A representation of extra-special 2-group, entanglement, and Berry phase of two qubits in Yang-Baxter system

In this paper we show another representations of extra-special 2-groups. Based on this new representation, we infer a M matrix which obeys the extra-special 2-groups algebra relations. We also derive a unitary R̆(θ, φ)matrix from theM using the Yang-Baxterization process. A Hamiltonian for the two qubits is constructed from the unitary R̆(θ, φ) matrix. In this way, we study the Berry phase and entanglement of the two-qubit system. The results also establish relations between topological and holonomic quantum computation.