  We propose a quantum gate architecture that allows for the systematic control
of the effective exchange interactions between magnetic impurities embedded in
nano-scale graphene flakes connected by a gated bridge. The entanglement
between the magnetic moment and the edge states of the fragments is used to
electrostatically tune the exchange interaction from ferro to antiferromagnetic
by merely changing the bridge's carrier density. By characterizing the effects
of size and coupling parameters, we explore different operation regimes of this
device by means of exact calculations with the density matrix renormalization
group (DMRG). We analyze the results utilizing a simplified model that accounts
for the main many-body mechanisms. Finally, we discuss how to use arrays of
these devices to build quantum simulators for quantum many-body Hamiltonians.
