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Compact Superconducting Microwave Resonators Based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mtext>Al-AlO</mml:mtext><mml:mi>x</mml:mi></mml:msub></mml:math> -Al Capacitors
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 (Al-${\mathrm{AlO}}_{x}$-Al) parallel-plate capacitors. The size of the resonators is only $0.04\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{2}$, which is more than one order smaller than the typical size of coplanar resonators ($1\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{2}$). The fabrication …