Abstract

We propose a protocol to construct shortcuts of adiabaticity for open quantum systems in unitary evolution. Using the dynamical invariants of open quantum systems, we design a convenient form of the driver Hamiltonian to accelerate the adiabatic decoherence free subspaces scheme (TDFs) and engineer a quantum state from the initial state into the target state. Since the trajectory of TDFSs is determined by the incoherent control process, we would like to call it as the inverse incoherent engineering protocol. We apply the method to a two-qubits system which interacts with a time-dependent vacuum squeezed field to prepare some maximally entangled states of it. The results illustrate that our protocol can be used both in the adiabatic and nonadiabatic regime with perfect fidelity.

© 2017 Optical Society of America

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References

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  1. M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009).
    [Crossref]
  2. M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107, 9937–9945 (2003).
    [Crossref]
  3. M. Demirplak and S. A. Rice, “On the consistency, extremal, and global properties of counterdiabatic fields,” J. Chem. Phys. 129, 154111 (2008).
    [Crossref] [PubMed]
  4. S. Campbell and S. Deffner, “Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity,” Phys. Rev. Lett. 118, 100601 (2017).
    [Crossref] [PubMed]
  5. A. C. Santos and M. S. Sarandy, “Superadiabatic Controlled Evolutions and Universal Quantum Computation,” Sci. Rep. 5, 15775 (2015).
    [Crossref] [PubMed]
  6. I. B. Coulamy, A. C. Santos, I. Hen, and M. S. Sarandy, “Energetic cost of superadiabatic quantum computation,” Front. ICT 3, 19 (2016).
    [Crossref]
  7. X. Chen, R. D. Wen, and S.Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Opt. Express 24, 18322–18331 (2016).
    [Crossref] [PubMed]
  8. J. Song, Z. J. Zhang, Y. Xia, X. D. Sun, and Y. Y. Jiang, “Fast coherent manipulation of quantum states in open systems,” Opt. Express 24, 21674–21683 (2016).
    [Crossref] [PubMed]
  9. G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
    [Crossref]
  10. X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
    [Crossref]
  11. S. Masuda and K. Nakamura, “Acceleration of adiabatic quantum dynamics in electromagnetic fields,” Phys. Rev. A 84, 043434 (2011).
    [Crossref]
  12. X. Chen and J. G. Muga, “Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator,” Phys. Rev. A,  82053403 (2010).
    [Crossref]
  13. J. Jing, L. A. Wu, M. S. Sarandy, and J. G. Muga, “Inverse engineering control in open quantum systems,” Phys. Rev. A 88, 53422 (2013).
    [Crossref]
  14. X. Chen, R. D. Wen, and S. Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Opt. Express 24, 18322–18331 (2016).
    [Crossref] [PubMed]
  15. J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
    [Crossref]
  16. S. L. Wu, X. L. Huang, and X. X. Yi, “Adiabatic Decoherence-Free Subspaces and its Shortcuts,” Arxiv: 1705.01695 (2017).
  17. S. L. Wu, L. C. Wang, and X. X. Yi, “Time-dependent decoherence-free subspace,” J. Phys. A: Math. Theor. 45, 405305 (2012).
    [Crossref]
  18. A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
    [Crossref] [PubMed]
  19. F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
    [Crossref] [PubMed]
  20. S. L. Wu, X. Y. Zhang, and X. X. Yi, “Dynamical invariants of open quantum systems,” Phys. Rev. A 92, 062122 (2015).
    [Crossref]
  21. A. Shabani and D. A. Lidar, “Theory of initialization-free decoherence-free subspaces and subsystems,” Phys. Rev. A 72042303 (2005).
    [Crossref]
  22. X. Chen, E. Torrontegui, and J.G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A. 8362116 (2011).
    [Crossref]
  23. A. C. Santos, R. D. Silva, and M. S. Sarandy, “Shortcut to adiabatic gate teleportation,” Phys. Rev. A 93, 012311 (2016).
    [Crossref]
  24. Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
    [Crossref]
  25. M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 22103 (2010).
    [Crossref]
  26. R. I. Karasik, K. P. Marzlin, B. C. Sanders, and K. B. Whaley, “Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences,” Phys. Rev. A 77, 52301 (2008).
    [Crossref]
  27. L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, “Adiabaticity in open quantum systems,” Phys. Rev. A 93, 32118 (2016).
    [Crossref]

