While Shor's algorithm may be of more immediate utility, Grover's algorithm seems more interesting in a theoretical sense, as it highlights an area of fundamental superiority in quantum computation.
The idea of Grover's algorithm is to place the register in an equal superposition of all states, and then selectively invert the phase of the marked state, and then perform an inversion about average operation a number of times.
This Grover's algorithm flow chart is as shown in Figure 1.
The proposed system is concerned with the simulation of Grover's Algorithm using MATLAB.
Appendix A contains the Matlab commands to simulate Grover's algorithm using six qubits.
In this simple example of Grover's algorithm, a haystack function is used to represent the database.
Grover's algorithm works by iteratively applying the inversion about the average operator to the current state.
Foremost among these is how many times exactly we should iterate step 2 of Grover's algorithm.
Deutsch-Jozsa's algorithm for the rapid solution [1-3], Shor's algorithm for the factorization [2-4], Grover's algorithms
for the database search [2,5-7] and so on are known, and efforts to expand applications of the quantum calculation are continued.