Genetic Synthesis of New Reversible/Quantum Ternary Comparator

Methods of quantum/reversible logic synthesis are based on the use of the binary nature of quantum computing. However, multiple-valued logic is a promising choice for future quantum computer technology due to a number of advantages over binary circuits. In this paper we have developed a synthesis of ternary reversible circuits based on Muthukrishnan-Stroud gates using a genetic algorithm. The method of coding chromosome is presented, and well-grounded choice of algorithm parameters allowed obtaining better circuit schemes of one- and n-qutrit ternary comparators compared with other methods. These parameters are quantum cost of received reversible devices, delay time and number of constant input (ancilla) lines. Proposed implementation of the genetic algorithm has led to reducing of the device delay time and the number of ancilla qutrits to 1 and 2n-1 for one- and n-qutrits full comparators, respectively. For designing of n-qutrit comparator we have introduced a complementary device which compares output functions of 1-qutrit comparators.