  Recently, the theory of quantized dipole polarization has been extended to
account for electric multipole moments, giving rise to the discovery of
multipole topological insulators (TIs). Both two-dimensional (2D) quadrupole
and three-dimensional (3D) octupole TIs with robust zero-dimensional (0D)
corner states have been realized in various classical systems. However, due to
the intrinsic 3D limitation, the higher dimensional multipole TIs, such as
four-dimensional (4D) hexadecapole TIs, are supposed to be extremely hard to
construct in real space, although some of their properties have been discussed
through the synthetic dimensions. Here, we theoretically propose and
experimentally demonstrate the realization of classical analog of 4D
hexadecapole TI based on the electric circuits in fully real space. The
explicit construction of 4D hexadecapole circuits, where the connection of
nodes is allowed in any desired way free from constraints of locality and
dimensionality, is provided. By direct circuit simulations and impedance
measurements, the in-gap corner states protected by the quantized hexadecapole
moment in the 4D circuit lattices are observed and the robustness of corner
state is also demonstrated. Our work offers a new pathway to study the higher
order/dimensional topological physics in real space.
