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

Optics Express, Vol. 21, Issue 16, pp. 19252-19260 (2013)

http://dx.doi.org/10.1364/OE.21.019252

Acrobat PDF (856 KB)

### 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

## 1. Introduction

1. 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]

*et al.*realized an all-optical quantum gate using semiconductor quantum dots [2

2. 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]

*et al.*demonstrated a nondestructive CNot gate for two photonic qubits [3

3. 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]

*et al.*presented a CNot gate between two individually addressed neutral atoms which uses Rydberg blockade interactions between neutral atoms held in optical traps [4

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). [CrossRef]

5. 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]

6. 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]

*et al.*[7

7. 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]

8. 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]

*et al.*discussed the dynamics of a single atom coupled with a microcavity resonator [9

9. 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]

*et al.*[10

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. A **83**, 054305 (2011). [CrossRef]

*et al.*[11

11. 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]

12. 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]

13. 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); [CrossRef] [PubMed] ;

13. 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]

## 2. Hybrid universal quantum phase gate based on nitrogen vacancy centers and micro-cavity system

*L*〉 represents the left circularly polarization of the photon. The interaction between a single N-V center and a cavity mode can be described by using the input-output process of the Jaynes-Cummings (JC) model [14]. The N-V center is assumed to be a three-level system as shown in the bubble of Fig. 1, with the excited state |

*A*〉 and two ground states with the angular momentum |

*m*= ±1〉. The Hamiltonian describes the interaction between the N-V center and the electric cavity field and is given by

_{s}*m*= −1 or

_{s}*m*= +1, respectively.

_{s}*a*

^{−}and

*a*

^{+}are the corresponding annihilation and creation operators for the cavity field. The level transition between |

*A*〉 and |±1〉 can only be excited by the single photon with the angular momentum which obeys the selection rules, for instance, the left circularly polarized photon can only couple with the N-V center in the level |−1〉 and the right circularly polarized one only couples with the N-V center in the level |+1〉.

15. 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]

*ϕ*〉 =

_{out}*exp*(

*iϕ*)|

*ϕ*〉, here the phase shift

_{in}*ϕ*is represented by the reflection coefficient

*r*(

*ω*) =

*â*. And the coefficient

_{out}/â_{in}*r*(

*ω*) can be solved as Here

*κ*and

*κ*are the cavity decay rate and the cavity leaky rate, respectively, and

_{s}*γ*/2 denotes the decay rate of the N-V center.

*ω*,

_{p}*ω*, and

_{c}*ω*

_{0}represent the frequencies of the input photon, cavity mode and the atomic energy level transitions, respectively. Here we set the resonant conditions with

*ω*=

_{c}*ω*

_{0}=

*ω*, the reflect coefficient

_{p}*r*

_{0}(

*ω*) under the uncoupling case with

*g*= 0 approaches to −1. However, the coupled reflection coefficient

*r*(

*ω*) can be described as As shown in the above equations, there is a phase shift on the output field with respect to the atomic state of the N-V center. If the N-V center is in the state |−〉, we can obtain the following evolution of atom-photon system: |

*ϕ*〉 =

_{out}*r*(

*ω*)|

*L*〉 =

*e*|

^{iϕ}*L*〉 or |

*ϕ*〉 =

_{out}*r*

_{0}(

*ω*)|

*R*〉 =

*e*

^{iϕ0}|

*R*〉, here the parameters

*ϕ*and

*ϕ*

_{0}represent the phase shift determined by the input-output relation. It is obvious that the uncoupled condition will introduce a

*π*phase shift on the input-output state.

*V*〉 and |

*H*〉), while the target qubit is encoded on the N-V center inside an optical microcavity. Our goal is to realize the photon-solid qubits CPHASE gate

*U*. This gate enables a controlled phase change process between the input-output single photon and an isolated spin qubit. Suppose the N-V center is initially prepared in the state

^{CP}*η*|+〉 +

*δ*|−〉, here we denote |±〉 as the state of the N-V center in the level |

*m*= ±1〉. The input photon is prepared in the state

_{s}*α*|

*H*〉 +

*β*|

*V*〉, here |

*H*〉 and |

*V*〉 represent the horizontal and vertical polarization of the photon, respectively. The state of the composite system can be described as

*H*〉 → |

*L*〉. Then the N-V center and microcavity system will interact with the photon and the composite system will evolve as:

*H*〉, compared with the original state of the two-qubit hybrid system. That is, the quantum circuit shown in Fig. 1 can be used to construct the CPHASE gate by using the photon as the controlling qubit and the N-V center as the target qubit. Following the interaction between the input single photon pulse and the N-V center, the process can be described by the unitary operator

*U*=

^{CP}*e*

^{i}^{π}^{(|}

^{H}^{〉〈}

^{H}^{|⊗|−〉〈−|)}.

