Abstract

A method for synthesizing the Toffoli gate is proposed based solely on the Stark shifts of three superconducting quantum interference devices (SQUIDs). This scheme is robust against the effect of decoherence, since it operates with no excitation of SQUIDs and the coplanar waveguide cavity. The obtained fidelity of the Toffoli gate is high, corresponding to the current typical experimental parameters, and an equivalent physical model for conveniently addressing qubits is also constructed in the coupled-cavity array system.

© 2012 Optical Society of America

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    [CrossRef]
  3. M. S. Zubairy, M. Kim, and M. O. Scully, “Cavity-QED-based quantum phase gate,” Phys. Rev. A 68, 033820 (2003).
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  5. L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
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  6. S. B. Zheng, “Quantum logic gates for two atoms with a single resonant interaction,” Phys. Rev. A 71, 062335 (2005).
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  7. Y. F. Xiao, X. B. Zou, and G. C. Guo, “Implementing a conditional N-qubit phase gate in a largely detuned optical cavity,” Phys. Rev. A 75, 014302 (2007).
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  8. X. B. Zou, Y. F. Xiao, S. B. Li, Y. Yang, and G. C. Guo, “Quantum phase gate through a dispersive atom-field interaction,” Phys. Rev. A 75, 064301 (2007).
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  15. W. L. Yang, C. Y. Chen, and M. Feng, “Implementation of three-qubit Grover search in cavity quantum electrodynamics,” Phys. Rev. A 76, 054301 (2007).
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  16. D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett. 81, 2152–2155 (1998).
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    [CrossRef]
  24. M. S. Tame, K. Özdemir Ş, M. Koashi, N. Imoto, and M. S. Kim, “Compact Toffoli gate using weighted graph states,” Phys. Rev. A 79, 020302(R) (2009).
    [CrossRef]
  25. T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009).
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    [CrossRef]
  27. J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
    [CrossRef]
  28. A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
    [CrossRef]
  29. T. Sleator and H. Weinfurter, “Realizable universal quantum logic gates,” Phys. Rev. Lett. 74, 4087–4090 (1995).
    [CrossRef]
  30. N. A. Gershenfeld and I. L. Chuang, “Bulk spin-resonance quantum computation,” Science 275, 350–356 (1997).
    [CrossRef]
  31. Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, “Coherent control of macroscopic quantum states in a single-Cooper-pair box,” Nature 398, 786–788 (1999).
    [CrossRef]
  32. K. Tordrup and K. Mølmer, “Quantum computing with a single molecular ensemble and a Cooper-pair box,” Phys. Rev. A 77, 020301(R) (2008).
    [CrossRef]
  33. Z. Kim, B. Suri, V. Zaretskey, S. Novikov, K. D. Osborn, A. Mizel, F. C. Wellstood, and B. S. Palmer, “Decoupling a Cooper-pair box to enhance the lifetime to 0.2 ms,” Phys. Rev. Lett. 106, 120501 (2011).
    [CrossRef]
  34. A. Shnirman, G. Schön, and Z. Hermon, “Quantum manipulations of small Josephson junctions,” Phys. Rev. Lett. 79, 2371–2374 (1997).
    [CrossRef]
  35. X. B. Wang and K. Matsumoto, “Nonadiabatic detection of the geometric phase of the macroscopic quantum state with a symmetric SQUID,” Phys. Rev. B 65, 172508 (2002).
    [CrossRef]
  36. G. Wendin and V. Shumeiko, “Quantum bits with Josephson junctions,” Low Temp. Phys. 33, 724–744(2007).
    [CrossRef]
  37. C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
    [CrossRef]
  38. C. P. Yang, “A proposal for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity QED,” J. Phys. Condens. Matter 23, 225702 (2011).
    [CrossRef]
  39. B. Ghosh, A. S. Majumdar, and N. Nayak, “Control of atomic entanglement by dynamic Stark effect,” J. Phys. B: At. Mol. Opt. Phys. 41, 065503 (2008).
    [CrossRef]
  40. P. Bohlouli-Zanjani, J. A. Petrus, and J. D. D. Martin, “Enhancement of Rydberg atom interactions using ac Stark shifts,” Phys. Rev. Lett. 98, 203005 (2007).
    [CrossRef]
  41. A. Retzker and M. B. Plenio, “Fast cooling of trapped ions using the dynamical Stark shift,” New J. Phys. 9, 279 (2007).
    [CrossRef]
  42. C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006).
    [CrossRef]
  43. M. A. Nielsen and I. L. ChuangQuantum Computation and Quantum Information (Cambridge University, 2000).
  44. M. O. Scully and M. S. ZubairyQuantum Optics (Cambridge University, 1997).
  45. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
    [CrossRef]

