  In Variational Quantum Simulations, the construction of a suitable parametric
quantum circuit is subject to two counteracting effects. The number of
parameters should be small for the device noise to be manageable, but also
large enough for the circuit to be able to represent the solution. Dimensional
expressivity analysis can optimize a candidate circuit considering both
aspects. In this article, we will first discuss an inductive construction for
such candidate circuits. Furthermore, it is sometimes necessary to choose a
circuit with fewer parameters than necessary to represent all relevant states.
To characterize such circuits, we estimate the best-approximation error using
Voronoi diagrams. Moreover, we discuss a hybrid quantum-classical algorithm to
estimate the worst-case best-approximation error, its complexity, and its
scaling in state space dimensionality. This allows us to identify some
obstacles for variational quantum simulations with local optimizers and
underparametrized circuits, and we discuss possible remedies.
