  The simplest technique for simulating a quantum algorithm - QA described
based on the direct matrix representation of the quantum operators. Using this
approach, it is relatively simple to simulate the operation of a QA and to
perform fidelity analysis. A more efficient fast QA simulation technique is
based on computing all or part of the operator matrices on an as needed current
computational basis. Using this technique, it is possible to avoid storing all
or part of the operator matrices. The compute on demand approach benefits from
a study of the quantum operators, and their structure so that the matrix
elements can be computed more efficiently. Effective simulation of Grover
quantum search algorithm as example on computer with classical architecture is
considered.