2011

Z. Kim, B. Suri, V. Zaretskey, S. Novikov, K. D. Osborn, A. Mizel, F. C. Wellstood, and B. S. Palmer, “Decoupling a Cooper-pair box to enhance the lifetime to 0.2 ms,” Phys. Rev. Lett. 106, 120501 (2011).
[CrossRef]

C. P. Yang, “A proposal for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity QED,” J. Phys. Condens. Matter 23, 225702 (2011).
[CrossRef]

2010

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and J. F. Du, “One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” Appl. Phys. Lett. 96, 241113 (2010).
[CrossRef]

H. Z. Wu, Z. B. Yang, and S. B. Zheng, “Implementation of a multiqubit quantum phase gate in a neutral atomic ensemble via the asymmetric Rydberg blockade,” Phys. Rev. A 82, 034307(2010).
[CrossRef]

C. P. Yang, S. B. Zheng, and F. Nori, “Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 82, 062326 (2010).
[CrossRef]

2009

X. Q. Shao, H. F. Wang, L. Chen, S. Zhang, and K. H. Yeon, “One-step implementation of the Toffoli gate via quantum Zeno dynamics,” Phys. Lett. A 374, 28–33 (2009).
[CrossRef]

G. W. Lin, X. B. Zou, X. M. Lin, and G. C. Guo, “Robust and fast geometric quantum computation with multiqubit gates in cavity QED,” Phys. Rev. A 79, 064303 (2009).
[CrossRef]

M. S. Tame, K. Özdemir Ş, M. Koashi, N. Imoto, and M. S. Kim, “Compact Toffoli gate using weighted graph states,” Phys. Rev. A 79, 020302(R) (2009).
[CrossRef]

T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009).
[CrossRef]

R. Ionicioiu, T. P. Spiller, and W. J. Munro, “Generalized Toffoli gates using qudit catalysis,” Phys. Rev. A 80, 012312 (2009).
[CrossRef]

2008

K. Tordrup and K. Mølmer, “Quantum computing with a single molecular ensemble and a Cooper-pair box,” Phys. Rev. A 77, 020301(R) (2008).
[CrossRef]

B. Ghosh, A. S. Majumdar, and N. Nayak, “Control of atomic entanglement by dynamic Stark effect,” J. Phys. B: At. Mol. Opt. Phys. 41, 065503 (2008).
[CrossRef]

2007

P. Bohlouli-Zanjani, J. A. Petrus, and J. D. D. Martin, “Enhancement of Rydberg atom interactions using ac Stark shifts,” Phys. Rev. Lett. 98, 203005 (2007).
[CrossRef]

A. Retzker and M. B. Plenio, “Fast cooling of trapped ions using the dynamical Stark shift,” New J. Phys. 9, 279 (2007).
[CrossRef]

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[CrossRef]

G. Wendin and V. Shumeiko, “Quantum bits with Josephson junctions,” Low Temp. Phys. 33, 724–744(2007).
[CrossRef]

X. Q. Shao, A. D. Zhu, S. Zhang, J. S. Chung, and K. H. Yeon, “Efficient scheme for implementing an N-qubit Toffoli gate by a single resonant interaction with cavity quantum electrodynamics,” Phys. Rev. A 75, 034307 (2007).
[CrossRef]

Y. F. Xiao, X. B. Zou, and G. C. Guo, “Implementing a conditional N-qubit phase gate in a largely detuned optical cavity,” Phys. Rev. A 75, 014302 (2007).
[CrossRef]

X. B. Zou, Y. F. Xiao, S. B. Li, Y. Yang, and G. C. Guo, “Quantum phase gate through a dispersive atom-field interaction,” Phys. Rev. A 75, 064301 (2007).
[CrossRef]

W. L. Yang, C. Y. Chen, and M. Feng, “Implementation of three-qubit Grover search in cavity quantum electrodynamics,” Phys. Rev. A 76, 054301 (2007).
[CrossRef]

2006

C. Y. Chen, M. Feng, and K. L. Gao, “Toffoli gate originating from a single resonant interaction with cavity QED,” Phys. Rev. A 73, 064304 (2006).
[CrossRef]

J. Fiurášek, “Linear-optics quantum Toffoli and Fredkin gates,” Phys. Rev. A 73, 062313 (2006).
[CrossRef]

C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006).
[CrossRef]

