  The geometric dimensionality of a physical system significantly impacts its
fundamental characteristics. While experiments are fundamentally limited to the
maximum of three spatial dimensions, there is a growing interest in harnessing
additional synthetic dimensions. In our work, we introduce a new paradigm for
the experimental realization of excitation dynamics associated with
many-dimensional systems. Crucially, it relies solely on static one-dimensional
equivalent structures with judiciously tailored parameters to faithfully
reproduce the same optical spectrum and density of states of the
high-dimensional system to be represented. In order to showcase the
capabilities of our approach, we fabricate 1D photonic lattices that exhibit
the characteristic non-monotonic excitation decays associated with quantum
walks in up to 7D square lattices. Furthermore, we find that a new type of
bound state at the edge of the continuum emerges in higher-than-three
dimensions and gives rise to a sharp localisation transition at defect sites.
In a series of experiments, we implement the mapped equivalent lattices of up
to 5D systems and observe an extreme increase of sensitivity with respect to
the detuning of the respective anchor sites. Our findings demonstrate the
feasibility and applicative potential of harnessing high-dimensional effects in
planar photonics for ultra-sensitive switching or sensing. Notably, our general
approach is by no means limited to optics, and can readily be adapted to a
variety of other physical contexts, including cold atoms and superconducting
qubits with exclusively nearest-neighbour interactions, promising to drive
significant advances in different fields including quantum simulations and
information processing.
