Combinatorial optimization with multimode cavity QED

We discuss how a particular driven-dissipative quantum system, which is both pumped by an external source and is open to environmental interactions, might serve as a platform for information processing. This driven-dissipative system is realized by coupling a network of ultracold atoms to a multimode optical cavity and its dynamics are shown to perform optimization of combinatorial problems. A compact description of multimode cavity QED using an appropriate mode basis, based on superpositions of bare cavity modes, makes tractable an exploration of the dynamics of the system across the superradiant phase transition. In the course of this transition and beyond, the system organizes into a state representing a solution to the optimization problem.  The roles of entanglement and driven-dissipative quantum dynamics in the optimization process will be explored, and experimental progress will be discussed that demonstrates the required ingredients for near-term realization.