A quantum genetic algorithm for optimization problems on the Bloch sphere

Optimization problems on the surface of a unit sphere are addressed using a quantum genetic algorithm. That a point on the surface of the Bloch sphere is representative of a pure state qubit is effectively used. Qubits are thought of as genes, and a sequence of qubits as a chromosome, and an ensemble of chromosomes as the population. The crossover and mutation of the genes are implemented using the superposition principle, and mutation is achieved through random phases in the superposition. As illustrations, examples pertaining to the Thomson optimization problem, the logarithmic Thomson optimization problem, and the evaluation of the geometric measure of entanglement are presented.