Universal quantum controlled phase gate on photonic qubits based on nitrogen vacancy centers and microcavity resonators

Chuan Wang; Yong Zhang; Rong-zhen Jiao; Guang-sheng Jin

doi:10.1364/OE.21.019252

Universal quantum controlled phase gate on photonic qubits based on nitrogen vacancy centers and microcavity resonators

Chuan Wang, Yong Zhang, Rong-zhen Jiao, and Guang-sheng Jin

Optics Express
Vol. 21,
Issue 16,
pp. 19252-19260
(2013)
•https://doi.org/10.1364/OE.21.019252

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Chuan Wang, Yong Zhang, Rong-zhen Jiao, and Guang-sheng Jin, "Universal quantum controlled phase gate on photonic qubits based on nitrogen vacancy centers and microcavity resonators," Opt. Express 21, 19252-19260 (2013)

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Related Topics
Table of Contents Category
- Quantum Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Quantum optics (270.0270)
- Quantum cryptography (270.5568)
- Quantum information and processing (270.5585)

About this Article
History
- Original Manuscript: May 8, 2013
- Revised Manuscript: July 20, 2013
- Manuscript Accepted: July 20, 2013
- Published: August 6, 2013

Accessible

Open Access

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.

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References

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Publication

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,” Nature 422, 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,” Science 301, 809–811 (2003).
[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]
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]
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]
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. A 84, 010301(R)(2011).
[Crossref]
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,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]
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. A 83, 054305 (2011).
[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, Nature 466, 730–734 (2010).
[Crossref] [PubMed]
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. B 29(12), 3349–3354 (2012).
[Crossref]
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,” Science 314, 281–285 (2006).
[Crossref] [PubMed]
D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin Heidelberg, 1994).
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. A 79, 032303 (2009).
[Crossref]
R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001)
[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,” Nature 434, 169–176 (2005)
[Crossref] [PubMed]
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. A 75, 034302 (2007).
[Crossref]
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]
Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A, 79, 022301 (2009).
[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]
M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. 93, 040503 (2004).
[Crossref] [PubMed]
S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 042323 (2007).
[Crossref]
Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
[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]
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. A 75, 052319 (2007).
[Crossref]
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]
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. Express 17, 9588–9601 (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. Express 17, 8081–8097 (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,” Science 320, 1326–1329 (2008).
[Crossref] [PubMed]
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. B 29(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. A 83, 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. A 84, 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, Nature 466, 730–734 (2010).
[Crossref] [PubMed]

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 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. Express 17, 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. Express 17, 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. A 79, 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,” Science 319, 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,” Science 320, 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. A 75, 052319 (2007).
[Crossref]

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 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. A 75, 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,” Science 314, 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,” Nature 434, 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,” Nature 422, 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,” Science 301, 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.

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. A 79, 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,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

Aspelmeyer, M.

Awschalom, D. D.

Balasubramanian, G.

Barclay, P. E.

Beausoleil, R. G.

Becher, C.

Beck, J.

Blatt, R.

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.

Chen, Q.

Chen, Y. A.

Chen, Y. L.

Childress, L.

Chu, Y.

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,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

Deuschle, T.

Du, J. F.

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]

Dusek, M.

Dutt, M.

Eisert, J.

Epstein, R. J.

Eschner, J.

Fang, M.

Feng, M.

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]

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. A 79, 032303 (2009).
[Crossref]

Fu, K. -M.

Fu, K.-M.

Furusawa, A.

Gaebel, T.

Gammon, D.

Gao, J.

Gilchrist, A.

Gill, A. T.

Gulde, S.

Guo, G. C.

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. A 75, 034302 (2007).
[Crossref]

Guo, G. P.

Häffner, H.

Han, Z. F.

Hanson, R.

He, B.

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
[Crossref]

Hemmer, P.

Hemmer, P. R.

Henage, T.

Hu, Y.

Isenhower, L.

Isoya, J.

Jacques, V.

Jelezko, F.

Jiang, L.

Jin, G. S.

Johnson, T. A.

Katzer, D. S.

Kieling, K.

Kimble, H. 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,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

Kolesov, R.

Lancaster, G. P. T.

Langford, N.K.

Lemr, K.

Li, J.

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

Li, K.

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. A 75, 034302 (2007).
[Crossref]

Li, X. Q.

Lin, Q.

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
[Crossref]

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

Lin, Z. R.

Liu, Y. X.

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]

Louis, S. G. R.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 042323 (2007).
[Crossref]

Lukin, M. D.

Markham, M.

Maze, J.

McMillan, J. F.

Mendoza, F. M.

Milburn, G. J.

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

Mizuochi, N.

Munro, W. J.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 042323 (2007).
[Crossref]

Nemoto, K.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 042323 (2007).
[Crossref]

Neumann, P.

Nielsen, M. A.

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

Nori, F.

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. A 75, 052319 (2007).
[Crossref]

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]

O’Brien, J. L.

Oh, C. 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. A 79, 032303 (2009).
[Crossref]

Ostby, E. P.

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,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

Painter, O.

Pan, J. W.

Park, D.

Parkins, A. S.

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,” Science 319, 1062–1065 (2008).
[Crossref] [PubMed]

Piermarocchi, C.

Prevedel, R.

Pryde, G. J.

Raussendorf, R.

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

Rempp, F.

Resch, K. J.

Riebe, M.

Roos, C. F.

Rudolph, T.

Saffman, M.

Santori, C.

Schenck, E.

Schmidt-Kaler, F.

Sham, L. J.

Sorensen, A. S.

Soubusta, J.

Spiller, T. P.

S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A 75, 042323 (2007).
[Crossref]

Steel, D.

