الفهرس 
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Abstract
The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. Quantum computing is reversible by nature, and one of the most important features is that there is no heat dissipation that is produced by the reversible system. The optimization of quantum circuits depends on decreasing the number of elementary gates to syntheses the quantum circuit by finding alternative designs for a particular permutation. Many methods and algorithms have been proposed to decrease the quantum cost by using only positive controls or mixed control Toffoli gates (positive and negative).