2017 (1)

S. Campbell and S. Deffner, “Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity,” Phys. Rev. Lett. 118, 100601 (2017).
[Crossref] [PubMed]

2016 (8)

I. B. Coulamy, A. C. Santos, I. Hen, and M. S. Sarandy, “Energetic cost of superadiabatic quantum computation,” Front. ICT 3, 19 (2016).
[Crossref]

X. Chen, R. D. Wen, and S.Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Opt. Express 24, 18322–18331 (2016).
[Crossref] [PubMed]

J. Song, Z. J. Zhang, Y. Xia, X. D. Sun, and Y. Y. Jiang, “Fast coherent manipulation of quantum states in open systems,” Opt. Express 24, 21674–21683 (2016).
[Crossref] [PubMed]

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
[Crossref]

X. Chen, R. D. Wen, and S. Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Opt. Express 24, 18322–18331 (2016).
[Crossref] [PubMed]

J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
[Crossref]

A. C. Santos, R. D. Silva, and M. S. Sarandy, “Shortcut to adiabatic gate teleportation,” Phys. Rev. A 93, 012311 (2016).
[Crossref]

L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, “Adiabaticity in open quantum systems,” Phys. Rev. A 93, 32118 (2016).
[Crossref]

2015 (2)

S. L. Wu, X. Y. Zhang, and X. X. Yi, “Dynamical invariants of open quantum systems,” Phys. Rev. A 92, 062122 (2015).
[Crossref]

A. C. Santos and M. S. Sarandy, “Superadiabatic Controlled Evolutions and Universal Quantum Computation,” Sci. Rep. 5, 15775 (2015).
[Crossref] [PubMed]

2014 (2)

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

2013 (1)

J. Jing, L. A. Wu, M. S. Sarandy, and J. G. Muga, “Inverse engineering control in open quantum systems,” Phys. Rev. A 88, 53422 (2013).
[Crossref]

2012 (1)

S. L. Wu, L. C. Wang, and X. X. Yi, “Time-dependent decoherence-free subspace,” J. Phys. A: Math. Theor. 45, 405305 (2012).
[Crossref]

2011 (2)

S. Masuda and K. Nakamura, “Acceleration of adiabatic quantum dynamics in electromagnetic fields,” Phys. Rev. A 84, 043434 (2011).
[Crossref]

X. Chen, E. Torrontegui, and J.G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A. 8362116 (2011).
[Crossref]

2010 (2)

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 22103 (2010).
[Crossref]

X. Chen and J. G. Muga, “Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator,” Phys. Rev. A,  82053403 (2010).
[Crossref]

2009 (2)

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009).
[Crossref]

F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
[Crossref] [PubMed]

2008 (2)

R. I. Karasik, K. P. Marzlin, B. C. Sanders, and K. B. Whaley, “Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences,” Phys. Rev. A 77, 52301 (2008).
[Crossref]

M. Demirplak and S. A. Rice, “On the consistency, extremal, and global properties of counterdiabatic fields,” J. Chem. Phys. 129, 154111 (2008).
[Crossref] [PubMed]

2006 (1)

A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
[Crossref] [PubMed]

2005 (1)

A. Shabani and D. A. Lidar, “Theory of initialization-free decoherence-free subspaces and subsystems,” Phys. Rev. A 72042303 (2005).
[Crossref]

2003 (1)

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107, 9937–9945 (2003).
[Crossref]

Ai, Q.

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
[Crossref]

Albash, T.

L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, “Adiabaticity in open quantum systems,” Phys. Rev. A 93, 32118 (2016).
[Crossref]

Ali, M. M.