2005

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

M. Sarovar and G. J. Milburn, “Continuous quantum error correction,” Proc. SPIE 5842, 158 (2005).
[CrossRef]

S. B. Zheng, “Quantum logic gates for two atoms with a single resonant interaction,” Phys. Rev. A 71, 062335 (2005).
[CrossRef]

2004

C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
[CrossRef]

2003

M. S. Zubairy, M. Kim, and M. O. Scully, “Cavity-QED-based quantum phase gate,” Phys. Rev. A 68, 033820 (2003).
[CrossRef]

X. X. Yi, X. H. Su, and L. You, “Conditional quantum phase gate between two 3-state atoms,” Phys. Rev. Lett. 90, 097902 (2003).
[CrossRef]

L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
[CrossRef]

2002

X. B. Wang and K. Matsumoto, “Nonadiabatic detection of the geometric phase of the macroscopic quantum state with a symmetric SQUID,” Phys. Rev. B 65, 172508 (2002).
[CrossRef]

2001

E. Solano, M. França Santos, and P. Milman, “Quantum phase gate with a selective interaction,” Phys. Rev. A 64, 024304 (2001).
[CrossRef]

L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang, “Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance,” Nature 414, 883–887 (2001).
[CrossRef]

J. Du, M. Shi, J. Wu, X. Zhou, and R. Han, “Implementing universal multiqubit quantum logic gates in three- and four-spin systems at room temperature,” Phys. Rev. A 63, 042302 (2001).
[CrossRef]

1999

Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, “Coherent control of macroscopic quantum states in a single-Cooper-pair box,” Nature 398, 786–788 (1999).
[CrossRef]

1998

D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett. 81, 2152–2155 (1998).
[CrossRef]

1997

N. A. Gershenfeld and I. L. Chuang, “Bulk spin-resonance quantum computation,” Science 275, 350–356 (1997).
[CrossRef]

A. Shnirman, G. Schön, and Z. Hermon, “Quantum manipulations of small Josephson junctions,” Phys. Rev. Lett. 79, 2371–2374 (1997).
[CrossRef]

1995

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef]

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

T. Sleator and H. Weinfurter, “Realizable universal quantum logic gates,” Phys. Rev. Lett. 74, 4087–4090 (1995).
[CrossRef]

D. P. DiVincenzo, “Two-bit gates are universal for quantum computation,” Phys. Rev. A 51, 1015–1022 (1995).
[CrossRef]

Barenco, A.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

Blatt, R.

T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009).
[CrossRef]

Bohlouli-Zanjani, P.

P. Bohlouli-Zanjani, J. A. Petrus, and J. D. D. Martin, “Enhancement of Rydberg atom interactions using ac Stark shifts,” Phys. Rev. Lett. 98, 203005 (2007).
[CrossRef]

Breyta, G.

L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang, “Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance,” Nature 414, 883–887 (2001).
[CrossRef]

Chen, C. Y.

W. L. Yang, C. Y. Chen, and M. Feng, “Implementation of three-qubit Grover search in cavity quantum electrodynamics,” Phys. Rev. A 76, 054301 (2007).
[CrossRef]

C. Y. Chen, M. Feng, and K. L. Gao, “Toffoli gate originating from a single resonant interaction with cavity QED,” Phys. Rev. A 73, 064304 (2006).
[CrossRef]

Chen, L.

X. Q. Shao, H. F. Wang, L. Chen, S. Zhang, and K. H. Yeon, “One-step implementation of the Toffoli gate via quantum Zeno dynamics,” Phys. Lett. A 374, 28–33 (2009).
[CrossRef]

Chu, S. I.

C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
[CrossRef]

Chuang, I. L.

L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang, “Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance,” Nature 414, 883–887 (2001).
[CrossRef]

N. A. Gershenfeld and I. L. Chuang, “Bulk spin-resonance quantum computation,” Science 275, 350–356 (1997).
[CrossRef]

M. A. Nielsen and I. L. ChuangQuantum Computation and Quantum Information (Cambridge University, 2000).

Chung, J. S.

X. Q. Shao, A. D. Zhu, S. Zhang, J. S. Chung, and K. H. Yeon, “Efficient scheme for implementing an N-qubit Toffoli gate by a single resonant interaction with cavity quantum electrodynamics,” Phys. Rev. A 75, 034307 (2007).
[CrossRef]

Chwalla, M.

