Abstract: Due to the non- intuitive nature of Quantum
algorithms, it becomes difficult for a classically trained person to
efficiently construct new ones. So rather than designing new
algorithms manually, lately, Genetic algorithms (GA) are being
implemented for this purpose. GA is a technique to automatically
solve a problem using principles of Darwinian evolution. This has
been implemented to explore the possibility of evolving an n-qubit
circuit when the circuit matrix has been provided using a set of
single, two and three qubit gates. Using a variable length population
and universal stochastic selection procedure, a number of possible
solution circuits, with different number of gates can be obtained for
the same input matrix during different runs of GA. The given
algorithm has also been successfully implemented to obtain two and
three qubit Boolean circuits using Quantum gates. The results
demonstrate the effectiveness of the GA procedure even when the
search spaces are large.
Abstract: Histogram plays an important statistical role in digital
image processing. However, the existing quantum image models are
deficient to do this kind of image statistical processing because
different gray scales are not distinguishable. In this paper, a novel
quantum image representation model is proposed firstly in which the
pixels with different gray scales can be distinguished and operated
simultaneously. Based on the new model, a fast quantum algorithm of
constructing histogram for quantum image is designed. Performance
comparison reveals that the new quantum algorithm could achieve an
approximately quadratic speedup than the classical counterpart. The
proposed quantum model and algorithm have significant meanings for
the future researches of quantum image processing.