  Quantum computing devices require exceptional control of their experimental
parameters to prepare quantum states and simulate other quantum systems.
Classical optimization procedures used to find such optimal control parameters,
have further been shown in idealized settings to exhibit different regimes of
learning. Of interest in this work is the overparameterization regime, where
for systems with a sufficient number of parameters, global optima for prepared
state and compiled unitary fidelities may potentially be reached exponentially
quickly. Here, we study the robustness of overparameterization phenomena in the
presence of experimental constraints on the controls, such as bounding or
sharing parameters across operators, as well as in the presence of noise
inherent to experimental setups. We observe that overparameterization phenomena
are resilient in these realistic settings at short times, however fidelities
decay to zero past a critical simulation duration due to accumulation of either
quantum or classical noise. This critical depth is found to be logarithmic in
the scale of noise, and optimal fidelities initially increase exponentially
with depth, before decreasing polynomially with depth, and with noise. Our
results demonstrate that parameterized ansatze can mitigate entropic effects
from their environment, offering tantalizing opportunities for their
application and experimental realization in near term quantum devices.
