Quantum Search Simulation with Wolfram Mathematica

We consider Grover's algorithm of quantum search for one or several integers out of N = 2(n), where n is a number of quantum bits in the memory register. There is a black-box or subroutine containing information about hidden integers and it can easily recognize these integers but we do not know which ones out of N they are. To find the hidden items we can do no better with a classical computer than to apply the subroutine repeatedly to all possible integers until we hit on the special one and in the worst case we have to repeat this procedure N times. We have analyzed the Grover algorithm carefully and showed that it enables to speed up this search quadratically, although its realization requires to know a number of hidden items. The lower bound for the probability of successful solving the search problem has been obtained. The validity of the results was demonstrated by simulation of the Grover search algorithm using the package QuantumCircuit written in the Wolfram Mathematica language.