Grover's search with an oracle distinguishing between solutions

Abstract: Here we suggest a modification of Grover's algorithm, based on a multiphase oracle which marks each solution with a different phase when there is more than one solution. Such a modification can be used to maintain a high probability of finding a solution for a number of iterations equal to or more than the one required by the deterministic Grover's algorithm (the one based on generalized Householder reflections). We use various semiempirical methods to show that the interval of number of iterations for which the algorithm keeps the probability of finding solution high depends on the register size and the oracle phases.