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 22103 (2010).
[Crossref]

Berry, M. V.

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009).
[Crossref]

Campbell, S.

S. Campbell and S. Deffner, “Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity,” Phys. Rev. Lett. 118, 100601 (2017).
[Crossref] [PubMed]

Carollo, A.

A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
[Crossref] [PubMed]

Chen, P. W.

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 22103 (2010).
[Crossref]

Chen, Q. Q.

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

Chen, X.

X. Chen, R. D. Wen, and S. Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Opt. Express 24, 18322–18331 (2016).
[Crossref] [PubMed]

X. Chen, R. D. Wen, and S.Y. Tseng, “Analysis of optical directional couplers using shortcuts to adiabaticity,” Opt. Express 24, 18322–18331 (2016).
[Crossref] [PubMed]

X. Chen, E. Torrontegui, and J.G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A. 8362116 (2011).
[Crossref]

X. Chen and J. G. Muga, “Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator,” Phys. Rev. A,  82053403 (2010).
[Crossref]

Chen, Y. H.

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

Coulamy, I. B.

I. B. Coulamy, A. C. Santos, I. Hen, and M. S. Sarandy, “Energetic cost of superadiabatic quantum computation,” Front. ICT 3, 19 (2016).
[Crossref]

de Almeida, N. G.

F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
[Crossref] [PubMed]

Deffner, S.

S. Campbell and S. Deffner, “Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity,” Phys. Rev. Lett. 118, 100601 (2017).
[Crossref] [PubMed]

Demirplak, M.

M. Demirplak and S. A. Rice, “On the consistency, extremal, and global properties of counterdiabatic fields,” J. Chem. Phys. 129, 154111 (2008).
[Crossref] [PubMed]

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107, 9937–9945 (2003).
[Crossref]

Deng, F. G.

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
[Crossref]

Duzzioni, E. I.

F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
[Crossref] [PubMed]

Fazio, R.

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

Goan, H. S.

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 22103 (2010).
[Crossref]

Hen, I.

I. B. Coulamy, A. C. Santos, I. Hen, and M. S. Sarandy, “Energetic cost of superadiabatic quantum computation,” Front. ICT 3, 19 (2016).
[Crossref]

Huang, X. L.

S. L. Wu, X. L. Huang, and X. X. Yi, “Adiabatic Decoherence-Free Subspaces and its Shortcuts,” Arxiv: 1705.01695 (2017).

Jiang, Y. Y.

Jing, J.

J. Jing, L. A. Wu, M. S. Sarandy, and J. G. Muga, “Inverse engineering control in open quantum systems,” Phys. Rev. A 88, 53422 (2013).
[Crossref]

Jun, J.

J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
[Crossref]

Karasik, R. I.

R. I. Karasik, K. P. Marzlin, B. C. Sanders, and K. B. Whaley, “Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences,” Phys. Rev. A 77, 52301 (2008).
[Crossref]

Lidar, D. A.

L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, “Adiabaticity in open quantum systems,” Phys. Rev. A 93, 32118 (2016).
[Crossref]

J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
[Crossref]

A. Shabani and D. A. Lidar, “Theory of initialization-free decoherence-free subspaces and subsystems,” Phys. Rev. A 72042303 (2005).
[Crossref]

Lozinski, Artur

A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
[Crossref] [PubMed]

Luo, D. W.

J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
[Crossref]

Marzlin, K. P.

R. I. Karasik, K. P. Marzlin, B. C. Sanders, and K. B. Whaley, “Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences,” Phys. Rev. A 77, 52301 (2008).
[Crossref]

Masuda, S.

S. Masuda and K. Nakamura, “Acceleration of adiabatic quantum dynamics in electromagnetic fields,” Phys. Rev. A 84, 043434 (2011).
[Crossref]

Montangero, S.

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

Moussa, M. H. Y.

F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
[Crossref] [PubMed]

Muga, J. G.

