  We show that a recent proposal for simulating planar hyperbolic lattices with
circuit quantum electrodynamics can be extended to accommodate also higher
dimensional lattices in Euclidean and non-Euclidean spaces if one allows for
circuits with more than three polygons at each vertex. The quantum dynamics of
these circuits, which can be constructed with present-day technology, are
governed by effective tight-binding Hamiltonians corresponding to
higher-dimensional Kagom\'{e}-like structures ($n$-dimensional zeolites), which
are well known to exhibit strong frustration and flat bands. We analyze the
relevant spectra of these systems and derive an exact expression for the
fraction of flat-band states. Our results expand considerably the range of
non-Euclidean geometry realizations with circuit quantum electrodynamics.
