  Quantum dot hybrid qubits formed from three electrons in double quantum dots
represent a promising compromise between high speed and simple fabrication for
solid state implementations of single qubit and two qubits quantum logic ports.
We derive the Schrieffer-Wolff effective Hamiltonian that describes in a simple
and intuitive way the qubit by combining a Hubbard-like model with a projector
operator method. As a result, the Hubbard-like Hamiltonian is transformed in an
equivalent expression in terms of the exchange coupling interactions between
pairs of electrons. The effective Hamiltonian is exploited to derive the
dynamical behaviour of the system and its eigenstates on the Bloch sphere to
generate qubits operation for quantum logic ports. A realistic implementation
in silicon and the coupling of the qubit with a detector are discussed.
