  Variational quantum algorithms are suitable for use on noisy quantum systems.
One of the most important use-cases is the quantum simulation of materials,
using the variational quantum eigensolver (VQE). To optimize VQE performance, a
suitable parameterized quantum circuit (ansatz) must be selected. We
investigate a class of ansatze that incorporates knowledge of the quantum
hardware, namely the hardware efficient ansatze. The performance of hardware
efficient ansatze is affected differently by noise, and our goal is to study
the effect of noise on evaluating which ansatz gives more accurate results in
practice. First, we study the effect of noise on the different hardware
efficient ansatze by benchmarking and ranking the performance of each ansatz
family (i) on a chemistry application using VQE and (ii) by the recently
established metric of "expressibility". The results demonstrate the ranking of
optimal circuits does not remain constant in the presence of noise. Second, we
evaluate the suitability of the expressibility measure in this context by
performing a correlation study between expressibility and the performance of
the same circuits on a chemistry application using VQE. Our simulations reveal
a weak correlation and therefore demonstrate that expressibility is not an
adequate measure to quantify the effectiveness of parameterized quantum
circuits for quantum chemistry. Third, we evaluate the effect of different
quantum device noise models on the ordering of which ansatz family is best.
Interestingly, we see that to decide which ansatz is optimal for use, one needs
to consider the specific hardware used even within the same family of quantum
hardware.
