Abstract

We propose an efficient protocol for optimizing the physical implementation of three-qubit quantum error correction with spatially separated quantum dot spins via virtual-photon-induced process. In the protocol, each quantum dot is trapped in an individual cavity and each two cavities are connected by an optical fiber. We propose the optimal quantum circuits and describe the physical implementation for correcting both the bit flip and phase flip errors by applying a series of one-bit unitary rotation gates and two-bit quantum iSWAP gates that are produced by the long-range interaction between two distributed quantum dot spins mediated by the vacuum fields of the fiber and cavity. The protocol opens promising perspectives for long distance quantum communication and distributed quantum computation networks.

© 2013 OSA

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  23. G. Burkard, D. Loss, D. P. DiVincenzo, and J. A. Smolin, “Physical optimization of quantum error correction circuits,” Phys. Rev. B60, 11404–11416 (1999).
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  24. O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor,” Phys. Rev. Lett.107, 160501 (2011).
    [CrossRef] [PubMed]
  25. J. W. Pan, C Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature410, 1067–1070 (2001).
    [CrossRef] [PubMed]
  26. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A77, 042308 (2008).
    [CrossRef]
  27. Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A81, 032307 (2010).
    [CrossRef]
  28. F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A83, 062316 (2011).
    [CrossRef]
  29. H. F. Wang, S. Zhang, and K. H. Yeon, “Linear optical scheme for entanglement concentration of two partially entangled three-photon W states,” Eur. Phys. J. D56, 271–275 (2010).
    [CrossRef]
  30. H. F. Wang, S. Zhang, and K. H. Yeon, “Linear-optics-based entanglement concentration of unknown partially entangled three-photon W states,” J. Opt. Soc. Am. B27, 2159–2164 (2010).
    [CrossRef]
  31. H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unknown atomic entangled states by interference of polarized photons,” J. Phys. B: At. Mol. Opt. Phys.43, 235501 (2010).
    [CrossRef]
  32. C. Wang, Y. Zhao, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A84, 032307 (2011).
    [CrossRef]
  33. Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A85, 012307 (2012).
    [CrossRef]
  34. Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A85, 042302 (2012).
    [CrossRef]
  35. Y. B. Sheng, L. Zhou, L. Wang, and S. M. Zhao, “Efficient entanglement concentration for quantum dot and optical microcavities systems,” Quantum. Inf. Process.12, 1885–1895 (2013).
    [CrossRef]
  36. Y. B. Sheng and L. Zhou, “Efficient W-state entanglement concentration using quantum-dot and optical micro-cavities,” J. Opt. Soc. Am. B30, 678–686 (2013).
    [CrossRef]
  37. D. Stepanenko and G. Burkard, “Quantum gates between capacitively coupled double quantum dot two-spin qubits,” Phys. Rev. B75, 085324 (2007).
    [CrossRef]
  38. J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, “Relaxation, dephasing, and quantum control of electron spins in double quantum dots,” Phys. Rev. B76, 035315 (2007).
    [CrossRef]
  39. K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009).
    [CrossRef] [PubMed]
  40. G. Shinkai, T. Hayashi, T. Ota, and T. Fujisawa, “Correlated Coherent Oscillations in Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 056802 (2009).
    [CrossRef] [PubMed]
  41. T. Meunier, V. E. Calado, and L. M. K. Vandersypen, “Efficient controlled-phase gate for single-spin qubits in quantum dots,” Phys. Rev. B83, 121403(R)(2011).
    [CrossRef]
  42. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, “Spins in few-electron quantum dots,” Rev. Mod. Phys.79, 1217–1265 (2007).
    [CrossRef]
  43. D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A57, 120–126 (1998)
    [CrossRef]
  44. A. Imamoḡlu, 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]
  45. C. Y. Hsieh and P. Hawrylak, “Quantum circuits based on coded qubits encoded in chirality of electron spin complexes in triple quantum dots,” Phys. Rev. B82, 205311 (2010).
    [CrossRef]
  46. C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B83, 115303 (2011).
    [CrossRef]
  47. A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, “Phonon mediated off-resonant quantum dot-cavity coupling under resonant excitation of the quantum dot,” Phys. Rev. B84, 085309 (2011).
    [CrossRef]
  48. A. Serafini, S. Mancini, and S. Bose, “Distributed Quantum Computation via Optical Fibers,” Phys. Rev. Lett.96, 010503 (2006).
    [CrossRef] [PubMed]
  49. H. F. Wang, S. Zhang, A. D. Zhu, and K. H. Yeon, “Fast and effective implementation of discrete quantum Fourier transform via virtual-photon-induced process in separate cavities,” J. Opt. Soc. Am. B29, 1078–1084 (2012).
    [CrossRef]
  50. S. B. Zheng, “Virtual-photon-induced quantum phase gates for two distant atoms trapped in separate cavities,” Appl. Phys. Lett.94, 154101 (2009).
    [CrossRef]
  51. S. B. Zheng, “Quantum communication and entanglement between two distant atoms via vacuum fields,” Chin. Phys. B19, 064204 (2010).
    [CrossRef]
  52. N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A67, 032301 (2003).
    [CrossRef]
  53. G. Burkard, D. Loss, and D. P. DiVincenzo, “Coupled quantum dots as quantum gates,” Phys. Rev. B59, 2070–2078 (1999).
    [CrossRef]
  54. D. P. DiVincenzo, “Quantum computing and single-qubit measurements using the spin-filter effect,” J. Appl. Phys.85, 4785–4787 (1999).
    [CrossRef]
  55. B. Schumacher, “Sending entanglement through noisy quantum channels,” Phys. Rev. A54, 2614–2628 (1996).
    [CrossRef] [PubMed]

