  The design of parametric quantum circuits (PQCs) for efficient use in
variational quantum simulations (VQS) is subject to two competing factors. On
one hand, the set of states that can be generated by the PQC has to be large
enough to contain the solution state. Otherwise, one may at best find the best
approximation of the solution restricted to the states generated by the chosen
PQC. On the other hand, the PQC should contain as few parametric quantum gates
as possible to minimize noise from the quantum device. Thus, when designing a
PQC one needs to ensure that there are no redundant parameters. The dimensional
expressivity analysis discussed in these proceedings is a means of addressing
these counteracting effects. Its main objective is to identify independent and
redundant parameters in the PQC. Using this information, superfluous parameters
can be removed and the dimension of the space of states that are generated by
the PQC can be computed. Knowing the dimension of the physical state space then
allows us to deduce whether or not the PQC can reach all physical states.
Furthermore, the dimensional expressivity analysis can be implemented
efficiently using a hybrid quantum-classical algorithm. This implementation has
relatively small overhead costs both for the classical and quantum part of the
algorithm and could therefore be used in the future for on-the-fly circuit
construction. This would allow for optimized circuits to be used in every loop
of a VQS rather than the same PQC for the entire VQS. These proceedings review
and extend work in [1, 2].
