Optimization of Reversible Circuits Using Toffoli Decompositions with Negative Controls

The synthesis and optimization of quantum circuits are essential for the construction computers. This paper proposes two methods to reduce cost 3-bit reversible circuits. first method utilizes basic building blocks gate pairs using different Toffoli decompositions. These used reconstruct where further rules will be applied synthesize optimized circuit. second suggests a new universal library, which provides better when compared with previous work in both cost015 cost115 metrics; this proposed library “Negative NCT” uses gates that operate on target qubit only control qubit’s state is zero. A combination Negative NCT optimization, showed after despite having same circuit size. over three bits form permutation group size 40,320 (23!), subset symmetric group, considered as generators group.