Robust quantum dots charge autotuning using neural network uncertainty

TL;DR

The paper tackles automating charge tuning of semiconductor spin qubits by using neural networks to detect transition lines in stability diagrams and quantify uncertainty to steer a robust exploration strategy. It compares CNN, BCNN, and FF architectures for line detection, introducing confidence thresholds to improve exploration reliability. Across three distinct offline datasets, the uncertainty-guided autotuning achieves high success (up to 99.5% in favorable cases) and demonstrates substantial gains over non-uncertainty strategies, while Bayesian uncertainty offers limited extra benefit. The approach promises hardware-agnostic, scalable autotuning suitable for integration near cryogenic qubits, with future work aimed at multi-QD systems and cryo-friendly implementations such as memristor-based inference hardware.

Abstract

This study presents a machine-learning-based procedure to automate the charge tuning of semiconductor spin qubits with minimal human intervention, addressing one of the significant challenges in scaling up quantum dot technologies. This method exploits artificial neural networks to identify noisy transition lines in stability diagrams, guiding a robust exploration strategy leveraging neural networks' uncertainty estimations. Tested across three distinct offline experimental datasets representing different single quantum dot technologies, the approach achieves over 99% tuning success rate in optimal cases, where more than 10% of the success is directly attributable to uncertainty exploitation. The challenging constraints of small training sets containing high diagram-to-diagram variability allowed us to evaluate the capabilities and limits of the proposed procedure.

Figures (14)

• Figure 1: *QD devices used to measure the stability diagrams. (a,b,c)*SEM images of experimental devices. A single QD can be created by tuning electrostatic gates 1 (G1) and 2 (G2) to appropriate voltages. (a) G2 controls the electronic density of an electron reservoir (R), and the *SET is used as a charge sensor. See Rochette_2019 for experimental details. (b) The tunnel barriers labeled B1 and B2 are set to a fixed voltage, as well as gate 3 (G3), which is required for more than one QD only. The *QPC is used as a charge sensor. See Gaudreau_2009 for experimental details. (c) G1 and G4 are tunnel barriers. The voltages at G3, G4, and R are fixed to allow for single-QD formation under G2 and an extended reservoir. The SET is used as a charge sensor. See Elsayed_2024 for experimental details. (d,e,f) Energy diagrams representing the formation of a single QD for each device.
• Figure 2: Example of one stability diagram from each dataset. (a,b,c) Representation of the stability diagrams as images, where pixels encode the measured current for given voltage values at the gates (G1 and G2). (d,e,f) Same diagrams with manual annotations of transition lines in green and charge regime areas in blue. The regions with more than 3.0 charges are grouped under the annotation "4+". A voltage area not annotated with a charge regime due to fading lines or ambiguous boundaries is considered an "unknown charge regime". More examples can be found in Supplementary Section \ref{['subsec:digram-samples']}.
• Figure 3: Automatic transition line detection using a *BCNN in a stability diagram. (a) A subsection (patch) of the voltage space is measured. This diagram presents strong oscillating background noise that should not be misinterpreted as a transition line. (b) To train the model, each patch is categorized as "line" if a transition line annotation intersects with the detection area (in pink) in the center of the patch. Otherwise, the patch is categorized as "no-line". (c) The patch is then sent as input to a model, where a forward pass propagates the information through convolutional and fully connected layers. In this example, a *BCNN is represented, where each parameter is encoded as a Gaussian distribution.
• Figure 4: (a) Example of a stability diagram from the Si-OG-QD dataset. This specific diagram presents a parasitic line in the low-voltage area. (b) The same stability diagram is divided into patches classified using CNN trained using cross-validation Raschka_2018 (Supplementary Figure \ref{['fig:cross-validation']}). The color gradient of the patches represents the model uncertainty, where 0.5 is the lowest confidence score according to Formula \ref{['eq:conf-heuristic']}. The confidence score is lower in low-contrast areas, around the parasitic line, and near transition lines (due to possible intersection ambiguity between the line labels and the detection area of the patch). (c) The same stability diagram after the application of the confidence threshold. Most errors are avoided, except for the end of a few fading lines and some line sections in the low-current area at the top of the diagram. The "soft errors" represent misclassifications near a line, which are not expected to induce tuning errors.
• Figure 5: (a) Schematic representation of the patch classification algorithm. The purple box encloses the logic of one exploration step. (b) Step-by-step example of the autotuning algorithm using the GaAs-QD dataset (complete diagram in Figure \ref{['fig:datasets']}b). The arrows represent the direction of the exploration, and the gray area is unmeasured space during the current step. (1) Search the first line by exploring the voltage space in 4.0 directions. (2) Estimate the line slope by scanning two sequences of patches in circular arcs around the first patch with a line. (3) Explore the space perpendicularly to the first line to gather information about the distance between lines. Stop after reaching 3.0 times the average distance without detecting a new line at lower voltages. (4) Search for possible missed lines under the first line by scanning multiple sections where we would expect to find a new line according to the average line distance and slope estimation. In this example, a fading line is correctly detected at the bottom of the image, but the low confidence of the model triggers a validation procedure. More scans are then processed on the hypothetical line direction (purple arrow) until a higher confidence inference validates or invalidates the line's existence. (5) Deduce the one-electron regime location based on the leftmost line position, the slope, and the average space between lines (all scans from previous steps are represented here). The algorithmic details of each step are available in Supplementary Section \ref{['subsec:suppl-exploration-algo']}.