2013 (2)

Y. B. Sheng, L. Zhou, L. Wang, and S. M. Zhao, “Efficient entanglement concentration for quantum dot and optical microcavities systems,” Quantum. Inf. Process.12, 1885–1895 (2013).
[CrossRef]

Y. B. Sheng and L. Zhou, “Efficient W-state entanglement concentration using quantum-dot and optical micro-cavities,” J. Opt. Soc. Am. B30, 678–686 (2013).
[CrossRef]

2012 (3)

Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A85, 012307 (2012).
[CrossRef]

Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A85, 042302 (2012).
[CrossRef]

H. F. Wang, S. Zhang, A. D. Zhu, and K. H. Yeon, “Fast and effective implementation of discrete quantum Fourier transform via virtual-photon-induced process in separate cavities,” J. Opt. Soc. Am. B29, 1078–1084 (2012).
[CrossRef]

2011 (7)

C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B83, 115303 (2011).
[CrossRef]

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, “Phonon mediated off-resonant quantum dot-cavity coupling under resonant excitation of the quantum dot,” Phys. Rev. B84, 085309 (2011).
[CrossRef]

T. Meunier, V. E. Calado, and L. M. K. Vandersypen, “Efficient controlled-phase gate for single-spin qubits in quantum dots,” Phys. Rev. B83, 121403(R)(2011).
[CrossRef]

C. Wang, Y. Zhao, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A84, 032307 (2011).
[CrossRef]

O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor,” Phys. Rev. Lett.107, 160501 (2011).
[CrossRef] [PubMed]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A83, 062316 (2011).
[CrossRef]

H. F. Wang, S. Zhang, A. D. Zhu, X. X. Yi, and K. H. Yeon, “Local conversion of four Einstein-Podolsky-Rosen photon pairs into four-photon polarization-entangled decoherence-free states with non-photon-number-resolving detectors,” Opt. Express19, 25433–25440 (2011)
[CrossRef]

2010 (6)

H. F. Wang, S. Zhang, and K. H. Yeon, “Linear optical scheme for entanglement concentration of two partially entangled three-photon W states,” Eur. Phys. J. D56, 271–275 (2010).
[CrossRef]

H. F. Wang, S. Zhang, and K. H. Yeon, “Linear-optics-based entanglement concentration of unknown partially entangled three-photon W states,” J. Opt. Soc. Am. B27, 2159–2164 (2010).
[CrossRef]

H. F. Wang, A. D. Zhu, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unknown atomic entangled states by interference of polarized photons,” J. Phys. B: At. Mol. Opt. Phys.43, 235501 (2010).
[CrossRef]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A81, 032307 (2010).
[CrossRef]

S. B. Zheng, “Quantum communication and entanglement between two distant atoms via vacuum fields,” Chin. Phys. B19, 064204 (2010).
[CrossRef]

C. Y. Hsieh and P. Hawrylak, “Quantum circuits based on coded qubits encoded in chirality of electron spin complexes in triple quantum dots,” Phys. Rev. B82, 205311 (2010).
[CrossRef]

