Delay optimization for ternary fixed polarity Reed–Muller circuits based on multilevel adaptive quantum genetic algorithm

Delay optimization has now emerged as an important optimization goal in logic synthesis. The delay optimization for ternary fixed polarity Reed–Muller (FPRM) circuits aims to find a ternary FPRM circuit with a minimum delay. Because the delay optimization for ternary FPRM circuits is a combinatorial optimization problem, in this paper, we first propose a multilevel adaptive quantum genetic algorithm (MAQGA), which divides individuals into three-level populations: high-level population, intermediate-level population, and low-level population and uses the proposed ternary quantum rotation gate, proposed ternary quantum correction gate, and proposed multi-operator adaptive mutation mechanism to make the three-level populations evolve. Moreover, based on the proposed delay decomposition strategy, we propose a delay optimization approach (DOA) for ternary FPRM circuits under the unit delay model, which searches for a ternary FPRM circuit with a minimum delay using the MAQGA. Experimental results demonstrated the effectiveness and superiority of the DOA in optimizing the delay of ternary FPRM circuits.