Research in contemporary physics is emphasizing the development and evolution of computer systems to facilitate the calculations. Quantum computing is a branch of modern physics is believed promising results for the future, Thanks to the ability of qubits to store more information than a bit. The work of this paper focuses on the simulation of certain quantum algorithms such as the prisoner's dilemma in its quantum version using the MATHEMATICA® software and implementing stochastic version of the software MAPLE ® and the Grover search algorithm that simulates finding a needle in a haystack.