Fetching the paper…

Reading the bibliography…

2008

Consistency of the Adiabatic Theorem

Amin, M. H. S.

Original
PDF
Post on X

Understand

The adiabatic theorem provides the basis for the adiabatic model of quantum computation.

Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy.
Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels.
In the absence of fast driven oscillations the traditional adiabatic theorem holds.

Consistency of the Adiabatic Theorem · Around

Built on

P. Ehrenfest, Ann. Phys. 356
1916
Earlier work this paper cites.
M. Born and V. Fock, Z. Phys. 51
1928
Earlier work this paper cites.
T. Kato, J. Phys. Soc. Jpn. 5
1950
Earlier work this paper cites.
L.I. Schiff, Quantum Mechanics
1968
Earlier work this paper cites.
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292
2001
Earlier work this paper cites.
J. Roland and N.J Cerf, Phys. Rev. A 65
2002
Earlier work this paper cites.
K.-P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.

Similar

D.M. Tong, K. Singh, L.C. Kwek, and C.H. Oh, Phys. Rev. Lett. 95
2005
Cited alongside, same era.
Z. Wu and H. Yang, Phys. Rev. A 72
2005
Cited alongside, same era.
S. Duki, H. Mathur, and O. Narayan, Phys. Rev. Lett. 97
2006
Cited alongside, same era.
J. Ma, Y. Zhang, E. Wang, and B. Wu, Phys. Rev. Lett. 97
2006
Cited alongside, same era.
K.-P. Marzlin and B.C. Sanders, Phys. Rev. Lett bf 97, 128903 (2006)
2006
Cited alongside, same era.
R. MacKenzie, E. Marcotte, and H. Paquette, Phys. Rev. A 73
2006
Cited alongside, same era.
D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, SIAM J. Comp. 37

Then

D.M. Tong, K. Singh, L.C. Kwek, and C.H. Oh, Phys. Rev. Lett. 98
2007
Later among the works it cites.
S. Jansen, M.-B. Ruskai, and R. Seiler, J. Math. Phys. 48
2007
Later among the works it cites.
Z. Wei and M. Ying, Phys. Rev. A 76
2007
Later among the works it cites.
M.S. Sarandy and D.A. Lidar, Phys. Rev. A 71
2008
Closest in time.
M.H.S. Amin, Phys. Rev. Lett. 100
2008
Closest in time.
M.H.S. Amin, P.J. Love, and C.J.S. Truncik, Phys. Rev. Lett. 100
Original
2008
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2007

Cited alongside, same era.

J. Du, L. Hu, Y. Wang, J. Wu, M. Zhao, and D. Suter, arXiv:0801.0361

Cited in the paper.

J.-L. Chen, M.-S. Zhao, J.-D. Wu, and Y.D. Zhang, eprint quant-ph/07060299

Cited in the paper.

J.-D. Wu, M.-S. Zhao, J.-L. Chen, and Y.-D. Zhang, eprint arXiv:0706.0264

Cited in the paper.

D.A. Lidar, A.T. Rezakhani, and A. Hamma, eprint arXiv:0808.2697

Cited in the paper.

The approximation becomes self-consistent by making sure that the error ε n \varepsilon_{n} is small at the end

Cited in the paper.