  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 quantum circuit related to a finite number
of zeros of the Riemann-zeta function. The existence of such circuit will
permit in the future the solution of some number theory problems through the
realization of quantum algorithms based on those zeros.