2009 (3)

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

K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009).
[CrossRef] [PubMed]

G. Shinkai, T. Hayashi, T. Ota, and T. Fujisawa, “Correlated Coherent Oscillations in Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 056802 (2009).
[CrossRef] [PubMed]

2008 (1)

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A77, 042308 (2008).
[CrossRef]

2007 (3)

D. Stepanenko and G. Burkard, “Quantum gates between capacitively coupled double quantum dot two-spin qubits,” Phys. Rev. B75, 085324 (2007).
[CrossRef]

J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, “Relaxation, dephasing, and quantum control of electron spins in double quantum dots,” Phys. Rev. B76, 035315 (2007).
[CrossRef]

R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, “Spins in few-electron quantum dots,” Rev. Mod. Phys.79, 1217–1265 (2007).
[CrossRef]

2006 (1)

A. Serafini, S. Mancini, and S. Bose, “Distributed Quantum Computation via Optical Fibers,” Phys. Rev. Lett.96, 010503 (2006).
[CrossRef] [PubMed]

2004 (1)

F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A69, 052319 (2004)
[CrossRef]

2003 (3)

F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A68, 042317 (2003).
[CrossRef]

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A68, 042315 (2003).
[CrossRef]

N. Schuch and J. Siewert, “Natural two-qubit gate for quantum computation using the XY interaction,” Phys. Rev. A67, 032301 (2003).
[CrossRef]

2001 (1)

J. W. Pan, C Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature410, 1067–1070 (2001).
[CrossRef] [PubMed]

1999 (4)

G. Burkard, D. Loss, D. P. DiVincenzo, and J. A. Smolin, “Physical optimization of quantum error correction circuits,” Phys. Rev. B60, 11404–11416 (1999).
[CrossRef]

G. Burkard, D. Loss, and D. P. DiVincenzo, “Coupled quantum dots as quantum gates,” Phys. Rev. B59, 2070–2078 (1999).
[CrossRef]

D. P. DiVincenzo, “Quantum computing and single-qubit measurements using the spin-filter effect,” J. Appl. Phys.85, 4785–4787 (1999).
[CrossRef]

A. Imamoḡlu, 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]

1998 (3)

D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A57, 120–126 (1998)
[CrossRef]

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

M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, “Tight Bounds on Quantum Searching,” Fortschr. Phys.46, 493–505 (1998).
[CrossRef]

1997 (2)

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

E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Phys. Rev. A55, 900–911 (1997).
[CrossRef]

1996 (5)

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect Quantum Error Correcting Code,” Phys. Rev. Lett.77, 198–201 (1996).
[CrossRef] [PubMed]

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A54, 3824–3851 (1996).
[CrossRef] [PubMed]

A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett.77, 793–797 (1996).
[CrossRef] [PubMed]

D. P. DiVincenzo and P. W. Shor, “Fault-Tolerant Error Correction with Efficient Quantum Codes,” Phys. Rev. Lett.77, 3260–3263 (1996).
[CrossRef] [PubMed]

B. Schumacher, “Sending entanglement through noisy quantum channels,” Phys. Rev. A54, 2614–2628 (1996).
[CrossRef] [PubMed]

1995 (1)

P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A52, 2493(R)–2496(R) (1995).
[CrossRef]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
[CrossRef] [PubMed]

1992 (2)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett.69, 2881–2884 (1992).
[CrossRef] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett.68, 3121–3124 (1992).
[CrossRef] [PubMed]

Anderson, D.

K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009).
[CrossRef] [PubMed]

Atkinson, P.

K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009).
[CrossRef] [PubMed]

Awschalom, D. D.

A. Imamoḡlu, 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]

Bajcsy, M.

A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, “Phonon mediated off-resonant quantum dot-cavity coupling under resonant excitation of the quantum dot,” Phys. Rev. B84, 085309 (2011).
[CrossRef]

Baugh, J.

O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor,” Phys. Rev. Lett.107, 160501 (2011).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A54, 3824–3851 (1996).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
[CrossRef] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett.69, 2881–2884 (1992).
[CrossRef] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett.68, 3121–3124 (1992).
[CrossRef] [PubMed]

Bose, S.

A. Serafini, S. Mancini, and S. Bose, “Distributed Quantum Computation via Optical Fibers,” Phys. Rev. Lett.96, 010503 (2006).
[CrossRef] [PubMed]

Boyer, M.

