  In this paper we consider the modelling and simulation of open quantum
systems from a device engineering perspective. We derive master equations at
different levels of approximation for a Superconducting Quantum Interference
Device (SQUID) ring coupled to an ohmic bath. We demonstrate that the master
equations we consider produce decoherences that are qualitatively and
quantitativly dependent on both the level of approximation and the ring's
external flux bias. We discuss the issues raised when seeking to obtain
Lindbladian dissipation and show, in this case, that the external flux (which
may be considered to be a control variable in some applications) is not
confined to the Hamiltonian, as often assumed in quantum control, but also
appears in the Lindblad terms.
