LC Filtered dc SQUID Phase Qubit with Low Dielectric Loss

We have investigated a dc SQUID phase qubit with LC filter, which has a relatively small ($\sim $4 $\mu $m$^{2})$ Al/AlO$_{x}$/Al Josephson junction shunted by an additional capacitor built using low-stress thin film SiN$_{x}$. The LC isolation provides an additional isolation factor at the junction plasma frequency and allows flexibility in the choice of SQUID parameters. We report Rabi oscillations with a 42 ns envelope decay time (T'), and a 32 ns energy relaxation time (T$_{1})$, consistent with a loss tangent of about 7 x 10$^{-4}$ in the loss-stress SiN$_{x}$. We also report on progress towards getting longer coherence times using a high-stress SiN$_{x}$ with a lower loss tangent.