Riemannian quantum circuit

•We show a quantum circuit related to the zeros of the Riemman-zeta function.•A quantum computer can work as a physical system related to any amount of zeros.•Entanglement of a state generated by the Riemannian quantum circuit is calculated.

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.