  Quadrupole topological insulators are a new class of topological insulators
with quantized quadrupole moments, which support protected gapless corner
states. The experimental demonstrations of quadrupole-topological insulators
were reported in a series of artificial materials, such as photonic crystals,
acoustic crystals, and electrical circuits. In all these cases, the underlying
structures have discrete translational symmetry and thus are periodic. Here we
experimentally realize two-dimensional aperiodic-quasicrystalline
quadrupole-topological insulators by constructing them in electrical circuits,
and observe the spectrally and spatially localized corner modes. In
measurement, the modes appear as topological boundary resonances in the corner
impedance spectra. Additionally, we demonstrate the robustness of corner modes
on the circuit. Our circuit design may be extended to study topological phases
in higher-dimensional aperiodic structures.
