  Basic logic gates and their operations in ternary quantum domain are involved
in the synthesis of ternary quantum circuits. Only a few works define ternary
algebra for ternary quantum logic realization. In this paper, a ternary logic
function is expressed in terms of projection operations including a new one. A
method to realize new multi-qutrit ternary gates in terms of generalized
ternary gates and projection operations is also presented. We also introduced
ten simplification rules for reducing ancilla qutrits and gate levels. Our
method yields lower gate cost and fewer gate levels and ancilla qutrits than
that obtained by earlier methods for the ternary benchmark circuits. The $n$
qutrit ternary sum function is synthesized without any ancilla qutrit by our
proposed methodology.
