The three state model is a geometric quantum computation model. We show that this one is an universal quantum computation model, with base in the work developed by Niskanen, Nakahara and Salomaa [16]. The U(2) and U(2n≥1) universalities are obtained from the construction of the rotations gates Rx(α) and Ry(α), and the Hadamard gate H and the phase gates B(η), respectively. For every quantum gate, we explicitly show the holonomy operator ΓA(γ) and the loop γ on which this is built. PACS: 03.67.Lx