## 3. Photonic quantum phase gate and cluster state generation

*α*

_{1}|

*L*〉 +

*β*

_{1}|

*R*〉 and

*α*

_{2}|

*L*〉 +

*β*

_{2}|

*R*〉, here |

*α*

_{1}|

^{2}+ |

*β*

_{1}|

^{2}= |

*α*

_{2}|

^{2}+ |

*β*

_{2}|

^{2}= 1. And the N-V center is prepared in the superposition state

*A*〉 and |−〉 → |

*A*〉 are coupled with the input photon with mode

*a*and

_{R}*a*respectively. Now we present the detailed theoretical model of the controlled phase operation on the photonic qubits. The process can be described by the following operations:

_{L}*R*(

*θ*) is the single qubit rotation on the N-V center which can be realized by a microwave pulse. The transformation of the rotations obey

*R*(

*θ*)|+〉 =

*cos*(

*θ*/2)|+〉 +

*sin*(

*θ*/2)|−〉 and

*R*(

*θ*)|−〉 = −

*sin*(

*θ*/2)|+〉+

*cos*(

*θ*/2)|−〉. The initial state is denoted by |

*ψ*〉

*⊗ |*

_{j}*ψ*〉

*⊗ |*

_{k}*ϕ*〉

_{N}_{−}

*, here the subscripts*

_{V}*j*and

*k*represent the two input photons. The rotation operations

*R*(

*π*/2) and

*R*(−

*π*/2) denote the single particle rotation on the state of the N-V centers.

*π*/2 microwave pulse is performed on the N-V center which made a Hadamard operation on the state, the system can be described as The k pulse is sent to the CPF gate and interacted with the N-V center as:

*π*/2 pulse is performed on the N-V center, the system can be described as: Following the circuits shown in Fig. 2, the j pulse is recycled and interacted with the N-V center again, then the state of the system evolves as: Then the remaining two photons are in the state: −

*α*

_{1}

*α*

_{2}|

*L,L*〉 +

*β*

_{1}

*α*

_{2}|

*R,L*〉 +

*α*

_{1}

*β*

_{2}|

*L,R*〉 +

*β*

_{1}

*β*

_{2}|

*R,R*〉.

*ϕ*that the gate imposes on the logical state of the signal qubit according to the state of the controlled qubit. Here we set the phase shift

*ϕ*=

*π*. In the realistic implementations, the fidelity of the gate operation relies on the key parameters of the system, including the coupling strength, the cavity decay and the decoherence time. Here we numerically simulated the success probability of the gate operation based on realistic experimental results. The relations between the success probability of our CPHASE gate is shown in Fig. 3. As the value of

*th*rounds iterations, the final cluster state of the composite system can be described as:

*g*, the cavity decay rate

*κ*and the decay rate of the N-V center

*γ*. We numerically simulated the fidelity of the generated cluster state versus different initial coefficients on the certain reflection coefficients. In Fig. 4 we labeled the fidelity of the generated cluster state and the coefficient

*κ*= 0. It is obvious that the efficiency of the scheme relies on the large coupling between the N-V center and the microcavity, also with less decay rate of

_{s}*γ*and

*κ*. Actually, the following numerical simulation results show that the CPHASE gate works remarkably well even if g ∼

*κ*. In the implementation of such devices, the coherent coupling between N-V centers and microcavities can be achieved as

*g/κ*= 0.5 and the decay rate is

*γ*= 2

*π*× 10

*MHz*as discussed in [28

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. Express **17**, 9588–9601 (2009). [CrossRef] [PubMed]

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. Express **17**, 8081–8097 (2009). [CrossRef] [PubMed]

*MHz*in the near field of a 100nm scale. On the other hand, the protocol is essentially based on the efficient output of photons which implies the large cavity decay rate [9

9. 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]

*et al.*designed and experimentally realized a photon turnstile exploiting the atom and microtoroidal resonator coupled system. The photon number at the output can be controlled by the atom dynamically. Also the fidelity of the CPHASE gate operation and the fidelity of the cluster state generation may be effected by the imperfect operation of the RF pulse on the N-V center, which may cause an imperfect Hadamard operation on the state. Of course this will reduce the success probability of the generated cluster state. Moreover, the present model relies on the decoherence time of the spins in N-V centers, which mainly characterized by the spin relaxation time

*T*

_{1}and the dephasing time

*T*

_{2}. According to Refs.[30

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,” Science **320**, 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]

## 4. Summary

## Acknowledgments

## References and links

1. | 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 |

2. | 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 |

3. | 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. |

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. |

5. | 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. |

6. | 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. |

7. | 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. |

8. | 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 |

9. | 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 |

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. A |

11. | 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 |

12. | 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 |

13. | R. Hanson, F. M. Mendoza, R. J. Epstein, and D. D. Awschalom, “Polarization and readout of coupled single spins in diamond,” Phys. Rev. Lett. 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 |

14. | D. F. Walls and G. J. Milburn, |

15. | 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 |

16. | R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. |

17. | P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature |

18. | 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 |

19. | 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. |

20. | Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A , |

21. | 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. |

22. | M. A. Nielsen, “Optical quantum computation using cluster states,” Phys. Rev. Lett. |

23. | S. G. R. Louis, K. Nemoto, W. J. Munro, and T. P. Spiller, “Weak nonlinearities and cluster states,” Phys. Rev. A |

24. | Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A |

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. |

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. A |

27. | Y. X. Liu, L. F. Wei, J. S. Tsai, and F. Nori, “Controllable coupling between flux qubits,” Phys. Rev. Lett. |

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. Express |

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. Express |

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,” Science |

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. |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5568) Quantum optics : Quantum cryptography

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: May 8, 2013

Revised Manuscript: July 20, 2013

Manuscript Accepted: July 20, 2013

Published: August 6, 2013

**Citation**

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)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19252

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### References

- 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]
- 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. A84, 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,” Science319, 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. A83, 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, Nature466, 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. B29(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,” Science314, 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. A79, 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,” Nature434, 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. A75, 034302 (2007). [CrossRef]
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