  The influence of a Gaussian environment on a quantum system can be described
by effectively replacing the continuum with a discrete set of ancillary quantum
and classical degrees of freedom. This defines a pseudomode model which can be
used to classically simulate the reduced system dynamics. Here, we consider an
alternative point of view and analyze the potential benefits of an analog or
digital quantum simulation of the pseudomode model itself. Superficially, such
a direct experimental implementation is, in general, impossible due to the
unphysical properties of the effective degrees of freedom involved. However, we
show that the effects of the unphysical pseudomode model can still be
reproduced using measurement results over an ensemble of physical systems
involving ancillary harmonic modes and an optional stochastic driving field.
This is done by introducing an extrapolation technique whose efficiency is
limited by stability against imprecision in the measurement data. We examine
how such a simulation would allow us to (i) perform accurate quantum simulation
of the effects of complex non-perturbative and non-Markovian environments in
regimes that are challenging for classical simulation, (ii) conversely,
mitigate potential unwanted non-Markovian noise present in quantum devices, and
(iii) restructure some of some of the properties of a given physical bath, such
as its temperature.
