  Search-base algorithms have widespread applications in different scenarios.
Grover's quantum search algorithms and its generalization, amplitude
amplification, provide a quadratic speedup over classical search algorithms for
unstructured search. We consider the problem of searching with prior knowledge.
More preciously, search for the solution among N items with a prior probability
distribution. This letter proposes a new generalization of Grover's search
algorithm which performs better than the standard Grover algorithm in average
under this setting. We prove that our new algorithm achieves the optimal
expected success probability of finding the solution if the number of queries
is fixed.
