Electron densities can, importantly, be reconstructed from the refinement of X-ray diffraction and scattering data, using, e.g., multipolar models, X-ray constrained wave functions, or the maximum entropy method. One motivation for our work is that experimentally determined electron densities can prove useful for testing the accuracy of future quantum computations of materials; simulations of which may be unfeasible with conventional computers. Today, it is often preferable, cheaper, and faster to obtain information on electron distribution through conventional quantum mechanical calculations, e.g., by solving the Schrödinger equation at some level of approximation. To obtain highly accurate computational results (energies, densities, or other properties), ab initio quantum mechanical methods are the most reliable. Unfortunately, the electronic structure problem scales exponentially with system size. In 1980 and 1981, Benioff , Manin and Feynman pointed out that quantum computers may offer a way forward, enabling larger and more reliable simulations of quantum systems. In recent years, several quantum devices have been developed and applied to compute energies of small molecules (see e.g., 19-21). No such calculation has, however, yet exceeded the accuracy or speed of a conventional quantum chemical calculation. So, just how far away are we from useful quantum computation of chemistry? To quantifiably answer that question, it is necessary to perform benchmarking and validate the results of quantum computation in some manner. Thus far, such efforts have almost exclusively focused on a comparison against total energies obtained using state-of-the-art (and near exact) quantum chemistry. However, whereas accurate energies for smaller molecules are available, such comparisons will not be possible if future quantum calculations of more complex systems are made possible. We emphasize at the onset that whether the crossing of such a technological threshold is made in the current noisy intermediate-scale quantum (NISQ) era or if it will require full fault tolerance quantum devices does not affect our main message or conclusions. Here, we suggest that the subtle variability of electron densities, accessible either computationally or experimentally, can act as a potent benchmark for the quantum computation of materials. We draw the colloquial analogy to fidelity witnesses in the title, by which we mean experimentally accessible observables whose values (here in terms of topological features) help to quantify the fidelity of a quantum calculation.