J. Jing, L. A. Wu, M. S. Sarandy, and J. G. Muga, “Inverse engineering control in open quantum systems,” Phys. Rev. A 88, 53422 (2013).
[Crossref]

X. Chen and J. G. Muga, “Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator,” Phys. Rev. A,  82053403 (2010).
[Crossref]

Muga, J.G.

X. Chen, E. Torrontegui, and J.G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A. 8362116 (2011).
[Crossref]

Nakamura, K.

S. Masuda and K. Nakamura, “Acceleration of adiabatic quantum dynamics in electromagnetic fields,” Phys. Rev. A 84, 043434 (2011).
[Crossref]

Palma, G. M.

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
[Crossref] [PubMed]

Paternostro, M.

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

Prado, F. O.

F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
[Crossref] [PubMed]

Qiu, J.

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
[Crossref]

Rice, S. A.

M. Demirplak and S. A. Rice, “On the consistency, extremal, and global properties of counterdiabatic fields,” J. Chem. Phys. 129, 154111 (2008).
[Crossref] [PubMed]

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107, 9937–9945 (2003).
[Crossref]

Sanders, B. C.

R. I. Karasik, K. P. Marzlin, B. C. Sanders, and K. B. Whaley, “Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences,” Phys. Rev. A 77, 52301 (2008).
[Crossref]

Santos, A. C.

A. C. Santos, R. D. Silva, and M. S. Sarandy, “Shortcut to adiabatic gate teleportation,” Phys. Rev. A 93, 012311 (2016).
[Crossref]

I. B. Coulamy, A. C. Santos, I. Hen, and M. S. Sarandy, “Energetic cost of superadiabatic quantum computation,” Front. ICT 3, 19 (2016).
[Crossref]

A. C. Santos and M. S. Sarandy, “Superadiabatic Controlled Evolutions and Universal Quantum Computation,” Sci. Rep. 5, 15775 (2015).
[Crossref] [PubMed]

Santos, Marcelo França

A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
[Crossref] [PubMed]

Sarandy, M. S.

J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
[Crossref]

I. B. Coulamy, A. C. Santos, I. Hen, and M. S. Sarandy, “Energetic cost of superadiabatic quantum computation,” Front. ICT 3, 19 (2016).
[Crossref]

A. C. Santos, R. D. Silva, and M. S. Sarandy, “Shortcut to adiabatic gate teleportation,” Phys. Rev. A 93, 012311 (2016).
[Crossref]

A. C. Santos and M. S. Sarandy, “Superadiabatic Controlled Evolutions and Universal Quantum Computation,” Sci. Rep. 5, 15775 (2015).
[Crossref] [PubMed]

J. Jing, L. A. Wu, M. S. Sarandy, and J. G. Muga, “Inverse engineering control in open quantum systems,” Phys. Rev. A 88, 53422 (2013).
[Crossref]

Shabani, A.

A. Shabani and D. A. Lidar, “Theory of initialization-free decoherence-free subspaces and subsystems,” Phys. Rev. A 72042303 (2005).
[Crossref]

Silva, R. D.

A. C. Santos, R. D. Silva, and M. S. Sarandy, “Shortcut to adiabatic gate teleportation,” Phys. Rev. A 93, 012311 (2016).
[Crossref]

Song, J.

J. Song, Z. J. Zhang, Y. Xia, X. D. Sun, and Y. Y. Jiang, “Fast coherent manipulation of quantum states in open systems,” Opt. Express 24, 21674–21683 (2016).
[Crossref] [PubMed]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

Song, X. K.

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
[Crossref]

Sun, X. D.

Torrontegui, E.

X. Chen, E. Torrontegui, and J.G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A. 8362116 (2011).
[Crossref]

Tseng, S. Y.

Tseng, S.Y.

Vacanti, G.

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

Vedral, V.

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

Vedral, Vlatko

A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
[Crossref] [PubMed]

Venuti, L. C.

L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, “Adiabaticity in open quantum systems,” Phys. Rev. A 93, 32118 (2016).
[Crossref]

Villas-Boas, C. J.

