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The emerging field of quantum simulation of many-body systems is widelyrecognized as a very important application of quantum computing. A crucial steptowards its realization in the context of many-electron systems requires arigorous quantum mechanical treatment of the different interactions. In thispilot study, we investigate the physical effects beyond the mean-fieldapproximation, known as electron correlation, in the ground state energies ofatomic systems using the classical-quantum hybrid variational quantumeigensolver (VQE) algorithm. To this end, we consider three isoelectronicspecies, namely Be, Li-, and B+. This unique choice spans three classes, aneutral atom, an anion, and a cation. We have employed the unitarycoupled-cluster (UCC) ansatz to perform a rigorous analysis of two veryimportant factors that could affect the precision of the simulations ofelectron correlation effects within a basis, namely mapping and backendsimulator. We carry out our all-electron calculations with four such basissets. The results obtained are compared with those calculated by using the fullconfiguration interaction, traditional coupled-cluster and the UCC methods, ona classical computer, to assess the precision of our results. A salient featureof the study involves a detailed analysis to find the number of shots (thenumber of times a VQE algorithm is repeated to build statistics) required forcalculations with IBM Qiskit's QASM simulator backend, which mimics an idealquantum computer. When more qubits become available, our study will serve asamong the first steps taken towards computing other properties of interest tovarious applications such as new physics beyond the Standard Model ofelementary particles and atomic clocks using the VQE algorithm.

Assessing the Precision of Quantum Simulation of Many-Body Effects in Atomic Systems using the Variational Quantum Eigensolver Algorithm