M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, “Tight Bounds on Quantum Searching,” Fortschr. Phys.46, 493–505 (1998).
[CrossRef]

Brassard, G.

M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, “Tight Bounds on Quantum Searching,” Fortschr. Phys.46, 493–505 (1998).
[CrossRef]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
[CrossRef] [PubMed]

Brukner, C.

J. W. Pan, C Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature410, 1067–1070 (2001).
[CrossRef] [PubMed]

Burkard, G.

D. Stepanenko and G. Burkard, “Quantum gates between capacitively coupled double quantum dot two-spin qubits,” Phys. Rev. B75, 085324 (2007).
[CrossRef]

A. Imamoḡlu, 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]

G. Burkard, D. Loss, D. P. DiVincenzo, and J. A. Smolin, “Physical optimization of quantum error correction circuits,” Phys. Rev. B60, 11404–11416 (1999).
[CrossRef]

G. Burkard, D. Loss, and D. P. DiVincenzo, “Coupled quantum dots as quantum gates,” Phys. Rev. B59, 2070–2078 (1999).
[CrossRef]

Calado, V. E.

T. Meunier, V. E. Calado, and L. M. K. Vandersypen, “Efficient controlled-phase gate for single-spin qubits in quantum dots,” Phys. Rev. B83, 121403(R)(2011).
[CrossRef]

Chuang, I. L.

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

Cory, D. G.

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

Crépeau, C.

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O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor,” Phys. Rev. Lett.107, 160501 (2011).
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F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A69, 052319 (2004)
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F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A68, 042317 (2003).
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G. Burkard, D. Loss, D. P. DiVincenzo, and J. A. Smolin, “Physical optimization of quantum error correction circuits,” Phys. Rev. B60, 11404–11416 (1999).
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D. Loss and D. P. DiVincenzo, “Quantum computation with quantum dots,” Phys. Rev. A57, 120–126 (1998)
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J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, “Relaxation, dephasing, and quantum control of electron spins in double quantum dots,” Phys. Rev. B76, 035315 (2007).
[CrossRef]

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D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett.81, 2152–2155 (1998).
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A. Majumdar, E. D. Kim, Y. Gong, M. Bajcsy, and J. Vučković, “Phonon mediated off-resonant quantum dot-cavity coupling under resonant excitation of the quantum dot,” Phys. Rev. B84, 085309 (2011).
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R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect Quantum Error Correcting Code,” Phys. Rev. Lett.77, 198–201 (1996).
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O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor,” Phys. Rev. Lett.107, 160501 (2011).
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J. W. Pan, C Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature410, 1067–1070 (2001).
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R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect Quantum Error Correcting Code,” Phys. Rev. Lett.77, 198–201 (1996).
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C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
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K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009).
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J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, “Relaxation, dephasing, and quantum control of electron spins in double quantum dots,” Phys. Rev. B76, 035315 (2007).
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[CrossRef]

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D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett.81, 2152–2155 (1998).
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C. Y. Hu and J. G. Rarity, “Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity,” Phys. Rev. B83, 115303 (2011).
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K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009).
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O. Moussa, J. Baugh, C. A. Ryan, and R. Laflamme, “Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid State Ensemble Quantum Information Processor,” Phys. Rev. Lett.107, 160501 (2011).
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Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A85, 012307 (2012).
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A. Imamoḡlu, 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).
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G. Shinkai, T. Hayashi, T. Ota, and T. Fujisawa, “Correlated Coherent Oscillations in Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 056802 (2009).
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K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, “Microwave-Driven Transitions in Two Coupled Semiconductor Charge Qubits,” Phys. Rev. Lett.103, 016805 (2009).
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G. Burkard, D. Loss, D. P. DiVincenzo, and J. A. Smolin, “Physical optimization of quantum error correction circuits,” Phys. Rev. B60, 11404–11416 (1999).
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D. G. Cory, M. D. Price, W. Maas, E. Knill, R. Laflamme, W. H. Zurek, T. F. Havel, and S. S. Somaroo, “Experimental quantum error correction,” Phys. Rev. Lett.81, 2152–2155 (1998).
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R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, “Spins in few-electron quantum dots,” Rev. Mod. Phys.79, 1217–1265 (2007).
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T. Meunier, V. E. Calado, and L. M. K. Vandersypen, “Efficient controlled-phase gate for single-spin qubits in quantum dots,” Phys. Rev. B83, 121403(R)(2011).
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Y. B. Sheng, L. Zhou, L. Wang, and S. M. Zhao, “Efficient entanglement concentration for quantum dot and optical microcavities systems,” Quantum. Inf. Process.12, 1885–1895 (2013).
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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of QD-cavity-fiber-coupling system. (b) The relevant levels of QD.

