escape rate, suggesting that heating due to the device switching to the voltage state had a minimal impact on the measurements. Because the large loop inductance of the SQUID resulted in about 20 possible flux states, the device was initialized to the zero trapped flux state with a flux shaking procedure before each repetition of the measurement cycle.[@Palomaki06a] We typically applied 50 oscillations of the flux current, which yielded a success rate better than 98%.

![\[FEnergyGamma\] Qubit energy-level spectroscopy and tunneling escape rates. (a) Open circles show the resonance frequency of the transition between the ground and first excited states of the qubit, measured at 20 mK. The scatter in the values is indicative of the uncertainty in the measurement. Also plotted are theoretical values of [$\omega_{0 1}$]{} (solid), [$\omega_{1 2}$]{} (dashed), and [$\omega_{2 3}$]{} (dotted) for $I_{01} = 17.930\ {\ensuremath{\mu {\ensuremath{\mathrm{A}}}}}$ and $C_1 = 4.50\ {\ensuremath{{\ensuremath{\mathrm{pF}}}}}$. (b) At high bias, the measured background escape rate (open circles) agrees with the predicted ground-state escape rate [$\Gamma_{0}$]{} (solid line) for the junction parameters given above. Calculated [$\Gamma_{1}$]{}, [$\Gamma_{2}$]{}, and [$\Gamma_{3}$]{} are plotted as dashed, dotted, and dashed-dotted lines. In both plots, the bottom axes show the total bias current $I_b$, while 