  It is well known that most of the frequently used reversible logic gates
(e.g., NOT, CNOT, SWAP, Toffoli, Fredkin) are self-inverse and are represented
by square matrices that are unitary and Hermitian. However, with a simple
minded argument, it is established that the most of the allowed reversible
gates are non-self-inverse (unitary but non-Hermitian) in nature. It is also
shown that the % of non-Hermitian gates increases with the dimension. For
example, 58.33% of the 2-bit gates, 98.10% of the 3-bit gates and 99.99% of the
4-bit gates are non-Hermitian. As classical reversible gates are essentially
permutation gates, above statistics is strictly valid for classical reversible
gates, but the argument can be easily extended to include quantum gates and to
establish that the majority of the quantum gates are also non-self-inverse.
Further, the % of genuinely 2-bit reversible gates (i.e., 2-bit gates that
cannot be decomposed as a product of two single bit gates) among all possible
gates has been computed as 83.3%, and the applicability of this analysis in the
optimization of circuit cost is discussed.
