  The recovery of classical chaotic dynamics from quantum systems has long been
a subject of interest. Furthermore, recent work indicates that quantum chaos
may well be significant in quantum information processing. In this paper we
discuss the quantum to classical crossover of a superconducting quantum
inference device (SQUID) ring. Such devices comprise of thick superconducting
loop enclosing a Josephson weak link. These devices are currently strong
candidates for many applications in quantum technologies. The weak link brings
with it a non-linearity such that semi-classical models of this system can
exhibit chaotic dynamics. For many similar systems an application of the
correspondence principle together with the inclusion of environmental degrees
of freedom through a quantum trajectories approach can be used to effectively
recover classical dynamics. Here we show (i) that the standard expression of
the correspondence principle is incompatible with the ring Hamiltonian and we
present a more pragmatic and general expression which finds application here
and (ii) that practical limitations to circuit parameters of the SQUID ring
prevent arbitrarily accurate recovery of classical chaotic dynamics.
