In principle, quantum computers can simulate gauge theory phenomena inaccessible to classical computers or analytic treatment. For the foreseeable future, however, quantum computers will be sharply limited by noise and memory constraints. To make the most of near-term hardware and develop simulation techniques, it is interesting to benchmark simpler theories that capture some essential physics of gauge theories, to test different platforms and encodings, and to explore hybrid classical/quantum algorithms. This talk will summarize work on digital quantum simulations of the ``femtouniverse," a quantum mechanical multi-matrix model derived from the dimensional reduction of Yang-Mills theory on a small spatial torus. Using the hybrid variational quantum eigensolver and quantum subspace expansion techniques, we obtain the low-lying spectrum and string tension / glueball mass ratio at couplings near the large-small volume transition. Limitations and directions for future development are described.