Preparation of three-qubit states

In this paper, we present a new and algebraically simple algorithm that prepares any pure three-qubit state using only local gates and at most three controlled-[Formula: see text] gates. In 2008, Znidaric et al. already showed that three is the optimal number of controlled-[Formula: see text] gates required for the preparation of three-qubit states if in addition to those gates only local gates are used. If we restrict the local gates to [Formula: see text] gates, our algorithm provides a way to prepare any pure three-qubit state [Formula: see text] with real amplitudes using at most four controlled-[Formula: see text] gates when its hyperdeterminant is negative and three or fewer controlled-[Formula: see text] gates otherwise. We conjecture the existence of three-qubit states with real amplitudes that cannot be prepared using only [Formula: see text] gates and less than four controlled-[Formula: see text] gates.