Whereas tests of quantum computational accuracy are straightforward for small computational problems, for which conventional computation can be referenced, this will not always be so. Due to the rapid advances in quantum computational hardware, we may eventually face situations when it is not easy to validate whether a given problem has been solved to our satisfaction. The motivation behind this work is a proof-of-concept for utilizing electron densities as fidelity witnesses, future-proof benchmarks, for the quality of the quantum computation of materials and molecules. To that end, we have demonstrated the first topological analyses of electron densities inside molecules carried out with the assistance of quantum computers. Our work focuses on measuring oneparticle reduced density matrices on real and simulated quantum hardware, how error mitigation can be applied to these entities, and how the resulting electron densities differ from near-exact reference calculations. The molecular systems studied herein are small enough to be treatable by current quantum hardware and small enough for comparisons with high-quality electron densities derived from conventional computations. Our examples are chosen to demonstrate the sometimes-detrimental effects of noise being imbalanced both spatially and with respect to 1-RDM entries. Therefore, we suggest that noise imbalance should be considered when designing or selecting error mitigation techniques, ansätze, encoding, and active spaces. Our work emphasizes the growing potential and need for high-quality (quantum) crystallography experiments, i.e., experimental determination of electron densities near the diffraction limit.