  Non-Trivial Reversible Identities (NTRIs) are reversible circuits that have
equal inputs and outputs. NTRIs cannot be detected using optimization
algorithms in the literature. Existence of NTRIs in a circuit will cause a slow
down by increasing the number of gates and the quantum cost. NTRIs might arise
due to integration between two or more optimal reversible circuits. In this
paper, an algorithm that detects and removes NTRIs in polynomial time will be
proposed. Experiments that show the bad effect of NTRIs and the enhancement
using the proposed algorithm will be presented.
