Implementation of neareast neighbor quantum circuit with low quantum cost

Primary purpose behind this work is to develop a type of quantum gate C
²
(iZ)/C
²
(-iZ) derived from unitary quantum gate C
²
(-I) by finding its 2
^nd
root. This newly introduced gate is nearest-neighbor compliant with a unit quantum cost. The main objective in deriving this quantum gate C
²
(iZ)/C
²
(-iZ) is to generate low cost MCT gates which eventually produces cost optimized NNC free reversible circuits. For systematic mapping and a fair comparison with prior works, we formed a quantum gate library that includes CNOT, NOT, H, CH, C
²
(-I) and C
²
(iZ)/C
²
(-iZ) gates. A mapping algorithm including the complete gate library is proposed alongwith necessary mathematical proofs. Using the gate library, we show significant cost savings is achievable over the state-of-the-art approaches, when mapping n-control Toffoli gates and chosen benchmark functions.