where |Φ e I ⟩ represents a determinant of electronic orbitals, |n p ⟩ is a photon-number state corresponding to n photons in the cavity mode, and C I,n is an expansion coefficient. In the CASCI ansatz for the electronic subspace, a subset of active electrons and orbitals are identified where a full CI expansion is performed within that active space. We use the convention (N el , N orb ) to denote an active space consisting N orb active orbitals including the m highest-energy occupied orbitals containing N el active electrons and the (N orbm) remaining lowest-energy unoccupied orbitals. A schematic of one possible determinant in a (6,6) active space is shown in Figure . As previously discussed, because we perform an FCI expansion within the active space, the number of electronic determinants N det in Eq. 7 scales factorially with the number of active electrons and orbitals. However, N det is insensitive to the total size of the single-electron orbital basis used for a given active space size. We can then see that the key to having a tractable CASCI (and QED-CASCI) method relies on having a reasonably sized active space. We also have additional scaling of the number of electronic-photonic product states in Eq. 7 by maximum photon occupation. For example, if we restrict the maximum photon occupation state to be 1 (so that the photon basis states include |0 p ⟩ and |1 p ⟩, then we will have twice as many configurations in Eq. 7 as compared to a cavity-free calculation with the same active space and the resulting Hamiltonian matrix will be four times as large.