F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
[Crossref] [PubMed]

Wang, L. C.

S. L. Wu, L. C. Wang, and X. X. Yi, “Time-dependent decoherence-free subspace,” J. Phys. A: Math. Theor. 45, 405305 (2012).
[Crossref]

Wen, R. D.

Whaley, K. B.

R. I. Karasik, K. P. Marzlin, B. C. Sanders, and K. B. Whaley, “Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences,” Phys. Rev. A 77, 52301 (2008).
[Crossref]

Wu, L. A.

J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
[Crossref]

J. Jing, L. A. Wu, M. S. Sarandy, and J. G. Muga, “Inverse engineering control in open quantum systems,” Phys. Rev. A 88, 53422 (2013).
[Crossref]

Wu, S. L.

S. L. Wu, X. Y. Zhang, and X. X. Yi, “Dynamical invariants of open quantum systems,” Phys. Rev. A 92, 062122 (2015).
[Crossref]

S. L. Wu, L. C. Wang, and X. X. Yi, “Time-dependent decoherence-free subspace,” J. Phys. A: Math. Theor. 45, 405305 (2012).
[Crossref]

S. L. Wu, X. L. Huang, and X. X. Yi, “Adiabatic Decoherence-Free Subspaces and its Shortcuts,” Arxiv: 1705.01695 (2017).

Xia, Y.

J. Song, Z. J. Zhang, Y. Xia, X. D. Sun, and Y. Y. Jiang, “Fast coherent manipulation of quantum states in open systems,” Opt. Express 24, 21674–21683 (2016).
[Crossref] [PubMed]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

Yi, X. X.

S. L. Wu, X. Y. Zhang, and X. X. Yi, “Dynamical invariants of open quantum systems,” Phys. Rev. A 92, 062122 (2015).
[Crossref]

S. L. Wu, L. C. Wang, and X. X. Yi, “Time-dependent decoherence-free subspace,” J. Phys. A: Math. Theor. 45, 405305 (2012).
[Crossref]

S. L. Wu, X. L. Huang, and X. X. Yi, “Adiabatic Decoherence-Free Subspaces and its Shortcuts,” Arxiv: 1705.01695 (2017).

Zanardi, P.

L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, “Adiabaticity in open quantum systems,” Phys. Rev. A 93, 32118 (2016).
[Crossref]

Zhang, H.

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
[Crossref]

Zhang, X. Y.

S. L. Wu, X. Y. Zhang, and X. X. Yi, “Dynamical invariants of open quantum systems,” Phys. Rev. A 92, 062122 (2015).
[Crossref]

Zhang, Z. J.

Front. ICT (1)

I. B. Coulamy, A. C. Santos, I. Hen, and M. S. Sarandy, “Energetic cost of superadiabatic quantum computation,” Front. ICT 3, 19 (2016).
[Crossref]

J. Chem. Phys. (1)

M. Demirplak and S. A. Rice, “On the consistency, extremal, and global properties of counterdiabatic fields,” J. Chem. Phys. 129, 154111 (2008).
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J. Phys. A: Math. Theor. (2)

M. V. Berry, “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42, 365303 (2009).
[Crossref]

S. L. Wu, L. C. Wang, and X. X. Yi, “Time-dependent decoherence-free subspace,” J. Phys. A: Math. Theor. 45, 405305 (2012).
[Crossref]

J. Phys. Chem. A (1)

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107, 9937–9945 (2003).
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New J. Phys. (2)

G. Vacanti, R. Fazio, S. Montangero, G. M. Palma, M. Paternostro, and V. Vedral, “Transitionless quantum driving in open quantum systems,” New J. Phys. 16, 53017 (2014).
[Crossref]

X. K. Song, H. Zhang, Q. Ai, J. Qiu, and F. G. Deng, “Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm,” New J. Phys. 18, 23001 (2016).
[Crossref]

Opt. Express (3)

Phys. Rev. A (11)

