{"title":"Implementation of Quantum Rotation Gates Using Controlled Non-Adiabatic Evolutions","authors":"Abdelrahman A. H. Abdelrahim, Gharib Subhi Mahmoud, Sherzod Turaev, Azeddine Messikh","volume":133,"journal":"International Journal of Nuclear and Quantum Engineering","pagesStart":12,"pagesEnd":17,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10008506","abstract":"Quantum gates are the basic building blocks in the<br \/>\r\nquantum circuits model. These gates can be implemented using<br \/>\r\nadiabatic or non adiabatic processes. Adiabatic models can be<br \/>\r\ncontrolled using auxiliary qubits, whereas non adiabatic models can<br \/>\r\nbe simplified by using one single-shot implementation. In this paper,<br \/>\r\nthe controlled adiabatic evolutions is combined with the single-shot<br \/>\r\nimplementation to obtain quantum gates with controlled non adiabatic<br \/>\r\nevolutions. This is an important improvement which can speed the<br \/>\r\nimplementation of quantum gates and reduce the errors due to the<br \/>\r\nlong run in the adiabatic model. The robustness of our scheme to<br \/>\r\ndifferent types of errors is also investigated.","references":"[1] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum\r\nInformation, Optical Science, Springer, 2004.\r\n[2] E. Farhi, J. Goldstoen, S. Gutmann, J. Lapan, A. Lundgren, D. Preda,\r\nA quantum adiabatic evolution algorithm applied to random instances\r\nof np-coplete problem, Science 292 (2001) 472.\r\n[3] D. Aharonov, W. Van Dam, J. Kempe, Z. Landau, S. Lloyd, O. Regev,\r\nAdiabatic quantum computation is equivalent to standard quantum\r\ncomputation, SIAM Journal on Computing 37 (1) (2007) 166\u2013194.\r\n[4] A. Messiah, Quantum mechanics: two volumes bound as one, Dover\r\nBooks on Physics, Dover, Mineola, NY, 2014.\r\n[5] D. J. Griffiths, Introduction to quantum mechanics, Pearson Education\r\nIndia, 2005.\r\n[6] M. Johansson, E. Sj\u00a8oqvist, L. M. Andersson, M. Ericsson, B. Hessmo,\r\nK. Singh, D. M. Tong, Robustness of nonadiabatic holonomic gates,\r\nPhys. Rev. A 86 (2012) 062322.\r\n[7] A. Abdumalikov Jr, J. Fink, K. Juliusson, M. Pechal, S. Berger,\r\nA. Wallraff, S. Filipp, Experimental realization of non-abelian\r\nnon-adiabatic geometric gates, Nature 496 (7446) (2013) 482\u2013485.\r\n[8] V. A. Mousolou, C. M. Canali, E. Sjqvist, Universal non-adiabatic\r\nholonomic gates in quantum dots and single-molecule magnets, New\r\nJournal of Physics 16 (1) (2014) 013029.\r\n[9] C. Zu, W.-B. Wang, L. He, W.-G. Zhang, C.-Y. Dai, F. Wang, L.-M.\r\nDuan, Experimental realization of universal geometric quantum gates\r\nwith solid-state spins, Nature 514 (7520) (2014) 72\u201375.\r\n[10] G. Xu, C. Liu, P. Zhao, D. Tong, Nonadiabatic holonomic gates realized\r\nby a single-shot implementation, Physical Review A 92 (5) (2015)\r\n052302.\r\n[11] I. Hen, Quantum gates wih controlled adiabatic evolutions, Phys. Rev.\r\nA 91 (2015) 022309.\r\n[12] H.-P. Breuer, F. Petruccione, The theory of open quantum systems,\r\nOxford University Press on Demand, 2002.\r\n[13] Z. Ficek, M. R. Wahiddin, Quantum Optics for Beginners, Pan Stanford\r\nPublishing, 2014.\r\n[14] H. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical\r\nFields, no. v. 2 in Theoretical and Mathematical Physics, Springer, 2009.\r\n[15] J. Dalibard, Y. Castin, K. M\u00f8lmer, Wave-function approach to dissipative\r\nprocesses in quantum optics, Phys. Rev. Lett. 68 (1992) 580\u2013583.\r\n[16] Y. Castin, J. Dalibard, Monte carlo wave-function method in quantum\r\noptics, J. Opt. Soc. Am. B 10 (1993) 524\u2013538.\r\n[17] M. B. Plenio, P. L. Knight, The quantum-jump approach to dissipative\r\ndynamics in quantum optics, Rev. Mod. Phys. 70 (1998) 101\u2013144.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 133, 2018"}