A route to quantum computing through the theory of quantum graphs

Based on our previous works, and in order to relate them with the theory of quantum graphs and the quantum computing principles, we once again try to introduce some newly developed technical structures just by relying on our toy example, i.e. the coordinate ring of n× n quantum matrix algebra Mq(n), and the associated directed locally finite graphs G(Πₙ), and the Cuntz-Krieger C^*-graph algebras. Meaningly, we introduce a $(4i-6)$-quantum entangled system by using the Cuntz-Krieger G(Πᵢ)-families associated to the $4i-6$ distinct Hamiltonian paths of G(Πᵢ), for i∈\2,⋯,n\.