Fig. 2
Fig. 2

Three-bit quantum circuit representation for correcting one bit flip error. Here the gate • − • corresponds to a two-qubit iSWAP gate and uij are single-qubit rotation gates.

Fig. 3
Fig. 3

(a) Three-bit quantum circuit representation for correcting one bit phase error. (b) Quantum circuit implementation of three-qubit Toffoli gate by applying two-qubit iSWAP gates and single-qubit rotation gates.

Fig. 4
Fig. 4

Schematic setup to implement the quantum circuits shown in Fig. 2 and Fig. 3 for correcting both the bit flip error and phase flip error. Here s1 and s2 are optical switches, which control two adjacent cavities whether have interaction or not.

Fig. 5
Fig. 5

The entanglement fidelities for one-qubit bit flip and phase flip errors correction, as the functions of pulse error ε.

Equations (19)

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H ^ = H ^ C + H ^ Q D + H ^ int + H ^ C F ,
H ^ C = j = A , B ω c j a ^ c j a ^ c j , H ^ Q D = j = A , B ( ε j ( 0 ) σ ^ j 00 + ε j ( 1 ) σ ^ j 11 + ε j ( v ) σ ^ j v v ) , H ^ int = j = A , B [ g j ( a ^ c j σ ^ j 1 v + a ^ c j σ ^ j v 1 ) + Ω j ( e i ω L j t σ ^ j 0 v + e i ω L j t σ ^ j v 0 ) ] , H ^ C F = [ η b ^ ( a ^ c A + a ^ c B ) + H . c . ] ,
H ^ I = H ^ I 0 + H ^ C F ,
H ^ I 0 = j = A , B [ ξ | 0 j j 0 | + ζ a ^ c j a ^ c j | 1 j j 1 | + λ ( e i δ t a ^ c j σ ^ j 10 + e i δ t a ^ c j σ ^ j 01 ) ] ,
c ^ 0 = 1 2 ( a ^ c A a ^ c B ) , c ^ 1 = 1 2 ( a ^ c A + a ^ c B + 2 b ^ ) , c ^ 2 = 1 2 ( a ^ c A + a ^ c B 2 b ^ ) ,
H ^ C F = 2 η c ^ 1 c ^ 1 2 η c ^ 2 c ^ 2 , H ^ I 0 = j = A , B [ ξ | 0 j j 0 | + ζ 4 ( c ^ 1 c ^ 1 + c ^ 2 c ^ 2 + c ^ 2 c ^ 2 ) | 1 j j 1 | ] + 1 2 { λ e i δ t [ ( c ^ 1 + c ^ 2 + 2 c ^ 0 ) σ ^ A 10 + ( c ^ 1 + c ^ 2 2 c ^ 0 ) σ ^ B 10 ] + ζ 2 [ ( c ^ 1 c ^ 2 + 2 c ^ 1 c ^ 0 + 2 c ^ 2 c ^ 0 ) | 1 A A 1 | + ( c ^ 1 c ^ 2 2 c ^ 1 c ^ 0 2 c ^ 2 c ^ 0 ) | 1 B B 1 | ] + H . c . } .
H ^ I = j = A , B [ ξ | 0 j j 0 | + ζ 4 ( c ^ 1 c ^ 1 + c ^ 2 c ^ 2 + c ^ 2 c ^ 2 ) | 1 j j 1 | ] + { λ 2 [ e i ( δ 2 η ) t c ^ 1 + e i ( δ + 2 η ) t c ^ 2 + 2 e i δ t c ^ 0 ] σ ^ A 10 + λ 2 [ e i ( δ 2 η ) t c ^ 1 + e i ( δ + 2 η ) t c ^ 2 2 e i δ t c ^ 0 ] σ ^ B 10 + ζ 4 [ e i 2 2 η t c ^ 1 c ^ 2 + 2 e i 2 η t c ^ 1 c ^ 0 + 2 e i 2 η t c ^ 2 c ^ 0 ] | 1 A A 1 | + ζ 4 [ e i 2 2 η t c ^ 1 c ^ 2 2 e i 2 η t c ^ 1 c ^ 0 2 e i 2 η t c ^ 2 c ^ 0 ] | 1 B B 1 | + H . c . } .
