  Quantum image processing is one of the promising fields of quantum
information. The complexity overhead to design circuits to represent quantum
images is a significant problem. So, we proposed a new method to minimize the
total number required of quantum gates to represent the quantum image. Our
approach uses ternary trees to reduce the number of Toffoli gates in a quantum
image circuit. Also, it uses the complement property of Boolean algebra on a
set of Toffoli gates to combine two Toffoli gates into one, therefore reducing
the number of overall gates. Ternary trees are used to represent Toffoli gates
as they significantly increase run time and is supported through experiments on
sample images. The experimental results show that there is a high-speed up
compared with previous methods, bringing the processing time for thousands of
Toffoli gates from minutes to seconds.
