With the emergence of more and more powerful quantum computers, synthesis of quantum circuits that realize a given quantum functionality on those devices has become an important research topic. As quantum algorithms often contain a substantial Boolean component, many synthesis approaches focus on reversible circuits. While some of these methods can be applied on rather large functions, they often yield circuits that are far from being optimal. Aiming at better solutions, evolutionary algorithms can be used as possible alternatives to above methods. However, while previous work in this area clearly demonstrated the potential of this direction, it often focuses on a single optimization objective and employs cost functions that are not very well suited for quantum-technological implementations of the resulting circuits. In this paper, we propose a framework for multi-objective synthesis of quantum circuits based on Genetic Programming that puts a focus on quantum-specific aspects and can be tuned towards several relevant/related cost metrics. A preliminary evaluation indicates that the proposed approach is competitive to previous ones. In some cases, the generated circuits even improve over existing results on all optimization objectives simultaneously, even though the latter were found by specifically targeting a single objective.
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