  We simulate the effects of different types of noise in state preparation
circuits of variational quantum algorithms. We first use a variational quantum
eigensolver to find the ground state of a Hamiltonian in presence of noise, and
adopt two quality measures in addition to the energy, namely fidelity and
concurrence. We then extend the task to the one of constructing, with a layered
quantum circuit ansatz, a set of general random target states. We determine the
optimal circuit depth for different types and levels of noise, and observe that
the variational algorithms mitigate the effects of noise by adapting the
optimised parameters. We find that the inclusion of redundant parameterised
gates makes the quantum circuits more resilient to noise. For such
overparameterised circuits different sets of parameters can result in the same
final state in the noiseless case, which we denote as parameter degeneracy.
Numerically, we show that this degeneracy can be lifted in the presence of
noise, with some states being significantly more resilient to noise than
others. We also show that the average deviation from the target state is linear
in the noise level, as long as this is small compared to a circuit-dependent
threshold. In this region the deviation is well described by a stochastic
model. Above the threshold, the optimisation can converge to states with
largely different physical properties from the true target state, so that for
practical applications it is critical to ensure that noise levels are below
this threshold.
