Abstract
Deutsch–Jozsa algorithm has been implemented via quantum adiabatic evolutions by Das et al. (Phys Rev A 65:062310, 2002) and Wei et al. (Phys Lett A 354:271, 2006). In the latter literature, the authors have shown a modified version of the adiabatic evolution which can improve the performance of the algorithm of S. Das et al’s to constant time. In this paper, we also improve the algorithm of S. Das et al’s in a constant time but by using a different construction of adiabatic evolution, i.e., adding ancillary qubits. The algorithm in this paper provides an alternative option to potential users.
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472 (2001)
Choi, V.: Different adiabatic quantum optimization algorithms for the NP-complete exact cover problem. Proc. Natl. Acad. Sci. USA 108(7), E19–E20 (2011)
Dickson, N.G., Amin, M.H.S.: Does adiabatic quantum optimization fail for NP-complete problems? Phys. Rev. Lett. 106, 050502 (2011)
Hen, I., Young, A.P.: Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems. Phys. Rev. E 84, 061152 (2011)
Farhi, E., Gosset, D., Hen, I., Sandvik, A.W., Shor, P., Young, A.P., Zamponi, F.: Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs. Phys. Rev. A 86, 052334 (2012)
Mizel, A., Lidar, D.A., Mitchell, M.: Simple proof of equivalence between adiabatic quantum computation and the circuit model. Phys. Rev. Lett. 99, 070502 (2007)
Aharonov, D., van Dam, W., Kempe, J., Landau, Z., Lloyd, S., Regev, O.: Adiabatic quantum computation is equivalent to standard quantum computation. SIAM J. Comput. 37(1), 166–194 (2007)
Gaitan, F., Clark, L.: Ramsey numbers and adiabatic quantum computing. Phys. Rev. Lett. 108, 010501 (2012)
Garnerone, S., Zanardi, P., Lidar, D.A.: Adiabatic quantum algorithm for search engine ranking. Phys. Rev. Lett. 108, 230506 (2012)
Somma, R.D., Nagaj, D., Kieferová, M.: Quantum speedup by quantum annealing. Phys. Rev. Lett. 109, 050501 (2012)
Messiah, A.: Quantum Mechanics. 1st ed., pp. 744–763. Dover, New York (1999)
Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. Ser. A 439, 553 (1992)
Das, S., Kobes, R., Kunstatter, G.: Adiabatic quantum computation and Deutsch’s algorithm. Phys. Rev. A 65, 062310 (2002)
Sarandy, M.S., Lidar, D.A.: Adiabatic quantum computation in open systems. Phys. Rev. Lett. 95, 250503 (2005)
Wei, Z., Ying, M.: A modified quantum adiabatic evolution for the Deutsch-Jozsa problem. Phys. Lett. A 354, 271 (2006)
Roland, J., Cerf, N.J.: Quantum search by local adiabatic evolution. Phys. Rev. A 65, 042308 (2002)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Tulsi, A.: Faster quantum-walk algorithm for the two-dimensional spatial search. Phys. Rev. A 78, 012310 (2008)
Author information
Authors and Affiliations
Corresponding author
Additional information
The work is supported by the National Natural Science Foundation of China under Grant No. 61173050 and No. U1233119.
Rights and permissions
About this article
Cite this article
Sun, J., Lu, S., Liu, F. et al. An alternate quantum adiabatic evolution for the Deutsch–Jozsa problem. Quantum Inf Process 13, 731–736 (2014). https://doi.org/10.1007/s11128-013-0685-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-013-0685-7