T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009).
[CrossRef]

Cirac, J. I.

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett. 74, 4091–4094 (1995).
[CrossRef]

Cory, D. G.

D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett. 81, 2152–2155 (1998).
[CrossRef]

Deutsch, D.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

DiVincenzo, D. P.

D. P. DiVincenzo, “Two-bit gates are universal for quantum computation,” Phys. Rev. A 51, 1015–1022 (1995).
[CrossRef]

Du, J.

J. Du, M. Shi, J. Wu, X. Zhou, and R. Han, “Implementing universal multiqubit quantum logic gates in three- and four-spin systems at room temperature,” Phys. Rev. A 63, 042302 (2001).
[CrossRef]

Du, J. F.

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and J. F. Du, “One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” Appl. Phys. Lett. 96, 241113 (2010).
[CrossRef]

Ekert, A.

A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. 74, 4083–4086 (1995).
[CrossRef]

Feng, M.

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and J. F. Du, “One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” Appl. Phys. Lett. 96, 241113 (2010).
[CrossRef]

W. L. Yang, C. Y. Chen, and M. Feng, “Implementation of three-qubit Grover search in cavity quantum electrodynamics,” Phys. Rev. A 76, 054301 (2007).
[CrossRef]

C. Y. Chen, M. Feng, and K. L. Gao, “Toffoli gate originating from a single resonant interaction with cavity QED,” Phys. Rev. A 73, 064304 (2006).
[CrossRef]

Fiurášek, J.

J. Fiurášek, “Linear-optics quantum Toffoli and Fredkin gates,” Phys. Rev. A 73, 062313 (2006).
[CrossRef]

França Santos, M.

E. Solano, M. França Santos, and P. Milman, “Quantum phase gate with a selective interaction,” Phys. Rev. A 64, 024304 (2001).
[CrossRef]

Gao, K. L.

C. Y. Chen, M. Feng, and K. L. Gao, “Toffoli gate originating from a single resonant interaction with cavity QED,” Phys. Rev. A 73, 064304 (2006).
[CrossRef]

Gershenfeld, N. A.

N. A. Gershenfeld and I. L. Chuang, “Bulk spin-resonance quantum computation,” Science 275, 350–356 (1997).
[CrossRef]

Ghosh, B.

B. Ghosh, A. S. Majumdar, and N. Nayak, “Control of atomic entanglement by dynamic Stark effect,” J. Phys. B: At. Mol. Opt. Phys. 41, 065503 (2008).
[CrossRef]

Gilchrist, A.

T. C. Ralph, K. J. Resch, and A. Gilchrist, “Efficient Toffoli gates using qudits,” Phys. Rev. A 75, 022313 (2007).
[CrossRef]

Goh, K. W.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Guo, G. C.

G. W. Lin, X. B. Zou, X. M. Lin, and G. C. Guo, “Robust and fast geometric quantum computation with multiqubit gates in cavity QED,” Phys. Rev. A 79, 064303 (2009).
[CrossRef]

Y. F. Xiao, X. B. Zou, and G. C. Guo, “Implementing a conditional N-qubit phase gate in a largely detuned optical cavity,” Phys. Rev. A 75, 014302 (2007).
[CrossRef]

X. B. Zou, Y. F. Xiao, S. B. Li, Y. Yang, and G. C. Guo, “Quantum phase gate through a dispersive atom-field interaction,” Phys. Rev. A 75, 064301 (2007).
[CrossRef]

Han, R.

J. Du, M. Shi, J. Wu, X. Zhou, and R. Han, “Implementing universal multiqubit quantum logic gates in three- and four-spin systems at room temperature,” Phys. Rev. A 63, 042302 (2001).
[CrossRef]

Han, S.

C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
[CrossRef]

Hänsel, W.

T. Monz, K. Kim, W. Hänsel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Lett. 102, 040501 (2009).
[CrossRef]

Havel, T. F.

D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett. 81, 2152–2155 (1998).
[CrossRef]

Hennrich, M.

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X. Q. Shao, H. F. Wang, L. Chen, S. Zhang, and K. H. Yeon, “One-step implementation of the Toffoli gate via quantum Zeno dynamics,” Phys. Lett. A 374, 28–33 (2009).
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L. You, X. X. Yi, and X. H. Su, “Quantum logic between atoms inside a high-Q optical cavity,” Phys. Rev. A 67, 032308 (2003).
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W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and J. F. Du, “One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” Appl. Phys. Lett. 96, 241113 (2010).
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Y. F. Xiao, X. B. Zou, and G. C. Guo, “Implementing a conditional N-qubit phase gate in a largely detuned optical cavity,” Phys. Rev. A 75, 014302 (2007).
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D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett. 81, 2152–2155 (1998).
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Figures (4)

Fig. 1.
Fig. 1.

