Abstract

We present a fast and effective scheme to implement the multiqubit discrete quantum Fourier transform (DQFT) for distant atoms trapped in separate cavities connected by optical fibers via a virtual-photon-induced process. The effective coupling between two distributed atoms is achieved without exciting and transporting photons through the optical fiber, and the gate operation is robust against the decoherence effect when the thermal photons in the environment are negligible. The implementation of the scheme is appealingly simple because the complex combination of quantum gate operations, which act on each two qubits in the rearranged DQFT circuit, is achieved only in one step through the interaction controlled by optical switches between two adjacent cavities. The scheme opens promising perspectives for scalable quantum communication networks and distributed quantum computation.

© 2012 Optical Society of America

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References

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  1. P. W. Shor, “Algorithms for quantum computer computation: discrete logarithms and factoring,” in Proceedings of the Symposium on the Foundations of Computer Science (IEEE, 1994), pp. 124–134.
  2. L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325–328 (1997).
    [CrossRef]
  3. A. Ekert and R. Jozsa, “Quantum computation and Shor’s factoring algorithm,” Rev. Mod. Phys. 68, 733–753 (1996).
    [CrossRef]
  4. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
  5. A. Chefles, “Distributed implementation of standard oracle operators,” Phys. Rev. A 78, 062304 (2008).
    [CrossRef]
  6. M. O. Scully and M. S. Zubairy, “Cavity QED implementation of the discrete quantum Fourier transform,” Phys. Rev. A 65, 052324 (2002).
    [CrossRef]
  7. H. F. Wang, S. Zhang, and K. H. Yeon, “Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics,” J. Korean Phys. Soc. 53, 1787–1790 (2008).
  8. H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
    [CrossRef]
  9. H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics,” New J. Phys. 13, 013021 (2011).
    [CrossRef]
  10. Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
    [CrossRef]
  11. J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
    [CrossRef]
  12. R. Barak and Y. Ben-Aryeh, “Quantum fast Fourier transform and quantum computation by linear optics,” J. Opt. Soc. Am. B 24, 231–240 (2007).
    [CrossRef]
  13. J. C. Howell and J. A. Yeazell, “Reducing the complexity of linear optics quantum circuits,” Phys. Rev. A 61, 052303(2000).
    [CrossRef]
  14. H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, “Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits,” J. Phys. B 44, 115502(2011).
    [CrossRef]
  15. A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
    [CrossRef]
  16. M. F. Santos, E. Solano, and R. L. de Matos Filho, “Conditional large Fock state preparation and field state reconstruction in cavity QED,” Phys. Rev. Lett. 87, 093601 (2001).
    [CrossRef]
  17. M. Feng, “Quantum computing with trapped ions in an optical cavity via Raman transition,” Phys. Rev. A 66, 054303 (2002).
    [CrossRef]
  18. A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
    [CrossRef]
  19. S. B. Zheng, “Virtual-photon-induced quantum phase gates for two distant atoms trapped in separate cavities,” Appl. Phys. Lett. 94, 154101 (2009).
    [CrossRef]
  20. S. B. Zheng, “Quantum communication and entanglement between two distant atoms via vacuum fields,” Chin. Phys. B 19, 064204 (2010).
    [CrossRef]
  21. A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
    [CrossRef]

2011

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics,” New J. Phys. 13, 013021 (2011).
[CrossRef]

H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, “Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits,” J. Phys. B 44, 115502(2011).
[CrossRef]

2010

H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
[CrossRef]

S. B. Zheng, “Quantum communication and entanglement between two distant atoms via vacuum fields,” Chin. Phys. B 19, 064204 (2010).
[CrossRef]

2009

S. B. Zheng, “Virtual-photon-induced quantum phase gates for two distant atoms trapped in separate cavities,” Appl. Phys. Lett. 94, 154101 (2009).
[CrossRef]

2008

H. F. Wang, S. Zhang, and K. H. Yeon, “Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics,” J. Korean Phys. Soc. 53, 1787–1790 (2008).

