  The emerging field of quantum simulation of many-body systems is widely
recognized as a killer application of quantum computing. A crucial step towards
realizing its full potential requires understanding the role of electron
correlation effects that lie at the heart of such calculations. In this pilot
study, we investigate the trends in the electron correlation effects in the
ground state energies of atomic systems using the classical-quantum hybrid
variational quantum eigensolver (VQE) algorithm. To facilitate a comparative
analysis, we consider three isoelectronic systems, namely Li$^-$, Be, and
B$^+$, that is, an anion, a neutral atom and a cation, respectively. We choose
the unitary coupled-cluster (UCC) ansatz for our computations. We conduct a
rigorous analysis of the factors that could affect the accuracy with which
electron correlation effects can be captured, namely mappings, backend
simulators, and basis sets. The obtained results are also compared with those
calculated by using the full configuration interaction method, coupled-cluster
theory and UCC method, on a classical computer. A noteworthy part of the study
involves a careful analysis to find the number of shots required for
calculations with Qiskit's QASM simulator backend, which mimics an ideal
quantum computer, at which one can obtain results in very good agreement with
those from a classical computer.
