Real-time tuning of a double quantum dot using a Josephson parametric amplifier*

Josephson parametric amplifiers (JPAs)\footnote{B.~Yurke, J.~Opt.~Soc.~Am.~B, \textbf{4} 1551 (1987).} have enabled advances in readout of quantum systems. Here we demonstrate JPA-assisted readout of a cavity-coupled double quantum dot (DQD).\footnote{ J.~Stehlik \textit{et al.}, Phys.~Rev.~Appl., \textbf{4} 014018 (2015).} Utilizing a JPA we improve the signal-to-noise ratio (SNR) by a factor of 2000 compared to the situation with the parametric amplifier turned off. At an interdot charge transition we achieve a SNR of 76 (19 dB) with an integration time $\tau = 400$ ns, which is limited by the linewidth of our cavity. By measuring the SNR as a function of $\tau$ we extract an equivalent charge sensitivity of $8 \times 10^{-5} \:\:e/\sqrt{\rm Hz}$. We develop a dual-gate-voltage rastering scheme that allows us to acquire a DQD charge stability diagram in just 20 ms. Such rapid data acquisition rates enable device tuning in live ``video-mode," where the results of parameter changes are immediately displayed. Live tuning allows the DQD confinement potential to be rapidly tuned, a capability that will become increasingly important as semiconductor spin qubits are scaled to a larger number of dots.