Implementation of Quantum Rotation Gates Using Controlled Non-Adiabatic Evolutions

Quantum gates are the basic building blocks in the
quantum circuits model. These gates can be implemented using
adiabatic or non adiabatic processes. Adiabatic models can be
controlled using auxiliary qubits, whereas non adiabatic models can
be simplified by using one single-shot implementation. In this paper,
the controlled adiabatic evolutions is combined with the single-shot
implementation to obtain quantum gates with controlled non adiabatic
evolutions. This is an important improvement which can speed the
implementation of quantum gates and reduce the errors due to the
long run in the adiabatic model. The robustness of our scheme to
different types of errors is also investigated.

Authors:

• Abdelrahman A. H. Abdelrahim
• Gharib Subhi Mahmoud
• Sherzod Turaev
• Azeddine Messikh

Keywords:

• Adiabatic evolutions
• non adiabatic evolutions
• controlled adiabatic evolutions
• quantum rotation gates
• dephasing rates
• master equation.

References:

[1] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum
Information, Optical Science, Springer, 2004.
[2] E. Farhi, J. Goldstoen, S. Gutmann, J. Lapan, A. Lundgren, D. Preda,
A quantum adiabatic evolution algorithm applied to random instances
of np-coplete problem, Science 292 (2001) 472.
[3] D. Aharonov, W. Van Dam, J. Kempe, Z. Landau, S. Lloyd, O. Regev,
Adiabatic quantum computation is equivalent to standard quantum
computation, SIAM Journal on Computing 37 (1) (2007) 166–194.
[4] A. Messiah, Quantum mechanics: two volumes bound as one, Dover
Books on Physics, Dover, Mineola, NY, 2014.
[5] D. J. Griffiths, Introduction to quantum mechanics, Pearson Education
India, 2005.
[6] M. Johansson, E. Sj¨oqvist, L. M. Andersson, M. Ericsson, B. Hessmo,
K. Singh, D. M. Tong, Robustness of nonadiabatic holonomic gates,
Phys. Rev. A 86 (2012) 062322.
[7] A. Abdumalikov Jr, J. Fink, K. Juliusson, M. Pechal, S. Berger,
A. Wallraff, S. Filipp, Experimental realization of non-abelian
non-adiabatic geometric gates, Nature 496 (7446) (2013) 482–485.
[8] V. A. Mousolou, C. M. Canali, E. Sjqvist, Universal non-adiabatic
holonomic gates in quantum dots and single-molecule magnets, New
Journal of Physics 16 (1) (2014) 013029.
[9] C. Zu, W.-B. Wang, L. He, W.-G. Zhang, C.-Y. Dai, F. Wang, L.-M.
Duan, Experimental realization of universal geometric quantum gates
with solid-state spins, Nature 514 (7520) (2014) 72–75.
[10] G. Xu, C. Liu, P. Zhao, D. Tong, Nonadiabatic holonomic gates realized
by a single-shot implementation, Physical Review A 92 (5) (2015)
052302.
[11] I. Hen, Quantum gates wih controlled adiabatic evolutions, Phys. Rev.
A 91 (2015) 022309.
[12] H.-P. Breuer, F. Petruccione, The theory of open quantum systems,
Oxford University Press on Demand, 2002.
[13] Z. Ficek, M. R. Wahiddin, Quantum Optics for Beginners, Pan Stanford
Publishing, 2014.
[14] H. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical
Fields, no. v. 2 in Theoretical and Mathematical Physics, Springer, 2009.
[15] J. Dalibard, Y. Castin, K. Mølmer, Wave-function approach to dissipative
processes in quantum optics, Phys. Rev. Lett. 68 (1992) 580–583.
[16] Y. Castin, J. Dalibard, Monte carlo wave-function method in quantum
optics, J. Opt. Soc. Am. B 10 (1993) 524–538.
[17] M. B. Plenio, P. L. Knight, The quantum-jump approach to dissipative
dynamics in quantum optics, Rev. Mod. Phys. 70 (1998) 101–144.