There are several open questions in Grover's paper. Foremost among
these is how many times exactly should we iterate step 2 of Grover's
algorithm. Grover proves the existence of some
*m* *O*(),
such that after *m* iterations of step 2 of the algorithm the
probability of finding the register in the marked state is greater
than 1/2. Since the amplitude of the desired state, and hence the
of probability of measuring the desired state, is not monotonic
increasing after *m* iterations, it is not enough to know know the
existence of *m*, it's value must be determined.

- How Many Iterations are Required
- Searching for More Than One Item
- Optimality of Grover's Algorithm
- Implications on P = NP