A. Chefles, “Distributed implementation of standard oracle operators,” Phys. Rev. A 78, 062304 (2008).
[CrossRef]

2007

2006

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

2004

J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
[CrossRef]

2002

M. Feng, “Quantum computing with trapped ions in an optical cavity via Raman transition,” Phys. Rev. A 66, 054303 (2002).
[CrossRef]

M. O. Scully and M. S. Zubairy, “Cavity QED implementation of the discrete quantum Fourier transform,” Phys. Rev. A 65, 052324 (2002).
[CrossRef]

2001

Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
[CrossRef]

M. F. Santos, E. Solano, and R. L. de Matos Filho, “Conditional large Fock state preparation and field state reconstruction in cavity QED,” Phys. Rev. Lett. 87, 093601 (2001).
[CrossRef]

2000

J. C. Howell and J. A. Yeazell, “Reducing the complexity of linear optics quantum circuits,” Phys. Rev. A 61, 052303(2000).
[CrossRef]

1999

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

1997

L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325–328 (1997).
[CrossRef]

1996

A. Ekert and R. Jozsa, “Quantum computation and Shor’s factoring algorithm,” Rev. Mod. Phys. 68, 733–753 (1996).
[CrossRef]

Awschalom, D. D.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

Barak, R.

Ben-Aryeh, Y.

Boca, A.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

Boozer, A. D.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

Bose, S.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Burkard, G.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

Chefles, A.

A. Chefles, “Distributed implementation of standard oracle operators,” Phys. Rev. A 78, 062304 (2008).
[CrossRef]

Chuang, I. L.

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

Cory, D. G.

Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
[CrossRef]

de Matos Filho, R. L.

M. F. Santos, E. Solano, and R. L. de Matos Filho, “Conditional large Fock state preparation and field state reconstruction in cavity QED,” Phys. Rev. Lett. 87, 093601 (2001).
[CrossRef]

Dheng, Z. W.

J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
[CrossRef]

DiVincenzo, D. P.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

Ekert, A.

A. Ekert and R. Jozsa, “Quantum computation and Shor’s factoring algorithm,” Rev. Mod. Phys. 68, 733–753 (1996).
[CrossRef]

Feng, M.

M. Feng, “Quantum computing with trapped ions in an optical cavity via Raman transition,” Phys. Rev. A 66, 054303 (2002).
[CrossRef]

Fortunato, E. M.

Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
[CrossRef]

Grover, L. K.

L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325–328 (1997).
[CrossRef]

Howell, J. C.

J. C. Howell and J. A. Yeazell, “Reducing the complexity of linear optics quantum circuits,” Phys. Rev. A 61, 052303(2000).
[CrossRef]

Imamoglu, A.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

Jiang, X. X.

H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, “Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits,” J. Phys. B 44, 115502(2011).
[CrossRef]

Jozsa, R.

A. Ekert and R. Jozsa, “Quantum computation and Shor’s factoring algorithm,” Rev. Mod. Phys. 68, 733–753 (1996).
[CrossRef]

Kimble, H. J.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

Liu, W. Z.

J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
[CrossRef]

Lloyd, S.

Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
[CrossRef]

Long, G. L.

J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
[CrossRef]

Loss, D.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

Lu, Z. H.

J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
[CrossRef]

Mancini, S.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Miller, R.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

Nielsen, M. A.

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

Northup, T. E.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

Pravia, M. A.

Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
[CrossRef]

Santos, M. F.

M. F. Santos, E. Solano, and R. L. de Matos Filho, “Conditional large Fock state preparation and field state reconstruction in cavity QED,” Phys. Rev. Lett. 87, 093601 (2001).
[CrossRef]

Scully, M. O.

M. O. Scully and M. S. Zubairy, “Cavity QED implementation of the discrete quantum Fourier transform,” Phys. Rev. A 65, 052324 (2002).
[CrossRef]

Serafini, A.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Shao, X. Q.

H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
[CrossRef]

Sherwin, M.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

Shor, P. W.

P. W. Shor, “Algorithms for quantum computer computation: discrete logarithms and factoring,” in Proceedings of the Symposium on the Foundations of Computer Science (IEEE, 1994), pp. 124–134.

Small, A.

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

Solano, E.