H ^ eff = j = A , B { ξ | 0 j j 0 | + ζ 4 ( c ^ 1 c ^ 1 + c ^ 2 c ^ 2 + c ^ 2 c ^ 2 ) | 1 j j 1 | + λ 2 4 [ ( 2 δ c ^ 0 c ^ 0 + 1 δ 2 η c ^ 1 c ^ 1 + 1 δ + 2 η c ^ 2 c ^ 2 ) | 0 j j 0 | + ( 2 δ c ^ 0 c ^ 0 + 1 δ 2 η c ^ 1 c ^ 1 + 1 δ 2 η c ^ 2 c ^ 2 ) | 1 j j 1 | ] } + ζ 2 32 2 η [ ( c ^ 1 c ^ 1 c ^ 2 c ^ 2 ) ( | 1 A A 1 | + | 1 B B 1 | ) 2 + 4 ( c ^ 1 c ^ 1 c ^ 2 c ^ 2 ) ( | 1 A A 1 | | 1 B B 1 | ) 2 ] ς ( σ ^ A 10 σ ^ B 01 + σ ^ A 01 σ ^ B 10 ) ,
ς = λ 2 4 ( 2 δ 1 δ 2 η 1 δ + 2 η ) .
H ^ eff = j = A , B ( ξ | 0 j j 0 | + ϑ | 1 j j 1 | ) ς ( σ ^ A 10 σ ^ B 01 + σ ^ A 01 σ ^ B 10 ) ,
ϑ = 1 4 [ 3 ζ + λ 2 ( 2 δ + 1 δ 2 η + 1 δ + 2 η ) ] .
U ^ eff ( t ) = e i H eff t = ( e i 2 ξ t 0 0 0 0 e i ( ξ + ϑ ) t cos ς t i e i ( ξ + ϑ ) t sin ς t 0 0 i e i ( ξ + ϑ ) t sin ς t e i ( ξ + ϑ ) t cos ς t 0 0 0 0 e i 2 ϑ t ) ,
| 0 A | 0 B = | 0 A | 0 B , | 1 A | 1 B = | 1 A | 1 B , | 0 A | 1 B = i | 1 A | 0 B , | 1 A | 0 B = i | 0 A | 1 B .
U ^ CNOT = e i ( π / 4 ) e i ( π / 2 ) σ ^ z 1 e i ( π / 4 ) σ ^ z 2 U ^ iSWAP e i ( π / 4 ) σ ^ x 1 U ^ iSWAP e i ( π / 4 ) σ ^ z 2 e i ( π / 4 ) σ ^ x 2 e i ( π / 4 ) σ ^ z 1 ,
u 11 = ( e i π / 4 0 0 e i π / 4 ) , u 12 = ( cos ( π / 4 ) sin ( π / 4 ) sin ( π / 4 ) cos ( π / 4 ) ) , u 13 = ( e i 3 π / 4 cos ( π / 4 ) e i 3 π / 4 sin ( π / 4 ) e i 3 π / 4 sin ( π / 4 ) e i 3 π / 4 cos ( π / 4 ) ) .
| Ψ E = E ^ ( | Ψ 1 | 0 2 | 0 3 ) = α | 0 2 | 0 3 | 0 1 + β | 1 2 | 1 3 | 1 1 .
u 21 = u 22 = u 23 = 1 2 ( 1 1 1 1 ) , u 11 = v 11 u 13 , u 22 = u 12 v 12 u 13 , u 12 = v 13 u 13 , u 24 = u 12 v 13 , u 13 = v 13 u 11 , u 26 = u 12 v 12 u 13 , u 14 = u 12 v 14 , u 32 = u 12 v 12 u 13 , u 21 = u 23 = u 25 = u 31 = u 11 ,
v 11 = ( 1 0 0 i ) , v 12 = 1 4 2 2 ( 1 1 2 2 1 1 ) , v 13 = ( 1 0 0 e i π / 4 ) , v 14 = 1 4 2 2 ( 1 2 1 i ( 2 1 ) i ) .
P 1 = λ 2 4 [ 1 ( δ 2 η ) 2 + 1 ( δ + 2 η ) 2 + 2 δ 2 ] 0.709 × 10 2 .

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