  We explore two flavor scalar electrodynamics on the lattice, which has a
complex phase problem at finite chemical potential. By rewriting the action in
terms of dual variables this complex phase problem can be solved exactly. The
dual variables are link- and plaquette occupation numbers, subject to local
constraints that have to be respected by the Monte Carlo algorithm. For the
simulation we use a local update as well as the newly developed "surface worm
algorithm", which is a generalization of the Prokof'ev Svistunov worm algorithm
concept for simulating the dual representation of abelian Gauge-Higgs models on
a lattice. We assess the performance of the two algorithms, present results for
the phase diagram and discuss condensation phenomena.
