  The emerging field of quantum simulation of many-body systems is widely
recognized as a very important application of quantum computing. A crucial step
towards its realization in the context of many-electron systems requires a
rigorous quantum mechanical treatment of the different interactions. In this
pilot study, we investigate the physical effects beyond the mean-field
approximation, known as electron correlation, in the ground state energies of
atomic systems using the classical-quantum hybrid variational quantum
eigensolver (VQE) algorithm. To this end, we consider three isoelectronic
species, namely Be, Li-, and B+. This unique choice spans three classes, a
neutral atom, an anion, and a cation. We have employed the unitary
coupled-cluster (UCC) ansatz to perform a rigorous analysis of two very
important factors that could affect the precision of the simulations of
electron correlation effects within a basis, namely mapping and backend
simulator. We carry out our all-electron calculations with four such basis
sets. The results obtained are compared with those calculated by using the full
configuration interaction, traditional coupled-cluster and the UCC methods, on
a classical computer, to assess the precision of our results. A salient feature
of the study involves a detailed analysis to find the number of shots (the
number of times a VQE algorithm is repeated to build statistics) required for
calculations with IBM Qiskit's QASM simulator backend, which mimics an ideal
quantum computer. When more qubits become available, our study will serve as
among the first steps taken towards computing other properties of interest to
various applications such as new physics beyond the Standard Model of
elementary particles and atomic clocks using the VQE algorithm.

Atomic Physics;Chemical Physics;Quantum Physics