Abstract

A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-vacancy centers, can be used to construct a universal set of quantum gates on the encoded logical qubits. Therefore, our scheme opens up the possibility of realizing universal holonomic quantum computation with cavity assisted interaction on solid-state spins characterized by long coherence times.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  29. L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
    [Crossref] [PubMed]
  30. Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
    [Crossref] [PubMed]
  31. P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
    [Crossref]
  32. N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
    [Crossref]
  33. C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
    [Crossref]
  34. P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
    [Crossref] [PubMed]
  35. V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
    [Crossref] [PubMed]
  36. G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119–130 (1976).
    [Crossref]
  37. P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
    [Crossref]
  38. S. Clark and A. Parkins, “Entanglement and entropy engineering of atomic two-qubit states,” Phys. Rev. Lett. 90, 047905 (2003).
    [Crossref] [PubMed]
  39. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
    [Crossref]

2014 (3)

Z.-T. Liang, Y.-X. Du, W. Huang, Z.-Y. Xue, and H. Yan, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 89, 062312 (2014).
[Crossref]

J. Zhang, L.-C. Kwek, E. Sjöqvist, D. M. Tong, and P. Zanardi, “Quantum computation in noiseless subsystems with fast non-Abelian holonomies,” Phys. Rev. A 89, 042302 (2014).
[Crossref]

G.-F. Xu and G.-L. Long, “Universal nonadiabatic geometric gates in two-qubit decoherence-free subspaces,” Sci. Rep. 4, 6814 (2014).
[Crossref] [PubMed]

2013 (2)

A. A. Abdumalikov, J. M. Fink, K. Juliusson, M. Pechal, S. Berger, A. Wallraff, and S. Filipp, “Experimental realization of non-Abelian non-adiabatic geometric gates,” Nature 496, 482–485 (2013).
[Crossref] [PubMed]

G. Feng, G. Xu, and G. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110, 190501 (2013).
[Crossref] [PubMed]

2012 (3)

E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
[Crossref]

G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 109, 170501 (2012).
[Crossref] [PubMed]

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

2011 (1)

J. T. Thomas, M. Lababidi, and M. Tian, “Robustness of single-qubit geometric gate against systematic error,” Phys. Rev. A 84, 042335 (2011).
[Crossref]

2010 (1)

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

2009 (4)

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

M. Stoneham, “Is a room-temperature, solid-state quantum computer mere fantasy,” Physics 2, 34 (2009).
[Crossref]

L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
[Crossref] [PubMed]

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[Crossref]

2006 (5)

Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[Crossref] [PubMed]

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
[Crossref]

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
[Crossref]

P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
[Crossref] [PubMed]

X.-D. Zhang, Q. H. Zhang, and Z. D. Wang, “Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 74, 34302 (2006).
[Crossref]

2005 (1)

L.-A. Wu, P. Zanardi, and D. A. Lidar, “Holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 95, 130501 (2005).
[Crossref] [PubMed]

2004 (2)

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

M. Bourennane, M. Eibl, S. Gaertner, and C. Kurtsiefer, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[Crossref] [PubMed]

2003 (3)

J. E. Ollerenshaw, D. A. Lidar, and L. E. Kay, “Magnetic resonance realization of decoherence-free quantum computation,” Phys. Rev. Lett. 91, 217904 (2003).
[Crossref] [PubMed]

S.-L. Zhu and Z. D. Wang, “Unconventional geometric quantum computation,” Phys. Rev. Lett. 91, 187902 (2003).
[Crossref] [PubMed]

S. Clark and A. Parkins, “Entanglement and entropy engineering of atomic two-qubit states,” Phys. Rev. Lett. 90, 047905 (2003).
[Crossref] [PubMed]

2002 (1)

S.-L. Zhu and Z. D. Wang, “Implementation of universal quantum gates based on nonadiabatic geometric phases,” Phys. Rev. Lett. 89, 097902 (2002).
[Crossref] [PubMed]

2001 (3)

