  As the realization of a fully operational quantum computer remains distant,
quantum simulation, whereby one quantum system is engineered to simulate
another, becomes a key goal of great practical importance. Here we report on a
variational method exploiting the natural physics of cavity QED architectures
to simulate strongly interacting quantum fields. Our scheme is broadly
applicable to any architecture involving tunable and strongly nonlinear
interactions with light; as an example, we demonstrate that existing cavity
devices could simulate models of strongly interacting bosons. The scheme can be
extended to simulate systems of entangled multicomponent fields, beyond the
reach of existing classical simulation methods.
