ESOP-Inspired Synthesis Method for Ternary Permutative Quantum Circuits

The goal of this paper is to improve synthesis of ternary-input, ternary-output quantum per mutative circuits realized with Muthukrishnan-Stroud (M-S) gates. In [1], quantum ternary circuits are designed based on DSOP (Disjoint Sum of Products) cascades of General Ternary Gates (GTGs). Here, we develop an approach to synthesize quantum ternary circuits that uses non-disjoint groups. Our CAD tool, TNGM (Ternary Non-disjoint Groups Minimizer), uses a probabilistic search algorithm to select the largest groups in an incompletely specified Ternary Map and produces more compact circuits.