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 λω with probability approaching 1 for N≫1. From λω, ω may be obtained.

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