Grover's Algorithm - Setup

Setup

Consider an unsorted database with N entries. The algorithm requires an N-dimensional state space H, which can be supplied by n=log₂ N qubits. Consider the problem of determining the index of the database entry which satisfies some search criterion. Let f be the function which maps database entries to 0 or 1, where f(ω)=1 if and only if ω satisfies the search criterion. We are provided with (quantum black box) access to a subroutine in the form of a unitary operator, U_ω, which acts as:

Our goal is to identify the index .