  Quantized electric quadrupole insulators have recently been proposed as novel
quantum states of matter in two spatial dimensions. Gapped otherwise, they can
feature zero-dimensional topological corner mid-gap states protected by the
bulk spectral gap, reflection symmetries and a spectral symmetry. Here we
introduce a topolectrical circuit design for realizing such corner modes
experimentally and report measurements in which the modes appear as topological
boundary resonances in the corner impedance profile of the circuit. Whereas the
quantized bulk quadrupole moment of an electronic crystal does not have a
direct analogue in the classical topolectrical-circuit framework, the corner
modes inherit the identical form from the quantum case. Due to the flexibility
and tunability of electrical circuits, they are an ideal platform for studying
the reflection symmetry-protected character of corner modes in detail. Our work
therefore establishes an instance where topolectrical circuitry is employed to
bridge the gap between quantum theoretical modelling and the experimental
realization of topological band structures.
