الفهرس 
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Abstract
This paperintroducesanovelalgorithmtosynthesizealow-costreversible circuits foranyBooleanfunctionwith n inputs representedasaPositivePolarity Reed–Muller expansion. Theproposedalgorithmappliesapredefinedrulestoreorder the termsinthe function to minimi zethemulti-calculation of common parts of the Boolean function to decrease the quantum costo fthereversiblecircuit. The paper achievesad ecreaseinthequantumcostand/orthecircuitlength,onaverage, when compared withrelevantworkintheliterature.This paperisorganize dasfollows.Thenecessarybackgroundi spresented in Sect. 2 The algorithmsforconstructionoftheBooleanfunctionusingtheproposedalgorithm are presentedinSect. 3. InSect. 4, the experimentalresultsandcomparisonwith related work are presented.Section 5 concludes thepaper.