The role of photonic dissipation or cavity losses on polaritonic structure and dynamics has recently been discussed in a number of studies utilizing model Hamiltonians , though to our knowledge the effort to pursue ab initio CQED methods has not explicitly included photonic loss. In this context, photonic dissipation refers to the finite lifetime of occupied photonic modes that exist within a cavity. Photonic dissipation occurs because the photons confined within a cavity can couple to the material degrees of freedom that exist in the cavity itself (which can be significant when considering plasmonic cavities), and also to the continuum of modes that exist outside the cavity (which causes leakage of photons in Fabry-Perot cavities, for example) . In this work we present a simple ab initio CQED method for treating ground and excited polaritonic states with explicit inclusion of photonic lifetimes via a non-Hermitian cavity quantum electrodynamicsconfiguration interaction singles approach (NH-CQED-CIS). This approach provides a simplification for the couplings between photon and material degrees of freedom that contribute to photon dissipation, and subsumes these complicated interactions into a complex frequency of the photon that quantifies the sum of all photon dissipation rates . Setting the imaginary part of the frequency to zero in this approach implies a lossless photonic mode that is perfectly isolated from the environment and returns the formulation to a Hermitian CQED-CIS theory. We implement this approach in the coherent state basis which results from solution of the CQED-Hartree-Fock (CQED-HF) equations. Both the Hermitian and non-Hermitian formulations of CQED-CIS in the CQED-HF basis contain additional couplings to the CQED-HF reference that are not present in canonical CIS theory, and as a results, our method also provides both ground-and excited-state information about the molecular system coupled to a cavity mode. We endeavor to provide a detailed picture of the key equations and algorithmic considerations for both the CQED-HF and NH-CQED-CIS approach, and therefore provide detailed equations of NH-CQED-CIS in the main text, detailed equations for CQED-HF in the appendix, and reference implementations of both methods through the Psi4Numpy project . We apply both methods to the analysis of several paradigmatic systems, including the ground-state polaritonic structure of formaldehyde coupled to cavity modes that can modify the symmetry of the ground-state wavefunction, and the polaritonic potential energy surfaces of the magnesium hydride ion coupled to a lossy photonic mode. We also compute the photon occupation of ground-states obtained from NH-CQED-CIS in the ultra-strong coupling regime for a variety of loss rates, showing qualitative agreement with analysis found in Ref. 6.