  It has been experimentally proven that realizing universal quantum gates
using higher-radices logic is practically and technologically possible. We
developed a Parallel Genetic Algorithm that synthesizes Boolean reversible
circuits realized with a variety of quantum gates on qudits with various
radices. In order to allow synthesizing circuits of medium sizes in the higher
radix quantum space we performed the experiments using a GPU accelerated
Genetic Algorithm. Using the accelerated GA we compare heuristic improvements
to the mutation process based on cost minimization, on the adaptive cost of the
primitives and improvements due to Baldwinian vs. Lamarckian GA. We also
describe various fitness function formulations that allowed for various
realizations of well known universal Boolean reversible or
quantum-probabilistic circuits.
