  We address the scaling-up problem for superconducting quantum circuits by
using lumped-element resonators based on an alternative fabrication method of
aluminum -- aluminum oxide -- aluminum ($\mathrm{Al/AlO_x/Al}$) parallel-plate
capacitors. The size of the resonators is only 0.04~$\mathrm{mm^2}$, which is
more than one order smaller than the typical size of coplanar resonators
(1~$\mathrm{mm^2}$). The fabrication method we developed easily fits into the
standard superconducting qubits fabrication process. We have obtained
capacitance per area 14~fF/$\mathrm{\mu m^2}$ and the internal quality factor
$\mathrm{1\times 10^3 - 8\times 10^3}$ at the single-photon level. Our results
show that such devices based on $\mathrm{Al/AlO_x/Al}$ capacitors could be
further applied to the qubit readout scheme, including resonators, filters,
amplifiers, as well as microwave metamaterials and innovative types of qubits,
such as $0-\pi$ qubit.
