On Fault-Tolerance Of Grover'S Algorithm

Grover's algorithm is a quantum search algorithm solving the unstructured search problem of size N in O(root N) queries, while any classical algorithm needs O(N) queries [1].However, if the query transformation might fail (with probability independent of the number of steps of the algorithm), then quantum speed-up disappears: no quantum algorithm can be faster than a classical exhaustive search by more than a constant factor [6].In this paper we study the effect of a small number of failed queries. We show that k failed queries with a very high probability change the number of actually executed steps of Grover's algorithm from l to O (l/root k).