Stievater, T. H.

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. A 75, 052319 (2007).
[Crossref]

Tissler, J.

Togan, E.

Trifonov, A. S.

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.

Twitchen, D.

Ukai, R.

Urban, E.

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,” Science 319, 1062–1065 (2008).
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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 H ⇔ L. In the bubble, the detailed energy configuration is described for N-V center in diamond nanocrystal.

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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.

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Fig. 3 The success probabilities of the CPHASE gate versus

g / \sqrt{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.

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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.

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Equations (14)

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\frac{d}{d t} \hat{a} (t) = - [i (ω_{c} - ω) + κ + κ_{s}] \hat{a} (t) - g {\hat{σ}}_{-} - \sqrt{κ} {\hat{a}}_{in} (t)

\frac{d}{d t} {\hat{σ}}_{-} = - [i (ω_{0} - ω) + κ] {\hat{σ}}_{-} - g {\hat{σ}}_{z} \hat{a} (t) .

r (ω) = \frac{[i (ω_{0} - ω_{p}) + \frac{γ}{2}] [i (ω_{c} - ω_{p}) - \frac{κ}{2} + \frac{κ_{s}}{2}] + g^{2}}{[i (ω_{0} - ω_{p}) + \frac{γ}{2}] [i (ω_{c} - ω_{p}) + \frac{κ}{2} + \frac{κ_{s}}{2}] + g^{2}} .

r (ω) = \frac{- γ κ + 4 g^{2}}{γ κ + 4 g^{2}} .

{| ψ 〉}_{in} = (α | H 〉 + β | V 〉) \otimes (η | + 〉 + δ | - 〉) .

\begin{array}{l} {| ψ 〉}_{out} & = & α | H 〉 (η | + 〉 + δ | - 〉) + β | V 〉 (η | + 〉 + δ | - 〉) \\ \to α η | L, + 〉 - α δ | L, - 〉 + β η | V, + 〉 + β δ | V, - 〉 \\ \to (α | H 〉 σ_{z}^{N - V} + β | V 〉) \otimes (η | + 〉 + δ | - 〉), \end{array}

U_{a j}^{C P} {| ψ 〉}_{j} {| ϕ 〉}_{N - V} {| ψ 〉}_{k} = [\frac{α_{1}}{\sqrt{2}} (| L 〉 | + 〉 - | L 〉 | - 〉) + \frac{β_{1}}{\sqrt{2}} (| R 〉 | + 〉 + | R 〉 | - 〉)] \otimes (α_{2} | L 〉 + β_{2} | R 〉) .

\begin{array}{l} R (π / 2) : \frac{α_{1}}{2} [| L 〉 (| + 〉 + | - 〉) - | L 〉 (| + 〉 - | - 〉)] \\ + \frac{β_{1}}{2} [| R 〉 (| + 〉 + | - 〉) + | R 〉 (| + 〉 - | - 〉)] \otimes (α_{2} | L 〉 + β_{2} | R 〉) . \end{array}

\begin{matrix} U_{a k}^{C P} : \frac{α_{1} α_{2}}{2} [| L, L 〉 (| + 〉 - | - 〉) - | L, L 〉 (| + 〉 + | - 〉)] \\ + \frac{β_{1} α_{2}}{2} [| R, L 〉 (| + 〉 - | - 〉) + | R, L 〉 (| + 〉 + | - 〉)] \\ + \frac{α_{1} β_{2}}{2} [| L, R 〉 (| + 〉 + | - 〉) - | L, R 〉 (| + 〉 - | - 〉)] \\ + \frac{β_{1} β_{2}}{2} [| R, R 〉 (| + 〉 + | - 〉) + | R, R 〉 (| + 〉 - | - 〉)] \end{matrix}

\begin{matrix} R (- π / 2) : \frac{α_{1} α_{2}}{\sqrt{2}} | L, L 〉 (- | + 〉 - | - 〉) - \frac{β_{1} α_{2}}{\sqrt{2}} | R, L 〉 (| + 〉 - | - 〉) \\ + \frac{α_{1} β_{2}}{\sqrt{2}} | L, R 〉 (| + 〉 + | - 〉) + \frac{β_{1} β_{2}}{\sqrt{2}} | R, R 〉 (| + 〉 - | - 〉) . \end{matrix}

\begin{matrix} U_{a j}^{C P} : \frac{α_{1} α_{2}}{\sqrt{2}} | L, L 〉 (| - 〉 - | + 〉) + \frac{β_{1} α_{2}}{\sqrt{2}} | R, L 〉 (| + 〉 - | - 〉) \\ + \frac{α_{1} β_{2}}{\sqrt{2}} | L, R 〉 (| + 〉 - | - 〉) + \frac{β_{1} β_{2}}{\sqrt{2}} (| R, R 〉 | + 〉 - | - 〉) . \end{matrix}

{| ψ 〉}_{2} = \frac{1}{2 \sqrt{2}} {(| R 〉 + | L 〉 σ_{z}^{1})}_{2} (| R 〉 + {| L 〉}_{1}) \otimes (| + 〉 - | - 〉) .

{| ψ 〉}_{3} = \frac{1}{4} {(| R 〉 + | L 〉 σ_{z}^{2})}_{3} \otimes {(| R 〉 + | L 〉 σ_{z}^{1})}_{2} \otimes {(| R 〉 + | L 〉)}_{1} \otimes (| + 〉 - | - 〉) .

{| ψ 〉}_{out} = \frac{1}{{\sqrt{2}}^{n + 2}} \prod_{i = 1}^{n - 1} (| R 〉 + | L 〉 σ_{z}^{n - i}) (| + 〉 - | - 〉) .