Implementation of Quantum Rotation Gates Using Controlled Non-Adiabatic Evolutions

Authors: Abdelrahman A. H. Abdelrahim, Gharib Subhi Mahmoud, Sherzod Turaev, Azeddine Messikh

Abstract:

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.

Keywords: Adiabatic evolutions, non adiabatic evolutions, controlled adiabatic evolutions, quantum rotation gates, dephasing rates, master equation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1315673

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.