الفهرس 
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Abstract
A genetic algorithm for xed polarity A Reed-Muller function f(x_ 1; :::; x_ n) is said to have xed polarity if through out the expansion each variable x_ k is either xk or x0 k exclusively, then there will be 2n possible expansions [9]. Searching for the expansion that gives a Boolean quantum circuit with minimum quantum cost is a hard problem for large n, so a genetic algorithm will be proposed to search for the xed polarity Reed-Muller expansion that gives a Boolean reversible circuit with the minimum cost.A genetic algorithm for mixed polarity A Reed-Muller function f(x_ 1; :::; x_ n) is said to have mixed polarity if for some variables, xk and x0 k occur in the same expansion, then there will be n 2n possible expansions [9]. Searching for the expansion that gives a Boolean quantum circuit with minimum quantum cost is a hard problem for large n so a genetic algorithm will be proposed to search for the mixed polarity Reed Muller expansion that gives a Boolean reversible circuit with the minimum cost.The idea is based on the fact that there is a direct equivalence between Boolean functions represented in Reed-Muller logic and Boolean quantum circuits [10]. Dif ferent Boolean quantum circuits with di erent quantum cost for the same Boolean function will arise from di erent polarity Reed-Muller expansions [10].