In what follows, we demonstrate calculations of electron densities (and their topological features) of molecular hydrogen (H2) and lithium hydride (LiH) using quantum computers. These molecules are archetypical examples of fundamentally different chemical bonds (covalent and ionic). Simulation of quantum hardware is also employed to derive the electron density of larger molecules, the lithium dimer (Li2) and hydrogen cyanide (HCN). The quantum volume and noise level of the devices we use are insufficient to demonstrate any advantage over classical implementations (details of the hardware are provided in the Methods section and Supporting Information). However, they suffice for our goal -a first proof-of-principle evaluation of electron densities using quantum devices. By comparing aspects of the electron density topology in these molecules, we showcase a different way to benchmark the quality of quantum hardware calculations of chemistry. To do so, we make use of the quantum theory of atoms in molecules (QTAIM), a wellestablished framework for performing topological analysis of electron densities, which can provide clues into atomic properties, 7 chemical bonding, 8,10 lattice energies, chemical bond strengths, and reactivity.