  Quantum algorithms for quantum dynamics simulations are traditionally based
on implementing a Trotter-approximation of the time-evolution operator. This
approach typically relies on deep circuits and is therefore hampered by the
substantial limitations of available noisy and near-term quantum hardware. On
the other hand, variational quantum algorithms have become an indispensable
alternative, enabling small-scale simulations on present-day hardware. However,
despite the recent development of variational quantum algorithms for quantum
dynamics, a detailed assessment of their efficiency and scalability is yet to
be presented. To fill this gap, we applied a variational quantum algorithm
based on McLachlan's principle to simulate the dynamics of a spin-boson model
subject to varying levels of realistic hardware noise as well as in different
physical regimes, and discuss the algorithm's accuracy and scaling behavior as
a function of system size. We observe a good performance of the variational
approach used in combination with a general, physically motivated wavefunction
ansatz, and compare it to the conventional first-order Trotter-evolution.
Finally, based on this, we make scaling predictions for the simulation of a
classically intractable system. We show that, despite providing a clear
reduction of quantum gate cost, the variational method in its current
implementation is unlikely to lead to a quantum advantage for the solution of
time-dependent problems.
