Quantum Image Preparation Based on Exclusive Sum-of-Product Minimization and Ternary Trees

Abstract: 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.