X.-B. Wang and K. Matsumoto, “Nonadiabatic conditional geometric phase shift with NMR,” Phys. Rev. Lett. 87, 097901 (2001).
[Crossref]

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[Crossref] [PubMed]

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[Crossref] [PubMed]

1999 (1)

P. Zanardi and M. Rasetti, “Holonomic quantum computation,” Phys. Lett. A 264, 94–99 (1999).
[Crossref]

1998 (2)

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594 (1998).
[Crossref]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
[Crossref]

1997 (2)

L.-M. Duan and G.-C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953 (1997).
[Crossref]

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306 (1997).
[Crossref]

1988 (1)

J. Anandan, “Non-adiabatic non-abelian geometric phase,” Phys. Lett. A 133, 171–175 (1988).
[Crossref]

1987 (1)

Y. Aharonov and J. Anandan, “Phase change during a cyclic quantum evolution,” Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

1984 (2)

F. Wilczek and A. Zee, “Appearance of gauge structure in simple dynamical systems,” Phys. Rev. Lett. 52, 2111 (1984).
[Crossref]

M. V. Berry, “Quantum phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A 392, 45–57 (1984).
[Crossref]

1976 (1)

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119–130 (1976).
[Crossref]

Abdumalikov, A. A.

A. A. Abdumalikov, J. M. Fink, K. Juliusson, M. Pechal, S. Berger, A. Wallraff, and S. Filipp, “Experimental realization of non-Abelian non-adiabatic geometric gates,” Nature 496, 482–485 (2013).
[Crossref] [PubMed]

Acosta, V. M.

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

Aharonov, Y.

Y. Aharonov and J. Anandan, “Phase change during a cyclic quantum evolution,” Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

Anandan, J.

J. Anandan, “Non-adiabatic non-abelian geometric phase,” Phys. Lett. A 133, 171–175 (1988).
[Crossref]

Y. Aharonov and J. Anandan, “Phase change during a cyclic quantum evolution,” Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

Balasubramanian, G.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[Crossref]

Barclay, P. E.

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

Batalov, A.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[Crossref]

Beausoleil, R. G.

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

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

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
[Crossref]

Beck, J.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[Crossref]

Berger, S.

A. A. Abdumalikov, J. M. Fink, K. Juliusson, M. Pechal, S. Berger, A. Wallraff, and S. Filipp, “Experimental realization of non-Abelian non-adiabatic geometric gates,” Nature 496, 482–485 (2013).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry, “Quantum phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A 392, 45–57 (1984).
[Crossref]

Bourennane, M.

M. Bourennane, M. Eibl, S. Gaertner, and C. Kurtsiefer, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[Crossref] [PubMed]

Chong, B.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Chuang, I. L.

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594 (1998).
[Crossref]

Cirac, J. I.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[Crossref] [PubMed]

Clark, S.

S. Clark and A. Parkins, “Entanglement and entropy engineering of atomic two-qubit states,” Phys. Rev. Lett. 90, 047905 (2003).
[Crossref] [PubMed]

Cook, A. K.

Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[Crossref] [PubMed]

Cory, D.

L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
[Crossref] [PubMed]

Du, J.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Du, Y.-X.

Z.-T. Liang, Y.-X. Du, W. Huang, Z.-Y. Xue, and H. Yan, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 89, 062312 (2014).
[Crossref]

Duan, L.-M.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[Crossref] [PubMed]

L.-M. Duan and G.-C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953 (1997).
[Crossref]

Eibl, M.

M. Bourennane, M. Eibl, S. Gaertner, and C. Kurtsiefer, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[Crossref] [PubMed]

Faraon, A.

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

Fattal, D.