S. Masuda and K. Nakamura, “Acceleration of adiabatic quantum dynamics in electromagnetic fields,” Phys. Rev. A 84, 043434 (2011).
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X. Chen and J. G. Muga, “Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator,” Phys. Rev. A,  82053403 (2010).
[Crossref]

J. Jing, L. A. Wu, M. S. Sarandy, and J. G. Muga, “Inverse engineering control in open quantum systems,” Phys. Rev. A 88, 53422 (2013).
[Crossref]

J. Jun, M. S. Sarandy, D. A. Lidar, D. W. Luo, and L. A. Wu, “Eigenstate tracking in open quantum systems,” Phys. Rev. A 94042131 (2016).
[Crossref]

S. L. Wu, X. Y. Zhang, and X. X. Yi, “Dynamical invariants of open quantum systems,” Phys. Rev. A 92, 062122 (2015).
[Crossref]

A. Shabani and D. A. Lidar, “Theory of initialization-free decoherence-free subspaces and subsystems,” Phys. Rev. A 72042303 (2005).
[Crossref]

A. C. Santos, R. D. Silva, and M. S. Sarandy, “Shortcut to adiabatic gate teleportation,” Phys. Rev. A 93, 012311 (2016).
[Crossref]

Y. H. Chen, Y. Xia, Q. Q. Chen, and J. Song, “Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems,” Phys. Rev. A 89, 033856 (2014).
[Crossref]

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 22103 (2010).
[Crossref]

R. I. Karasik, K. P. Marzlin, B. C. Sanders, and K. B. Whaley, “Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences,” Phys. Rev. A 77, 52301 (2008).
[Crossref]

L. C. Venuti, T. Albash, D. A. Lidar, and P. Zanardi, “Adiabaticity in open quantum systems,” Phys. Rev. A 93, 32118 (2016).
[Crossref]

Phys. Rev. A. (1)

X. Chen, E. Torrontegui, and J.G. Muga, “Lewis-Riesenfeld invariants and transitionless quantum driving,” Phys. Rev. A. 8362116 (2011).
[Crossref]

Phys. Rev. Lett. (3)

A. Carollo, G. M. Palma, Artur Łozinski, Marcelo França Santos, and Vlatko Vedral, “Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir,” Phys. Rev. Lett. 96, 150403 (2006).
[Crossref] [PubMed]

F. O. Prado, E. I. Duzzioni, M. H. Y. Moussa, N. G. de Almeida, and C. J. Villas-Boas, “Nonadiabatic Coherent Evolution of Two-Level Systems under Spontaneous Decay,” Phys. Rev. Lett. 102, 073008 (2009).
[Crossref] [PubMed]

S. Campbell and S. Deffner, “Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity,” Phys. Rev. Lett. 118, 100601 (2017).
[Crossref] [PubMed]

Sci. Rep. (1)

A. C. Santos and M. S. Sarandy, “Superadiabatic Controlled Evolutions and Universal Quantum Computation,” Sci. Rep. 5, 15775 (2015).
[Crossref] [PubMed]

Other (1)

S. L. Wu, X. L. Huang, and X. X. Yi, “Adiabatic Decoherence-Free Subspaces and its Shortcuts,” Arxiv: 1705.01695 (2017).

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Figures (3)

Fig. 1
Fig. 1 Final fidelity, defined as F =〈ψ(T)|ρ(T)|ψ(T)〉, vs the total engineering time T for the adiabatic engineering program (red dash line) and the incoherent engineering program(blue solid line). The change rates of the parameters are μ = ν = π/T, and γ = 1 are used as the unit of the change rates.
Fig. 2
Fig. 2 (a)The final fidelity vs the total engineering time T for the adiabatic engineering protocol (red dash line) and the inverse incoherent engineering protocol(blue solid line). (b) The dynamics of the Fidelity with different change rates μ for the adiabatic engineering protocol (red dash line) and the inverse incoherent engineering protocol(blue solid line). For both figures, the total evolution time satisfies T = π/μ, and γ = 1 are used as the unit of the change rates. The initial state is chosen as Eq. (21) with = 0.1.
Fig. 3
Fig. 3 (a) Final purity, defined as P = Tr [ρ(T)2], and (b) Final fidelity, defined as F = 〈ψ(T)|ρ(T)|ψ(T)〉, vs the total engineering time T for the adiabatic engineering program (red dash line) and the incoherent engineering program(blue solid line). The change rates of the parameters are μ = ν = 2π/T, and γ = 1 are used as the unit of the change rates.

