[CrossRef] [PubMed]

Y. X. Liu, L. F. Wei, J. S. Tsai, and F. Nori, “Controllable coupling between flux qubits,” Phys. Rev. Lett.96, 067003 (2006).
[CrossRef] [PubMed]

Science (3)

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef] [PubMed]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

X. Q. Li, Y. W. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science301, 809–811 (2003).
[CrossRef]

Other (1)

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin Heidelberg, 1994).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the setup for the construction of CPHASE gate between the photon and the N-V center. PBSs represent the polarization beam splitters which transmit horizontal polarized photons and reflect the vertical polarized photons; and QWPs denote the quarter-wave plates that achieve the polarization changes of the single-photon pulse as HL. In the bubble, the detailed energy configuration is described for N-V center in diamond nanocrystal.

Fig. 2
Fig. 2

Schematic diagram of the setup for the construction of controlled phase gate based on photonic qubits. CPF represents the controlled phase flip operation between the single photon and the N-V centers.

Fig. 3
Fig. 3

The success probabilities of the CPHASE gate versus g / γ κ. Here g represents the coupling strength between the N-V center and the microcavity. κ and γ denote the decay rates of the cavity and the N-V centers, respectively. The left figure represents the success probability of the photon and N-V center CPHASE gate, and the right figure illustrates the success probability of the photonic CPHASE gate operation.

Fig. 4
Fig. 4

The fidelity of the generated cluster state. Here we consider the ideal condition with no cavity leakage. The four curves describe the fidelity of the final cluster state with 2-qubit, 3-qubit, 5-qubit and 7-qubit, respectively.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

d d t a ^ ( t ) = [ i ( ω c ω ) + κ + κ s ] a ^ ( t ) g σ ^ κ a ^ in ( t )
d d t σ ^ = [ i ( ω 0 ω ) + κ ] σ ^ g σ ^ z a ^ ( t ) .
r ( ω ) = [ i ( ω 0 ω p ) + γ 2 ] [ i ( ω c ω p ) κ 2 + κ s 2 ] + g 2 [ i ( ω 0 ω p ) + γ 2 ] [ i ( ω c ω p ) + κ 2 + κ s 2 ] + g 2 .
r ( ω ) = γ κ + 4 g 2 γ κ + 4 g 2 .
| ψ in = ( α | H + β | V ) ( η | + + δ | ) .
| ψ out = α | H ( η | + + δ | ) + β | V ( η | + + δ | ) α η | L , + α δ | L , + β η | V , + + β δ | V , ( α | H σ z N V + β | V ) ( η | + + δ | ) ,
U a j C P | ψ j | ϕ N V | ψ k = [ α 1 2 ( | L | + | L | ) + β 1 2 ( | R | + + | R | ) ] ( α 2 | L + β 2 | R ) .
R ( π / 2 ) : α 1 2 [ | L ( | + + | ) | L ( | + | ) ] + β 1 2 [ | R ( | + + | ) + | R ( | + | ) ] ( α 2 | L + β 2 | R ) .
U a k C P : α 1 α 2 2 [ | L , L ( | + | ) | L , L ( | + + | ) ] + β 1 α 2 2 [ | R , L ( | + | ) + | R , L ( | + + | ) ] + α 1 β 2 2 [ | L , R ( | + + | ) | L , R ( | + | ) ] + β 1 β 2 2 [ | R , R ( | + + | ) + | R , R ( | + | ) ]
R ( π / 2 ) : α 1 α 2 2 | L , L ( | + | ) β 1 α 2 2 | R , L ( | + | ) + α 1 β 2 2 | L , R ( | + + | ) + β 1 β 2 2 | R , R ( | + | ) .
U a j C P : α 1 α 2 2 | L , L ( | | + ) + β 1 α 2 2 | R , L ( | + | ) + α 1 β 2 2 | L , R ( | + | ) + β 1 β 2 2 ( | R , R | + | ) .
| ψ 2 = 1 2 2 ( | R + | L σ z 1 ) 2 ( | R + | L 1 ) ( | + | ) .
| ψ 3 = 1 4 ( | R + | L σ z 2 ) 3 ( | R + | L σ z 1 ) 2 ( | R + | L ) 1 ( | + | ) .
| ψ out = 1 2 n + 2 i = 1 n 1 ( | R + | L σ z n i ) ( | + | ) .

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