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V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
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E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
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L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
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P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
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V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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Itano, W. M.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
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P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
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E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
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J. E. Ollerenshaw, D. A. Lidar, and L. E. Kay, “Magnetic resonance realization of decoherence-free quantum computation,” Phys. Rev. Lett. 91, 217904 (2003).
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D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
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M. Bourennane, M. Eibl, S. Gaertner, and C. Kurtsiefer, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
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J. Zhang, L.-C. Kwek, E. Sjöqvist, D. M. Tong, and P. Zanardi, “Quantum computation in noiseless subsystems with fast non-Abelian holonomies,” Phys. Rev. A 89, 042302 (2014).
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P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
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E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
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L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
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D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
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D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
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P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
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V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
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F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
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D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
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V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett. 95, 191115 (2009).
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C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
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F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
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F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
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E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
[Crossref]

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J. Zhang, L.-C. Kwek, E. Sjöqvist, D. M. Tong, and P. Zanardi, “Quantum computation in noiseless subsystems with fast non-Abelian holonomies,” Phys. Rev. A 89, 042302 (2014).
[Crossref]

E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
[Crossref]

G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 109, 170501 (2012).
[Crossref] [PubMed]

Stacey, A.

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

Stoneham, M.

M. Stoneham, “Is a room-temperature, solid-state quantum computer mere fantasy,” Physics 2, 34 (2009).
[Crossref]

Streed, E. W.

Tamarat, P.

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
[Crossref]

P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
[Crossref] [PubMed]

Taylor, J. M.

L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
[Crossref] [PubMed]

Thomas, J. T.

J. T. Thomas, M. Lababidi, and M. Tian, “Robustness of single-qubit geometric gate against systematic error,” Phys. Rev. A 84, 042335 (2011).
[Crossref]

Tian, M.

J. T. Thomas, M. Lababidi, and M. Tian, “Robustness of single-qubit geometric gate against systematic error,” Phys. Rev. A 84, 042335 (2011).
[Crossref]

Tisler, J.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[Crossref]

Tomljenovic-Hanic, S.

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

Tong, D. M.

J. Zhang, L.-C. Kwek, E. Sjöqvist, D. M. Tong, and P. Zanardi, “Quantum computation in noiseless subsystems with fast non-Abelian holonomies,” Phys. Rev. A 89, 042302 (2014).
[Crossref]

E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
[Crossref]

G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 109, 170501 (2012).
[Crossref] [PubMed]

Vernooy, D. W.

Wallraff, A.

A. A. Abdumalikov, J. M. Fink, K. Juliusson, M. Pechal, S. Berger, A. Wallraff, and S. Filipp, “Experimental realization of non-Abelian non-adiabatic geometric gates,” Nature 496, 482–485 (2013).
[Crossref] [PubMed]

Walsworth, R. L.

L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
[Crossref] [PubMed]

Wang, H.

Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[Crossref] [PubMed]

Wang, X.-B.

X.-B. Wang and K. Matsumoto, “Nonadiabatic conditional geometric phase shift with NMR,” Phys. Rev. Lett. 87, 097901 (2001).
[Crossref]

Wang, Y.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Wang, Z. D.

X.-D. Zhang, Q. H. Zhang, and Z. D. Wang, “Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 74, 34302 (2006).
[Crossref]

S.-L. Zhu and Z. D. Wang, “Unconventional geometric quantum computation,” Phys. Rev. Lett. 91, 187902 (2003).
[Crossref] [PubMed]

S.-L. Zhu and Z. D. Wang, “Implementation of universal quantum gates based on nonadiabatic geometric phases,” Phys. Rev. Lett. 89, 097902 (2002).
[Crossref] [PubMed]

Whaley, K. B.

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594 (1998).
[Crossref]

Wilczek, F.

F. Wilczek and A. Zee, “Appearance of gauge structure in simple dynamical systems,” Phys. Rev. Lett. 52, 2111 (1984).
[Crossref]

Wilson, H.

P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
[Crossref] [PubMed]

Wineland, D. J.

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[Crossref] [PubMed]

Wrachtrup, J.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[Crossref]

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
[Crossref]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

Wu, J.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Wu, L.-A.

L.-A. Wu, P. Zanardi, and D. A. Lidar, “Holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 95, 130501 (2005).
[Crossref] [PubMed]

Xu, G.

G. Feng, G. Xu, and G. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110, 190501 (2013).
[Crossref] [PubMed]

Xu, G. F.