Equations (45)

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t ρ ^ ( t ) = ^ ( ρ ^ ) , ^ ( ρ ^ ) = i [ H ^ 0 , ρ ^ ] + α ( F ^ α ρ ^ F ^ α 1 2 { F ^ α F ^ α , ρ ^ } ) ,
F ^ α ( t ) | Φ i ( t ) = c α ( t ) | Φ i ( t ) ;
Φ n ( t ) | H ^ eff 0 ( t ) | Φ i ( t ) = 0 , i , n ,
H ^ eff 0 ( t ) = H ^ 0 ( t ) + i 2 α ( c α * ( t ) F ^ α ( t ) c α ( t ) F ^ α ( t ) ) .
H ^ 1 ( t ) = i n k Φ n ( t ) | t | Φ k ( t ) | Φ n ( t ) Φ k ( t ) | + h . c .
DFS ( t ) = Span { | Φ 1 ( t ) , | Φ 2 ( t ) , , | Φ M ( t ) }
F ^ α ( t ) | Φ j ( t ) = c α ( t ) | Φ j ( t ) , j = 1 , , M ; α = 1 , , K ,
H ^ eff ( t ) = G ^ ( t ) + H ^ ( t ) + i 2 α ( c α * ( t ) F ^ α ( t ) c α ( t ) F ^ α ( t ) ) .
U ^ ( t ) = j = 1 M | Φ j ( 0 ) Φ j ( t ) | + n = 1 N M | Φ n ( 0 ) Φ n ( t ) | .
i ρ ^ ( t ) = [ H ^ eff ( t ) , ρ ^ ( t ) ] .
t I ^ ( t ) + i [ H ^ ( t ) , I ^ ( t ) ] + α ( F ^ α ( t ) I ^ ( t ) F ^ α ( t ) 1 2 { F ^ α ( t ) F ^ α ( t ) , I ^ ( t ) } ) = 0 ,
H ^ = ( H ^ D H ^ N H ^ N H ^ C ) , F ^ α = ( F ^ α D A ^ α 0 B ^ α ) ,
t I ^ D + i [ H ^ D , I ^ D ] = 0
i ( G ^ N + H ^ N ) α c α * 2 A ^ α = 0 ,
I ^ D ( t ) = i = 1 M λ i | Φ i ( t ) Φ i ( t ) | ,
F ^ α D ( t ) = c α ( t ) i = 1 M | Φ i ( t ) Φ i ( t ) | .
H ^ N = G ^ N α i c α * 2 A ^ α .
U ^ D ( t ) = i = 1 M exp ( i α i ( t ) ) | Φ i ( t ) Φ i ( 0 ) | ,
α i ( t ) 0 t Φ i ( t ) | ( i t H ^ D ) | Φ i ( t ) d t .
i t U ^ D = H ^ D ( t ) U ^ D ,
H ^ D ( t ) = i t U ^ D U ^ D .
H ^ D ( t ) = i i = 1 M | t Φ i ( t ) Φ i ( t ) | i = 1 M t α i | Φ i ( t ) Φ i ( t ) | .
ρ t = i [ H S , ρ ] + γ 2 ( 2 S ρ S S S ρ ρ S S ) ,
S = cosh ( r ) S + sinh ( r ) exp ( i θ ) S + ,
| Φ 1 ( t ) = | ϕ 0 1 | ϕ 1 2 , | Φ 2 ( t ) = | ϕ 0 1 | ϕ 0 2 , | Φ 3 ( t ) = | ϕ 0 1 | ϕ 0 2 , | Φ 4 ( t ) = | ϕ 1 1 | ϕ 1 2 ,
