  We show that a system of Josephson junctions coupled via low-resistance
tunneling contacts to graphene substrate(s) may effectively operate as a
current switching device. The effect is based on the dissipation-driven
superconductor-to-insulator quantum phase transition, which happens due to the
interplay of the Josephson effect and Coulomb blockade. Coupling to a graphene
substrate with gapless excitations further enhances charge fluctuations
favoring superconductivity. The effect is shown to scale exponentially with the
Fermi energy in graphene, which can be controlled by the gate voltage. We
develop a theory, which quantitatively describes the quantum phase transition
in a two-dimensional Josephson junction array, but it is expected to provide a
reliable qualitative description for one-dimensional systems as well. We argue
that the local effect of dissipation-induced enhancement of superconductivity
is very robust and a similar sharp crossover should be present in finite
Josephson junction chains.