G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 109, 170501 (2012).
[Crossref] [PubMed]

Xu, G.-F.

G.-F. Xu and G.-L. Long, “Universal nonadiabatic geometric gates in two-qubit decoherence-free subspaces,” Sci. Rep. 4, 6814 (2014).
[Crossref] [PubMed]

Xu, N.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

Xue, Z.-Y.

Z.-T. Liang, Y.-X. Du, W. Huang, Z.-Y. Xue, and H. Yan, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 89, 062312 (2014).
[Crossref]

Yacoby, A.

L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
[Crossref] [PubMed]

Yan, H.

Z.-T. Liang, Y.-X. Du, W. Huang, Z.-Y. Xue, and H. Yan, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 89, 062312 (2014).
[Crossref]

Zanardi, P.

J. Zhang, L.-C. Kwek, E. Sjöqvist, D. M. Tong, and P. Zanardi, “Quantum computation in noiseless subsystems with fast non-Abelian holonomies,” Phys. Rev. A 89, 042302 (2014).
[Crossref]

L.-A. Wu, P. Zanardi, and D. A. Lidar, “Holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 95, 130501 (2005).
[Crossref] [PubMed]

P. Zanardi and M. Rasetti, “Holonomic quantum computation,” Phys. Lett. A 264, 94–99 (1999).
[Crossref]

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306 (1997).
[Crossref]

Zee, A.

F. Wilczek and A. Zee, “Appearance of gauge structure in simple dynamical systems,” Phys. Rev. Lett. 52, 2111 (1984).
[Crossref]

Zhang, J.

J. Zhang, L.-C. Kwek, E. Sjöqvist, D. M. Tong, and P. Zanardi, “Quantum computation in noiseless subsystems with fast non-Abelian holonomies,” Phys. Rev. A 89, 042302 (2014).
[Crossref]

G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 109, 170501 (2012).
[Crossref] [PubMed]

Zhang, Q. H.

X.-D. Zhang, Q. H. Zhang, and Z. D. Wang, “Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 74, 34302 (2006).
[Crossref]

Zhang, X.-D.

X.-D. Zhang, Q. H. Zhang, and Z. D. Wang, “Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 74, 34302 (2006).
[Crossref]

Zhu, S.-L.

S.-L. Zhu and Z. D. Wang, “Unconventional geometric quantum computation,” Phys. Rev. Lett. 91, 187902 (2003).
[Crossref] [PubMed]

S.-L. Zhu and Z. D. Wang, “Implementation of universal quantum gates based on nonadiabatic geometric phases,” Phys. Rev. Lett. 89, 097902 (2002).
[Crossref] [PubMed]

Zibrov, A. S.

L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
[Crossref] [PubMed]

Zoller, P.

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

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

Commun. Math. Phys. (1)

G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys. 48, 119–130 (1976).
[Crossref]

Nano Lett. (1)

Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[Crossref] [PubMed]

Nature (1)

A. A. Abdumalikov, J. M. Fink, K. Juliusson, M. Pechal, S. Berger, A. Wallraff, and S. Filipp, “Experimental realization of non-Abelian non-adiabatic geometric gates,” Nature 496, 482–485 (2013).
[Crossref] [PubMed]

New J. Phys. (2)

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[Crossref]

E. Sjöqvist, D. M. Tong, L. Mauritz Andersson, B. Hessmo, M. Johansson, and K. Singh, “Non-adiabatic holonomic quantum computation,” New J. Phys. 14, 103035 (2012).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (2)

J. Anandan, “Non-adiabatic non-abelian geometric phase,” Phys. Lett. A 133, 171–175 (1988).
[Crossref]

P. Zanardi and M. Rasetti, “Holonomic quantum computation,” Phys. Lett. A 264, 94–99 (1999).
[Crossref]

Phys. Rev. A (4)

X.-D. Zhang, Q. H. Zhang, and Z. D. Wang, “Physical implementation of holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 74, 34302 (2006).
[Crossref]

J. T. Thomas, M. Lababidi, and M. Tian, “Robustness of single-qubit geometric gate against systematic error,” Phys. Rev. A 84, 042335 (2011).
[Crossref]

