Abstract
Local adiabatic search has been implemented on the quantum circuit model, and the time steps necessary to guarantee the approximation precision are of the same order as the time complexity of the algorithm. However, it is easy to verify that this conclusion doesn’t hold for global adiabatic search. But we know that adiabatic computing is equivalent to the circuit model of quantum computation. Therefore, there must exist a corresponding quantum circuit that correctly implements such a global adiabatic search. In this Letter, we show that this indeed could be true.
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References
Deutsch, D., Jozsa, R.: Proc. R. Soc. London, Ser. A 439, 553 (1992)
Shor, P.W.: SIAM Rev. 41, 303–332 (1999)
Grover, L.K.: Phys. Rev. Lett. 79, 325 (1997)
Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: Science 292, 472 (2001)
Aharonov, D, W V, Dam, Kempe, J, Landau, Z, Lloyd, S, Regev, O: SIAM J. Comput. 50, 166–194 (2007)
Mizel, A., Lidar, D.A., Mitchell, M.: Phys. Rev. Lett. 99, 070502 (2007)
žnidarič, M., Horvat, M.: Phys. Rev. A 73, 022–329 (2006)
Hen, I., Young, A.P.: Phys. Rev. E 84, 061–152 (2011)
Dickson, N.G., Amin, M.H.S.: Phys. Rev. Lett. 106, 050–502 (2011)
Farhi, E., Gosset, D., Hen, I., Sandvik, A.W., Shor, P., Young, A.P., Zamponi, F.: Phys. Rev. A 86, 052–334
Farhi, E., Goldstone, J., Gutmann, S., Sipser, M. arXiv:quant-ph/0001106 (2000)
Peng, X.H., Liao, Z.Y., Xu, N.Y., Qin, G., Zhou, X.Y., Suter, D., Du, J.F.: Phys. Rev. Lett. 101, 220–405 (2012)
Xu, N.Y., Zhu, J., Lu, D.W., Zhou, X.Y., Peng, X.H., Du, J.F.: Phys. Rev. Lett. 108, 130–501 (2012)
Messiah, A.: Quantum Mechanics, 1st, pp 744–763. Dover, New York (1999)
Zhang, D.J., Yu, X.D., Tong, D.M.: Phys. Rev. A 90, 042–321 (2014)
Roland, J., Cerf, N.J.: Phys. Rev. A 65, 042–308 (2002)
Roland, J., Cerf, N.J.: Phys. Rev. A 68, 062–311 (2003)
Dam, W.v., Mosca, M., Vazirani, U.. In: IEEE FOCS Proceedings of the 42nd, pp 279–287 (2001)
Acknowledgements
The first author gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041 and the support from the National Natural Science Foundation of China under Grant No. 61402188. This work is also supported by the National Natural Science Foundation of China under Grant No. 61173050 and Grant No. U1233119.
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Sun, J., Lu, S., Liu, F. et al. On the Circuit Model of Global Adiabatic Search Algorithm. Int J Theor Phys 54, 3628–3633 (2015). https://doi.org/10.1007/s10773-015-2600-8
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DOI: https://doi.org/10.1007/s10773-015-2600-8