  Advances in quantum computation for electronic structure, and particularly
heuristic quantum algorithms, create an ongoing need to characterize the
performance and limitations of these methods. Here we discuss some potential
pitfalls connected with the use of hardware-efficient Ansatze in variational
quantum simulations of electronic structure. We illustrate that
hardware-efficient Ansatze may break Hamiltonian symmetries and yield
non-differentiable potential energy curves, in addition to the well-known
difficulty of optimizing variational parameters. We discuss the interplay
between these limitations by carrying out a comparative analysis of
hardware-efficient Ansatze versus unitary coupled cluster and full
configuration interaction, and of second- and first-quantization strategies to
encode fermionic degrees of freedom to qubits. Our analysis should be useful in
understanding potential limitations and in identifying possible areas of
improvement in hardware-efficient Ansatze.