M. F. Santos, E. Solano, and R. L. de Matos Filho, “Conditional large Fock state preparation and field state reconstruction in cavity QED,” Phys. Rev. Lett. 87, 093601 (2001).
[CrossRef]

Wang, H. F.

H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, “Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits,” J. Phys. B 44, 115502(2011).
[CrossRef]

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics,” New J. Phys. 13, 013021 (2011).
[CrossRef]

H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
[CrossRef]

H. F. Wang, S. Zhang, and K. H. Yeon, “Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics,” J. Korean Phys. Soc. 53, 1787–1790 (2008).

Weinstein, Y. S.

Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
[CrossRef]

Yeazell, J. A.

J. C. Howell and J. A. Yeazell, “Reducing the complexity of linear optics quantum circuits,” Phys. Rev. A 61, 052303(2000).
[CrossRef]

Yeon, K. H.

H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, “Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits,” J. Phys. B 44, 115502(2011).
[CrossRef]

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics,” New J. Phys. 13, 013021 (2011).
[CrossRef]

H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
[CrossRef]

H. F. Wang, S. Zhang, and K. H. Yeon, “Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics,” J. Korean Phys. Soc. 53, 1787–1790 (2008).

Zhang, J. F.

J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
[CrossRef]

Zhang, S.

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics,” New J. Phys. 13, 013021 (2011).
[CrossRef]

H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, “Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits,” J. Phys. B 44, 115502(2011).
[CrossRef]

H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
[CrossRef]

H. F. Wang, S. Zhang, and K. H. Yeon, “Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics,” J. Korean Phys. Soc. 53, 1787–1790 (2008).

Zhao, Y. F.

H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
[CrossRef]

Zheng, S. B.

S. B. Zheng, “Quantum communication and entanglement between two distant atoms via vacuum fields,” Chin. Phys. B 19, 064204 (2010).
[CrossRef]

S. B. Zheng, “Virtual-photon-induced quantum phase gates for two distant atoms trapped in separate cavities,” Appl. Phys. Lett. 94, 154101 (2009).
[CrossRef]

Zhu, A. D.

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics,” New J. Phys. 13, 013021 (2011).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, “Cavity QED implementation of the discrete quantum Fourier transform,” Phys. Rev. A 65, 052324 (2002).
[CrossRef]

Appl. Phys. Lett.

S. B. Zheng, “Virtual-photon-induced quantum phase gates for two distant atoms trapped in separate cavities,” Appl. Phys. Lett. 94, 154101 (2009).
[CrossRef]

Chin. Phys. B

S. B. Zheng, “Quantum communication and entanglement between two distant atoms via vacuum fields,” Chin. Phys. B 19, 064204 (2010).
[CrossRef]

J. Korean Phys. Soc.

H. F. Wang, S. Zhang, and K. H. Yeon, “Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics,” J. Korean Phys. Soc. 53, 1787–1790 (2008).

J. Opt. Soc. Am. B

J. Phys. B

H. F. Wang, X. Q. Shao, Y. F. Zhao, S. Zhang, and K. H. Yeon, “Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED,” J. Phys. B 43, 065503 (2010).
[CrossRef]

H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, “Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits,” J. Phys. B 44, 115502(2011).
[CrossRef]

New J. Phys.

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics,” New J. Phys. 13, 013021 (2011).
[CrossRef]

Phys. Rev. A

A. Chefles, “Distributed implementation of standard oracle operators,” Phys. Rev. A 78, 062304 (2008).
[CrossRef]

M. O. Scully and M. S. Zubairy, “Cavity QED implementation of the discrete quantum Fourier transform,” Phys. Rev. A 65, 052324 (2002).
[CrossRef]

J. F. Zhang, G. L. Long, Z. W. Dheng, W. Z. Liu, and Z. H. Lu, “Nuclear magnetic resonance implementation of a quantum clock synchronization algorithm,” Phys. Rev. A 70, 062322 (2004).
[CrossRef]

J. C. Howell and J. A. Yeazell, “Reducing the complexity of linear optics quantum circuits,” Phys. Rev. A 61, 052303(2000).
[CrossRef]

