  We propose a simple realization of a quantum simulator of the Riemann-Hurwitz
(RH) \zeta\ function based on a truncation of its Dirichlet representation. We
synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property
that the temporal evolution of the autocorrelation function of an initial bare
state of the Hamiltonian reproduces the RH function along the line \sigma+i
\omega t of the complex plane, with \sigma>1. The tight-binding Hamiltonian
with engineered hopping rates and site energies can be implemented in a variety
of physical systems, including trapped ion systems and optical waveguide
arrays. The proposed method is scalable, which means that the simulation can be
in principle arbitrarily accurate. Practical limitations of the suggested
scheme, arising from a finite number of lattice sites N and from decoherence,
are briefly discussed.
