Evolution of quantum circuits faces two major challenges: complex and huge search spaces and the high costs of simulating quantum circuits on conventional computers. In this paper we analyze different selection strategies, which are applied to the Deutsch-Jozsa problem and the 1-SAT problem using our GP system. Furthermore, we show the effects of adding randomness to the selection mechanism of a (1,10) selection strategy. It can be demonstrated that this boosts the evolution of quantum algorithms on particular problems. © Springer-Verlag Berlin Heidelberg 2004.