  We demonstrate that substantial progress can be achieved in the study of the
phase structure of 4-dimensional compact QED by a joint use of hybrid Monte
Carlo and multicanonical algorithms, through an efficient parallel
implementation. This is borne out by the observation of considerable speedup of
tunnelling between the metastable states, close to the phase transition, on the
Wilson line. Our approach leads to a general parallelization scheme for the
efficient stochastic sampling of systems where (a part of) the Hamiltonian
involves the total action or energy in each update step.
