We use a model of hard-core bosons to describe a SQUID built with two crystals of dx2-y2-superconductors with orientations (1 0 0) and (1 1 0). Across the two faceted (1 0 0)/(1 1 0) interfaces, the structure of the superconducting order parameter leads to an alternating sign of the local Josephson coupling, and the possibility of quartet formation. Using a mapping of the boson model to an XXZ model, we calculate numerically the energy of the system as a function of the applied magnetic flux, finding signals of hc/4e oscillations in a certain region of parameters. This region has a large overlap to that at which binding of bosons exists. © 2005 Elsevier B.V. All rights reserved.