| ϕ 0 = cosh ( r ) | 0 + sinh ( r ) exp ( i θ / 2 ) | 1 sinh ( r ) + cosh ( r ) , | ϕ 1 = cosh ( r ) | 0 + sinh ( r ) exp ( i θ / 2 ) | 1 sinh ( r ) + cosh ( r ) ,
| v 1 = | 01 | 10 2 , | v 2 = cosh ( r ) | 00 sinh ( r ) exp ( i θ ) | 11 cosh ( 2 r ) ,
| v 3 c = | 01 + | 10 2 , | v 4 c = sinh ( r ) | 00 + cosh ( r ) exp ( i θ ) | 11 cosh ( 2 r ) .
I D ( t ) = i = 1 2 ( 1 ) i ω 0 2 | v i ( t ) v i ( t ) | ,
α 1 = 0 , α 2 = 0 t θ ˙ ( t ) sinh 2 ( r ( t ) ) 2 cosh ( 2 r ( t ) ) d t .
H N = i < j ( g i j x Σ i j x + g i j y Σ i j y ) ,
g 12 x = 1 2 ( 2 r ˙ sin ( θ ) cosh ( 2 r ) + ( θ ˙ ) sinh ( 2 r ) cos ( θ ) ) ,
g 12 y = 1 2 ( 2 r ˙ cos ( θ ) cosh ( 2 r ) ( θ ˙ ) sinh ( 2 r ) sin ( θ ) ) ;
Σ 12 x = σ x 1 σ x 2 σ y 1 σ y 2 2 Σ 12 y = σ x 1 σ y 2 + σ y 1 σ x 2 2 .
| ψ ( T ) = | v 2 ( T ) 2 2 ( | 00 + | 11 ) .
r ( t ) = μ t , θ ( t ) = ν t ,
ρ ( 0 ) = ( 1 ) | 00 00 | + 2 ( | 01 01 | + | 10 10 | ) .
| ψ ( T ) = | 00 + exp ( i θ T ) | 11 2 + exp ( i θ T / 2 ) ( | 01 + | 10 ) 2 ,
| v 1 : = | Φ 3 ( t ) = cosh ( r ) | 00 + sinh ( r ) exp ( i θ ) | 11 sinh ( r ) + cosh ( r ) + sinh ( r ) cosh ( r ) exp ( i θ / 2 ) ( | 01 + | 10 ) sinh ( r ) + cosh ( r ) .
| v 2 c = sinh ( r ) cosh ( r ) ( | 00 exp ( i θ ) | 11 ) sinh ( r ) + cosh ( r ) + exp ( i θ / 2 ) ( sinh ( r ) | 01 + cosh ( r ) | 10 ) sinh ( r ) + cosh ( r ) ,
| v 3 c = sinh ( r ) cosh ( r ) ( | 00 exp ( i θ ) | 11 ) sinh ( r ) + cosh ( r ) + exp ( i θ / 2 ) ( cosh ( r ) | 01 sinh ( r ) | 10 ) sinh ( r ) + cosh ( r ) ,
| v 4 c = cosh ( r ) | 00 + sinh ( r ) exp ( i θ ) | 11 sinh ( r ) + cosh ( r ) sinh ( r ) cosh ( r ) exp ( i θ / 2 ) ( | 01 + | 10 ) sinh ( r ) + cosh ( r ) .
I D ( t ) = ω 0 | v 1 ( t ) v 1 ( t ) | ,
H N = i = 1 2 ( B 0 2 I 2 i + B y 2 σ y y + B z 2 σ z i ) ,
B 0 = B z = θ ˙ 2 , B y = ( r ˙ sinh ( 2 r ) ) exp ( r + i θ / 2 ) sinh ( r ) cosh ( r ) .

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