Autotuning of Double-Dot Devices In Situ with Machine Learning

The current practice of manually tuning quantum dots (QDs) for qubit operation is a relatively time-consuming procedure that is inherently impractical for scaling up and applications. In this work, we report on the in situ implementation of a recently proposed autotuning protocol that combines machine learning (ML) with an optimization routine to navigate the parameter space. In particular, we show that a ML algorithm trained using exclusively simulated data to quantitatively classify the state of a double-QD device can be used to replace human heuristics in the tuning of gate voltages in real devices. We demonstrate active feedback of a functional double-dot device operated at millikelvin temperatures and discuss success rates as a function of the initial conditions and the device performance. Modifications to the training network, fitness function, and optimizer are discussed as a path toward further improvement in the success rate when starting both near and far detuned from the target double-dot range.

Figure 1

Visualization of the autotuning loop. In Step 1, we show a false-color scanning electron micrograph of a $\mathrm{Si}$/${\mathrm{Si}}_x$${\mathrm{Ge}}_{1-x}$ quadruple-dot device identical to the one measured. The double dot used in the experiment is highlighted by the inset, which shows a cross section through the device along the dashed white line and a schematic of the electric potential of a tuned double dot. $B_i$ ($i=1,2,3$) and $P_j$ ($j=1,2$) are the barrier and plunger gates, respectively, used to form dots, while $S{B}_1$, $S{B}_2$, and $SP$ are gates (two barriers and a plunger, respectively) used to control the sensing dot. In Step 2, to assure compatibility with the CNN, the raw data are processed and (if necessary) downsized to $(30\times 30)$ pixel size. The processed image $V_{\mathcal{R}}$ is analyzed by the CNN (Step 3), resulting in a probability vector $\mathbf{p}(V_{\mathcal{R}})$ quantifying the current state of the device. In the optimization phase (Step 4), the algorithm decides whether the state is sufficiently close to the desired one (termination) or whether additional tuning steps are necessary. If the latter, the optimizer returns the position of the consecutive scan (Step 5).

Figure 2

A sample run of the autotuning protocol. (a) The measured raw scans in the space of plunger gates $(V_{P_1},V_{P_2})$ show data available to the autotuning protocol at a given time. (b) The change of the fitness value as a function of time. (c) The change in probability of each state over time as returned by the CNN. For an overview of the tuning path in the space of plunger gates on a larger scan measured once the autotuning tests are completed, see Fig. 3.

Figure 3

An overview of a sample run of the autotuning protocol in the space of plunger gates $(V_{P_1},V_{P_2})$. The arrows and the intensity of the color indicate the progress of the autotuner. The palette corresponds to colors used in the fitness-function plot in Fig. 2.

Figure 4

Visualizations of the “ideal” (marked with dashed green triangle) and the “sufficiently close” (marked with solid magenta diamond) regions used to determine the success rate for the off-line tuning. All considered initial regions listed in Table 1 are marked with squares. The intensities of the colors correspond to the success rate when using dynamic simplex (a darker color denotes a higher success rate).

Figure 5

A heat map of the probability of success when tuning off-line over a set of $N=4$ premeasured devices. The intensity of the colors corresponds to the success rate, with a darker color denoting a higher success rate.

Figure 6

The relationship between the simulated, raw, and processed data. The top row consists of sample scans with single-dot regions and the bottom row of scans with double-dot regions. The left-hand column shows the simulated data, the middle column shows the raw acquired experimental data, and the right-hand column shows the processed experimental data (as “seen” by the CNN classifier).

Figure 7

The fitness function over a sample device shown in Fig. 4.