الفهرس 
Introduction and OverviewOnly 14 pages are availabe for public view
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Abstract
Concerning the rstaim, ascalable protocolisde scribed foroptimizing the quantumcost of the3-qubitre versiblecircuit sbuilt using NCT library isproposed.This technique takes in to account agroup theory approach. Thealgorith manalyzestheequi valent quantum circuits obtainedbyde composing the reversible circuit toitsel ement aryquant umgates, and thenapplies optimization rules toreduce the number of the used elementary quantum gates. The obtained algorithmis applied usin gdi erent quantum costme tricst hatcom pare favorably with therele vantmethods. Applyingthe propose doptimization algorithm on the reversible circui tsgives quantum cost of 10.348 when calculated using cost015 metric and aquantum costof12.59 when calculatedusing cost115 metric .Providi nganenhanced results better than the obtained resultsint heliterature. There sult spresent edtoachieve the rstaimareimpl ementedand tested using the group theory algebraicsoftwareGAP[81].