  Classical simulations of time-dependent quantum systems are widely used in
quantum control research. In particular, these simulations are commonly used to
host iterative optimal control algorithms. This is convenient for algorithms
which are too onerous to run in the loop with current-day quantum hardware, as
well as for researchers without consistent access to said hardware. However, if
the model used to represent the system is not selected carefully, an optimised
control protocol may be rendered futile when applied to hardware. We present a
series of models, ordered in a hierarchy of progressive approximation, which
appear in quantum control literature. Significant model deviations are
highlighted, with a focus on simulated dynamics under simple single-qubit
protocols. The validity of each model is characterised experimentally by
designing and benchmarking control protocols for an IBMQ cloud quantum device.
This result demonstrates an error amplification exceeding 100%, induced by the
application of a first-order perturbative approximation. Finally, an evaluation
of simulated control dynamics reveals that despite the substantial variance in
numerical predictions across the proposed models, the complexity of discovering
local optimal control protocols appears invariant for a simple control scheme.
The set of findings presented heavily encourage practitioners of this field to
ensure that their system models do not contain assumptions that markedly
decrease applicability to hardware in experimentally relevant control parameter
regimes.
