  The real-time flux dynamics of up to three superconducting quantum
interference devices (SQUIDs) are studied by numerically solving the
time-dependent Schr\"odinger equation. The numerical results are used to
scrutinize the mapping of the flux degrees of freedom onto two-level systems
(the qubits) as well as the performance of the intermediate SQUID as a tunable
coupling element. It is shown that the qubit representation yields a good
description of the flux dynamics during quantum annealing and the presence of
the tunable coupling element does not have negative effects on the overall
performance. Additionally, data obtained from a simulation of the dynamics of
two-level systems during quantum annealing are compared to experimental data
produced by the D-Wave 2000Q quantum annealer. The effects of finite
temperature are incorporated in the simulation by coupling the qubit system to
a bath of two-level systems. It is shown that an environment modeled as
non-interacting two-level systems coupled to the qubits can produce data which
matches the experimental data much better than the simulation data of the
qubits without coupling to an environment and better than data obtained from a
simulation of an environment modeled as interacting two-level systems coupling
to the qubits.