M. Feng, “Quantum computing with trapped ions in an optical cavity via Raman transition,” Phys. Rev. A 66, 054303 (2002).
[CrossRef]

Phys. Rev. Lett.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

M. F. Santos, E. Solano, and R. L. de Matos Filho, “Conditional large Fock state preparation and field state reconstruction in cavity QED,” Phys. Rev. Lett. 87, 093601 (2001).
[CrossRef]

L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325–328 (1997).
[CrossRef]

Y. S. Weinstein, M. A. Pravia, E. M. Fortunato, S. Lloyd, and D. G. Cory, “Implementation of the quantum Fourier transform,” Phys. Rev. Lett. 86, 1889–1891 (2001).
[CrossRef]

Rev. Mod. Phys.

A. Ekert and R. Jozsa, “Quantum computation and Shor’s factoring algorithm,” Rev. Mod. Phys. 68, 733–753 (1996).
[CrossRef]

Other

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

P. W. Shor, “Algorithms for quantum computer computation: discrete logarithms and factoring,” in Proceedings of the Symposium on the Foundations of Computer Science (IEEE, 1994), pp. 124–134.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of atom-cavity-fiber system. (b) Involved atomic levels and transitions in cavity.

Fig. 2.
Fig. 2.

(a) Naive quantum circuit diagram of DQFT. Rk (k=2,3,,n) are a series of phase transformations denoted by Eq. (13) and H is the Hadamard gate transformation. The black dots present the control bits. (b) Rearranged quantum circuit for the implementation of DQFT. In this way the interaction model governed by the Hamiltonian (10) will be possible between arbitrary qubit pairs.

Fig. 3.
Fig. 3.

Schematic setup to implement DQFT for distant atoms trapped in separate cavities coupled by optical fibers. The detunings Δ3j are adjusted by the classical laser fields by changing the frequencies of laser fields. The optical switches s1,s2,,sN1 control two adjacent cavities whether have interaction or not and the CRk+SWAP represents the combinative gate operation performing on the corresponding qubits.

Tables (1)

Tables Icon

Table 1. Values That the Δ3j Can Hold Corresponding to Different Values of k When Setting gj=g, Ω1j=Ω2j=g, ν=2g, Δ1j=10g, and Δ2j=13g (j=1, 2)

Equations (20)

