  In this paper we present Quanrum Encoded Quantum Evolutionary Algorithm
(QEQEA) and compare its performance against a a classical GPU accelerated
Genetic Algorithm (GPUGA). The proposed QEQEA differs from existing quantum
evolutionary algorithms in several points: representation of candidates
circuits is using qubits and qutrits and the proposed evolutionary operators
can in theory be implemented on quantum computer provided a classical control
exists. The synthesized circuits are obtained by a set of measurements
performed on the encoding units of quantum representation. Both algorithms are
accelerated in GPGPU. The main target of this paper, is not to propose a
completely novel quantum genetic algorithm but to rather experimentally
estimate the advantages of certain components of genetic algorithm being
encoded and implemented in a quantum compatible manner. The algorithms are
compared and evaluated on several reversible and quantum circuits. The results
demonstrate that on one hand the quantum encoding and quantum implementation
compatible implementation provides certain disadvantages with respect to the
classical evolutionary computation. On the other hand, encoding certain
components in a quantum compatible manner could in theory allow to accelerate
the search. This acceleration would in turn counter weight the implementation
limitations.