Schematic representation of three SQUIDs (1, 2, 3) in a standing-wave quasi-one-dimensional coplanar waveguide (CPW) cavity. Each SQUID with Λ configuration is placed in the plane of the resonator between the two lateral ground planes (xy plane). The transition between levels, |2i|1i, is coupled simultaneously to the cavity mode with the coupling constant gi,and the classical field with the Rabi frequency Ω. Δ represents the corresponding one-photon detuning parameter.

Fig. 2.
Fig. 2.

The fidelities are simulated numerically in subspaces with total excitation numbers from N=1 to N=6. Other parameters: Ω=0.05g3, Δ=2g3, and g=g3/2.

Fig. 3.
Fig. 3.

Evolution of fidelity for generating the maximal entanglement state |ϕ versus the decoherence factor κ/g3 and the operation time t/T. The corresponding parameters are set as γ=κ, Ω=0.05g3, Δ=2g3, and g=g3/2.

Fig. 4.
Fig. 4.

Equivalent physical model for achieving the Toffoli gate in a coupled-cavity array system, where qubit one and qubit two are trapped in one cavity alone for collective control. A common classical field is applied to drive the transition between levels, |2i|1i, with detuning δ, which is different from Δ in Fig. 1. The photon can hop between two cavities with coupling strength A.

Equations (18)

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HI=i=13gi(a|2ii1|+|1ii2|a)+Ω(|2ii1|+|1ii2|)Δ|2ii2|,
gi(x)=MscLihνcL0l1|Φ|2isin(2πλx),
Ω=1L1|Φ|2SBμw(r)·dS.
HI001=(Δ+4g32+Δ2)Ω8g32+2Δ(Δ+4g32+Δ2)|001|0cΨ|+(Δ4g32+Δ2)Ω8g32+2Δ(Δ4g32+Δ2)|001|0cΨ+|+H.c.+E|ΨΨ|+E+|Ψ+Ψ+|,
E=12Δ4g32+Δ2,
|Ψ=Δ±4g32+Δ28g32+2Δ(Δ±4g32+Δ2)|002|0c+2g38g32+2Δ(Δ±4g32+Δ2)|001|1c.
λ001=Ω2E(Δ+4g32+Δ2)2[8g32+2Δ(Δ+4g32+Δ2)]Ω2E+(Δ4g32+Δ2)2[8g32+2Δ(Δ4g32+Δ2)]=0,
HI101=2(g3g)Ω8g32+8g2+2Δ(Δ4g32+4g2+Δ2)|101|0cΨb|+2(g3g)Ω8g32+8g2+2Δ(Δ+4g32+4g2+Δ2)|101|0cΨc|+(g3+g)Ωg32+g2|101|0cΨa|+H.c.+Ea|ΨaΨa|+Eb|ΨbΨb|+Ec|ΨcΨc|,
Ea=Δ,Eb/c=12(Δ4g2+4g32+Δ2),
|Ψa=1g32+g2(g3|201+g|102)|0c,
|Ψb/c=18g32+8g2+2Δ(Δ4g32+4g2+Δ2)[2g3|102|0c2g|201|0c(Δ4g32+4g2+Δ2)|101|1c].
λ101=1Eb4Ω2(g3g)2[8g32+8g2+2Δ(Δ4g32+4g2+Δ2)]1Ec4Ω2(g3g)2[8g32+8g2+2Δ(Δ+4g32+4g2+Δ2)]1Ea(g3+g)2Ω2(g32+g2)=(g3+g)2Ω2(g32+g2)Δ,
2(g3+g)2Ω2(g32+2g2)Δ.
Heff=Ω2Δ[(g3+g)2(g32+g2)(|101101|+|011011|)+2(g3+g)2(g32+2g2)|111111|]|0c0c|.
Toffoli=H3TpH3=(1000000001000000001000000001000000001000000001000000000100000010),
|ϕ=122(|000+|001+|010+|011+|100+|101+|110|111),
|ϕ0=122(|000+|001+|010+|011+|100+|101+|110+|111),
ρ˙=i[HI,ρ]κ2(aaρ2aρa+ρaa)j=0,1n=13γn2j2(σ22nρ2σj2nρσ2jn+ρσ22n),

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