  The quantum-classical hybrid Variational Quantum Eigensolver (VQE) algorithm
is recognized to be the most suitable approach to obtain ground state energies
of quantum many-body systems in the noisy intermediate scale quantum era. In
this work, we extend the VQE algorithm to the relativistic regime and carry out
quantum simulations to obtain ground state energies as well as molecular
permanent electric dipole moments of single-valence diatomic molecules,
beginning with the light BeH molecule and all the way to the heavy radioactive
RaH molecule. We study the correlation trends in these systems as well as
assess the precision in our results within our active space of 12 qubits.
