Grover's search with an oracle distinguishing between solutions

TL;DR

This paper proposes a modified version of Grover's algorithm using a multiphase oracle to improve the probability of finding solutions in cases with multiple solutions, with analysis on how iteration intervals depend on system size and phases.

Contribution

It introduces a multiphase oracle modification to Grover's algorithm that enhances solution probability in multi-solution scenarios.

Findings

High probability of solution detection maintained over extended iterations

Interval of effective iterations depends on register size and oracle phases

Semiempirical methods demonstrate the effectiveness of the modification

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.