Grover's Algorithm - Algorithm Steps

Algorithm Steps

The steps of Grover's algorithm are given as follows. Let denote the uniform superposition over all states

.

Then the operator

is known as the Grover diffusion operator.

Here is the algorithm:

1. Initialize the system to the state

2. Perform the following "Grover iteration" r(N) times. The function r(N), which is asymptotically O(N½), is described below.
   1. Apply the operator .
   2. Apply the operator .
3. Perform the measurement Ω. The measurement result will be λ_ω with probability approaching 1 for N≫1. From λ_ω, ω may be obtained.