Abstract
We consider the running time of the generalized quantum search Hamiltonian. We provide the surprising result that the maximum speedup of quantum search in the generalized Hamiltonian is an O(1) running time regardless of the number of total states. This seems to violate the proof of Zalka that the quadratic speedup is optimal in quantum search. However the argument of Giovannetti et al. that a quantum speedup comes from the interaction between subsystems (or, equivalently entanglement) (and is concerned with the Margolus and Levitin theorem) supports our result.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bae, J. and Kwon, Y. (2002). Physical Review A 66, 012314.
Bae, J. and Kwon, Y. Note on the generalized quantum search Hamiltonian. Preprint.
Deutsch, D. (1985). Quantum theory, the Church—Turing principle and the universal quantum computer. Proceedings of the Royal Society of London A 400, 97-117.
Farhi, E. and Gutmann, S. (1998). Physical Review A 57, 2403.
Giovannetti, V., Lloyd, S., and Maccone, L. (2002). LANL Report No. quant-ph/0206001.
Grover, L. K. (1997). Physical Review Letters 79, 325.
Grover, L. (2002). From coupled pendulums to quantum search. I. Mathematics of Quantum Computation, CRC Press, Boca Raton, FL.
Margolus, N. and Levitin, L. (1998). Physica D 120, 188-195.
Zalka, C. (1999). Physical Review A 60, 2748.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bae, J., Kwon, Y. Maximum Speedup in Quantum Search: O(1) Running Time. International Journal of Theoretical Physics 42, 2069–2074 (2003). https://doi.org/10.1023/A:1027391204528
Issue Date:
DOI: https://doi.org/10.1023/A:1027391204528