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The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state^,. This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator^, and the quantum spin Hall insulator^,,, as well as quantized adiabatic pumping processes^,,. A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments, revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials—a quantized quadrupole topological insulator—produced using a gigahertz-frequency reconfigurable microwave circuit …