  The difference between classical and quantum algorithms (QA) is following:
problem solved by QA is coded in the structure of the quantum operators. Input
to QA in this case is always the same. Output of QA says which problem coded.
In some sense, give a function to QA to analyze and QA returns its property as
an answer without quantitative computing. QA studies qualitative properties of
the functions. The core of any QA is a set of unitary quantum operators or
quantum gates. In practical representation, quantum gate is a unitary matrix
with particular structure. The size of this matrix grows exponentially with an
increase in the number of inputs, which significantly limits the QA simulation
on a classical computer with von Neumann architecture. Quantum search algorithm
(QSA) - models apply for the solution of computer science problems as searching
in unstructured data base, quantum cryptography, engineering tasks, control
system design, robotics, smart controllers, etc. Grovers algorithm is explained
in details along with implementations on a local computer simulator. The
presented article describes a practical approach to modeling one of the most
famous QA on classical computers, the Grover algorithm.