Z.-T. Liang, Y.-X. Du, W. Huang, Z.-Y. Xue, and H. Yan, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions,” Phys. Rev. A 89, 062312 (2014).
[Crossref]

J. Zhang, L.-C. Kwek, E. Sjöqvist, D. M. Tong, and P. Zanardi, “Quantum computation in noiseless subsystems with fast non-Abelian holonomies,” Phys. Rev. A 89, 042302 (2014).
[Crossref]

Phys. Rev. B (1)

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B 74, 104303 (2006).
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Phys. Rev. Lett. (19)

C. Santori, P. Tamarat, P. Neumann, J. Wrachtrup, D. Fattal, R. G. Beausoleil, J. Rabeau, P. Olivero, A. Greentree, S. Prawer, F. Jelezko, and P. Hemmer, “Coherent population trapping of single spins in diamond under optical excitation,” Phys. Rev. Lett. 97, 247401 (2006).
[Crossref]

P. Tamarat, T. Gaebel, J. R. Rabeau, M. Khan, A. D. Greentree, H. Wilson, L. C. L. Hollenberg, and S. Prawer, “Stark shift control of single optical centers in diamond,” Phys. Rev. Lett. 97, 083002 (2006).
[Crossref] [PubMed]

V. M. Acosta, C. Santori, A. Faraon, Z. Huang, K.-M. C. Fu, A. Stacey, D. A. Simpson, K. Ganesan, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and R. G. Beausoleil, “Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond,” Phys. Rev. Lett. 108, 206401 (2012).
[Crossref] [PubMed]

S. Clark and A. Parkins, “Entanglement and entropy engineering of atomic two-qubit states,” Phys. Rev. Lett. 90, 047905 (2003).
[Crossref] [PubMed]

S.-L. Zhu and Z. D. Wang, “Unconventional geometric quantum computation,” Phys. Rev. Lett. 91, 187902 (2003).
[Crossref] [PubMed]

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[Crossref] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
[Crossref] [PubMed]

X.-B. Wang and K. Matsumoto, “Nonadiabatic conditional geometric phase shift with NMR,” Phys. Rev. Lett. 87, 097901 (2001).
[Crossref]

S.-L. Zhu and Z. D. Wang, “Implementation of universal quantum gates based on nonadiabatic geometric phases,” Phys. Rev. Lett. 89, 097902 (2002).
[Crossref] [PubMed]

Y. Aharonov and J. Anandan, “Phase change during a cyclic quantum evolution,” Phys. Rev. Lett. 58, 1593 (1987).
[Crossref] [PubMed]

F. Wilczek and A. Zee, “Appearance of gauge structure in simple dynamical systems,” Phys. Rev. Lett. 52, 2111 (1984).
[Crossref]

G. Feng, G. Xu, and G. Long, “Experimental realization of nonadiabatic holonomic quantum computation,” Phys. Rev. Lett. 110, 190501 (2013).
[Crossref] [PubMed]

L.-M. Duan and G.-C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953 (1997).
[Crossref]

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306 (1997).
[Crossref]

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594 (1998).
[Crossref]

J. E. Ollerenshaw, D. A. Lidar, and L. E. Kay, “Magnetic resonance realization of decoherence-free quantum computation,” Phys. Rev. Lett. 91, 217904 (2003).
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[Crossref] [PubMed]

L.-A. Wu, P. Zanardi, and D. A. Lidar, “Holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 95, 130501 (2005).
[Crossref] [PubMed]

G. F. Xu, J. Zhang, D. M. Tong, E. Sjöqvist, and L. C. Kwek, “Nonadiabatic holonomic quantum computation in decoherence-free subspaces,” Phys. Rev. Lett. 109, 170501 (2012).
[Crossref] [PubMed]

Physics (1)

M. Stoneham, “Is a room-temperature, solid-state quantum computer mere fantasy,” Physics 2, 34 (2009).
[Crossref]

Proc. R. Soc. Lond. A (1)

