Transmon qubits coupled to compact resonators

Compact resonators comprising of a meander inductor and an interdigitated capacitor are desirable building blocks for a multi-qubit processor due to their small size. We present an experiment on a superconducting transmon qubit coupled capacitively to such a compact resonator. We have fabricated low-loss Nb based compact resonators with an area within 1 mm$^2$ on a sapphire substrate to operate between 5 and 8 GHz. The resonator geometry was optimized to achieve an intrinsic quality factor above 300,000 at single-photon microwave powers and temperatures below 100 mK. Transmon qubits were made using Al/AlOx/Al Josephson junctions shunted by an Al interdigitated capacitor with an identical width and gap as the resonator. We will present our experimental progress towards measuring relaxation times of these qubits.