  We derive a microscopic model for dissipative dynamics in a system of
mutually interacting qubits coupled to a thermal bath that generalises the
dissipative model of Landau-Lifschitz-Gilbert to the case of anisotropic bath
couplings. We show that the dissipation acts to bias the quantum trajectories
towards a reduced phase space. This model applies to a system of
superconducting flux qubits whose coupling to the environment is necessarily
anisotropic. We study the model in the context of the D-Wave computing device
and show that the form of environmental coupling in this case produces dynamics
that are closely related to several models proposed on phenomenological
grounds.