M. V. Berry, “Quantum phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A 392, 45–57 (1984).
[Crossref]

Sci. Rep. (1)

G.-F. Xu and G.-L. Long, “Universal nonadiabatic geometric gates in two-qubit decoherence-free subspaces,” Sci. Rep. 4, 6814 (2014).
[Crossref] [PubMed]

Science (3)

L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, “Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae,” Science 326, 267–272 (2009).
[Crossref] [PubMed]

D. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “A decoherence-free quantum memory using trapped ions,” Science 291, 1013–1015 (2001).
[Crossref] [PubMed]

L.-M. Duan, J. I. Cirac, and P. Zoller, “Geometric manipulation of trapped ions for quantum computation,” Science 292, 1695–1697 (2001).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic setup of the fused-silica microsphere cavity, where N identical NV centers (red dots) in diamond nanocrystals are equidistantly attached around the equator of the cavity. (b) Level diagram for a NV center, with gL) is the coupling strength between NV center and the WGM (laser pulse). We encode a physical qubit in the subspace spanned by the states of ms = 0 and ms = −1.
Fig. 2
Fig. 2 Qubit states population and fidelity under single-qubit operator U1(θ, φ) with initial state |0〉L, the red (dot) line represents the fidelity. (a) θ = π/2 and φ = 0. (b) θ = π/4 and φ = 0.
Fig. 3
Fig. 3 Maximum fidelity as the function of Θ in unit of π with line (circle) the identical (different) decoherence of qubits under gate operations (a) U1(π/2, 0), (b) U1(π/4, 0).
Fig. 4
Fig. 4 Qubit states population and fidelity under two-qubit operator U2(π/4, 0), the red line represents the fidelity. (a) Initial state of qubit |00〉L. (b) Initial state of qubit |01〉L.

Equations (13)

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

H 0 = ω c a a + i ω i | i i | , H S = H 0 + j = 1 N [ η j a | e j 0 | + Ω L , j e i ( ω L t + φ j ) | e j 1 | + H . c . ] ,
H I = j = 1 N g j ( a σ j + e i ( δ ± , j t φ j ) + H . c . ) ,
H m , n = j = m , n g m n 2 δ ± ( a a | 0 j 0 | + a a | 1 j 1 | ) + g m n 2 δ ± ( e i φ m n σ m σ n + + H . c . ) ,
H m , n = g m , n 2 δ ± ( e i φ m n σ m σ n + + H . c . ) .
S 1 = { | 100 , | 001 , | 010 } ,
H 1 = λ 1 ( sin θ 2 e i φ | a 1 L 0 | cos θ 2 | a 1 L 1 | ) + H . c . ,
| d L = cos θ 2 | 0 L + sin θ 2 e i φ | 1 L , | b L = sin θ 2 e i φ | 0 L cos θ 2 | 1 L .
U 1 ( θ , φ ) = ( cos θ sin θ e i φ sin θ e i φ cos θ ) ,
ρ ˙ = i [ H I ( 3 ) , ρ ] + 1 2 [ κ ( a ) + γ ( S ) + γ ϕ ( S z ) ] ,
S 2 = { | 100100 , | 100001 , | 001100 , | 001001 , | 101000 , | 000101 } ,
H 2 = λ 2 [ sin ϑ 2 e i φ ( | a 2 L 00 | + | a 3 L 11 | ) cos ϑ 2 ( | a 2 L 01 | + | a 3 L 10 | ) ] + H . c . ,
H a = sin ϑ 2 e i ϕ | a 2 L 00 | cos ϑ 2 | a 2 L 01 | + H . c . , H b = sin ϑ 2 e i ϕ | a 3 L 11 | cos ϑ 2 | a 3 L 10 | + H . c . .
U 2 ( ϑ , ϕ ) = ( cos ϑ sin ϑ e i ϕ 0 0 sin ϑ e i ϕ cos ϑ 0 0 0 0 cos ϑ sin ϑ e i ϕ 0 0 sin ϑ e i ϕ cos ϑ ) .

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