Noise in Grover's Quantum Search Algorithm

Details Noise in Grover's Quantum Search Algorithm Noise in Grover's Quantum Search Algorithm

1999-03-20

arxiv.org/abs/quant-ph/9903070v3

AIP Conf.Proc. 490 (1999) 405-408

Physics

Quantum Physics

17 pages, 2 eps figures. Revised version. To be published in PRA, December 1999

Scientific paper

10.1103/PhysRevA.61.012301

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.

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