  Recent experimental advances in strongly coupled light-matter systems has
sparked the development of general ab-initio methods capable of describing
interacting light-matter systems from first principles. One of these methods,
quantum-electrodynamical density-functional theory (QEDFT), promises
computationally efficient calculations for large correlated light-matter
systems with the quality of the calculation depending on the underlying
approximation for the exchange-correlation functional. So far no true
density-functional approximation has been introduced limiting the efficient
application of the theory. In this paper, we introduce the first gradient-based
density functional for the QEDFT exchange-correlation energy derived from the
adiabatic-connection fluctuation-dissipation theorem. We benchmark this
simple-to-implement approximation on small systems in optical cavities and
demonstrate its relatively low computational costs for fullerene molecules up
to C$_{180}$ coupled to 400,000 photon modes in a dissipative optical cavity.
This work now makes first principle calculations of much larger systems
possible within the QEDFT framework effectively combining quantum optics with
large-scale electronic structure theory.
