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This paper presents a heuristic cost minimization approach to synthesizinglinear reversible circuits. Two bidirectional linear reversible circuitsynthesis methods are introduced, the Alternating Elimination with CostMinimization method (AECM) and the Multiple CNOT Gate method (MCG). Algorithms,example syntheses, and extensions to these methods are presented. An MCGvariant which incorporates line reordering is introduced. Tests comparing thenew cost minimization methods with the best known method for large circuits arepresented. Results show that of the three methods MCG had the lowest averageCNOT gate counts for linear reversible circuits up to 24 lines, and that AECMhad the lowest counts between 28 and 60 lines.

A Cost Minimization Approach to Synthesis of Linear Reversible Circuits