  State-of-the-art algorithms for simulating fermions coupled to gauge fields
often rely on integrating fermion degrees of freedom. While successful in
simulating QCD at zero chemical potential, at finite density these approaches
are hindered by the sign problem. We discuss the simulation of lattice gauge
theories in the Hamiltonian formalism and present a generalized meron-cluster
algorithm for the simulation of the $U\left(1\right)$ Quantum Link Model for
spin $1/2$. This enables the study of models directly relevant to current
quantum simulators and is a promising first step toward constructing new
efficient algorithms for more complicated gauge theories.
