Riemannian quantum circuit

Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we present the theory of a unitary matrix related to a finite number of zeros of the Riemann-zeta function. The equivalent quantum circuit and the calculation of the entanglement of a multipartite quantum state produced by the Riemannian quantum circuit are also shown.