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

Hc,f=νb(a1+a2)+H.c.,
Hi=j=12[(gjajeiΔ1jt+Ω1jeiΔ2jt)|rjej|+Ω2jeiΔ3jt|rjgj|+H.c.].
Hi=j=12[ξ1jajaj|ejej|+ξ2j|ejej|+ξ3j|gjgj|+λ1j(ajSj+eiδ1jt+ajSjeiδ1jt)+λ2j(Sj+eiδ2jt+Sjeiδ2jt)+λ3j(ajeiδ3jt+ajeiδ3jt)|ejej|],
λ1j=gjΩ2j2(1Δ1j+1Δ3j),λ2j=Ω1jΩ2j2(1Δ2j+1Δ3j),λ3j=gjΩ1j2(1Δ1j+1Δ2j),ξ1j=gj2Δ1j,ξ2j=Ω1j2Δ2j,ξ3j=Ω2j2Δ3j,δ1j=Δ3jΔ1j,δ2j=Δ3jΔ2j,δ3j=Δ2jΔ1j.
c0=12(a1a2),c1=12(a1+a2+2b),c2=12(a1+a22b),
H=Hc,f+Hi,
Hc,f=2νc1c12νc2c2,Hi=12[λ11eiδ11t(c1+c2+2c0)S1++λ12eiδ12t(c1+c22c0)S2++λ31eiδ31t(c1+c2+2c0)|e1e1|+λ32eiδ32t(c1+c22c0)|e2e2|+ξ112(c1c2+2c1c0+2c2c0)|e1e1|+ξ122(c1c22c1c02c2c0)|e2e2|+H.c.]j=12{[ξ2j+ξ1j4(c1c1+c2c2+2c0c0)]|ejej|+ξ3j|gjgj|+λ2j(eiδ2jtSj++eiδ2jtSj)}.
Hi=j=12{[ξ2j+ξ1j4(c1c1+c2c2+2c0c0)]|ejej|+ξ3j|gjgj|+λ2j(eiδ2jtSj++eiδ2jtSj)}{λ112[ei(δ11+2ν)tc1+ei(δ112ν)tc2+2eiδ11tc0]S1++λ122[ei(δ12+2ν)tc1+ei(δ122ν)tc22eiδ12tc0]S2++λ312[ei(δ31+2ν)tc1+ei(δ312ν)tc2+2eiδ31tc0]|e1e1|+λ322[ei(δ32+2ν)tc1+ei(δ322ν)tc22eiδ32tc0]|e2e2|+ξ114(ei22νtc1c2+2ei2νtc1c0+2ei2νtc2c0)|e1e1|+ξ124(ei22νtc1c22ei2νtc1c02ei2νtc2c0)|e2e2|+H.c.}.
He=j=12{[ξ2j+ξ1j4(c1c1+c2c2+2c0c0)]|ejej|+ξ3j|gjgj|}+j=12{λ1j24[(2δ1jc0c0+1δ1j+2νc1c1+1δ1j2νc2c2)|gjgj|+(2δ1jc0c0+1δ1j+2νc1c1+1δ1j2νc2c2)|ejej|]+λ2j2δ2j(|gjgj|+|ejej|)}+1322ν(c1c1c2c2)[5(ξ112|e1e1|+ξ122|e2e2|)6ξ11ξ12|e1e2e1e2|]+14[(λ312δ312ν+λ312δ31+2ν)|e1e1|+(λ322δ322ν+λ322δ32+2ν)|e2e2|]+λ31λ324(1δ312ν+1δ322ν+1δ31+2ν+1δ32+2ν)|e1e2e1e2|+12[λ312δ31|e1e1|+λ322δ32|e2e2|λ31λ32(1δ31+1δ32)|e1e2e1e2|]+[λ11λ128(1δ112ν+1δ122ν+1δ11+2ν+1δ12+2ν2δ112δ12)+λ21λ22(1δ21+1δ22)](S1+S2+S1S2+).
He=j=12(ηj|gjgj|+ϑj|ejej|)+μ|e1e2e1e2|+ζ(S1+S2+S1S2+),
ηj=λ1j24(2δ1j+1δ1j2ν+1δ1j+2ν)+λ2j2δ2jξ3j,ϑj=λ3j24(1δ3j2ν+1δ3j+2ν)+λ3j22δ3j+λ2j2δ2jξ2j,μ=λ31λ324[1δ312ν+1δ322ν+1δ31+2ν+1δ32+2ν2(1δ31+1δ32)],ζ=λ11λ128(1δ112ν+1δ122ν+1δ11+2ν+1δ12+2ν2δ112δ12)+λ21λ22(1δ21+1δ22).
|j12N/2k=02N1e2πijk/2N|k=12N/2(|0+e2πi0.jN|1)(|0+e2πi0.jN1jN|1)(|0+e2πi0.j1j2jN|1),
Rj=(100ei2π/2j),j=2,3,,N.
|g1g2=ei(η1+η2)t|g1g2,|g1e2=ei(η1+ϑ2)t(cosζt|g1e2isinζt|e1g2),|e1g2=ei(η2+ϑ1)t(cosζt|e1g2isinζt|g1e2),|e1e2=ei(ϑ1+ϑ2+μ)t|e1e2.
|g1|g2|g1|g2,|g1|e2cosζt|g1|e2isinζt|e1|g2,|e1|g2cosζt|e1|g2isinζt|g1|e2,|e1|e2eiμt|e1|e2.
V=(100001000010000ei2π/2k)(1000001001000001),
|ψ0=j=02N1αj|j,
|ψr=k=02N1bk|k,
bk=12Nj=02N1aje2πijk/2N.
Pmax3=λ11λ128[1(δ112ν)2+1(δ122ν)2+1(δ11+2ν)2+1(δ12+2ν)22δ1122δ122]+λ21λ22(1δ212+1δ222).4.81×104.

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