Higher-order subspaces have also been explored, 180 but even including the second excited subspace produces highly unfavorable scaling with a realistic number of molecules N mol ∼ 10 6 . Fig. presents the numerical scaling (i.e. the number of possible configurations/basis states) as solid curves as well as the required memory to store the Hamiltonian (dashed curves) as a function of the number of molecules. Here, we assume only two electronic states per molecule, a single photonic mode with two Fock states, and a real-valued Hamiltonian (i.e., complex would simply double the memory requirements). The thick gray line represents 100 GB of memory, a typical node on a typical high-performance computing cluster. In the S 1 subspace (black), the 100-GB line is reached with a little over 10 5 molecules, while for the second excited subspace S 2 (red), this line is reached with a little less than 1000 molecules. Third subspace S 3 (green) only allows for 100 molecules. The full Hilbert space scales exponentially (blue). This exemplifies the need for the truncation of the total Hilbert space in order to perform meaningful theoretical explorations with realistic cavity designs and environments.