Intermediate measurements in quantum circuits compare to conditional branchings in programming languages. Due to this, quantum circuits have a natural linear-tree structure. In this paper a Genetic Programming system based on linear-tree genome structures developed for the purpose of automatic quantum circuit design is introduced. It was applied to instances of the 1-SAT problem, resulting in evidently and "visibly" scalable quantum algorithms, which correspond to Hogg's quantum algorithm. © Springer-Verlag Berlin Heidelberg 2003.