Universality of geometric quantum computing three-state model (2005)
The three-state model is a geometric quantum computing model. It is illustrated that this is a universal quantum computing model, based on the work developed by Niskanen, Nakahara and Salomaa [16]. The universals U (2) and U (2n≥ 1) of the model are obtained from the construction of the Rx (α) and R (α) rotation gates, and the Hadamard H and B phase (η) gates ), respectively. For each gate, it is explicitly presented operator Holonomy ΓAy (γ) and γ cycle on which it is constructed.