Automatic detection of single-electron regime of quantum dots and definition of virtual gates using U-Net and clustering

To realize practical quantum computers, a large number of quantum bits (qubits) will be required. Semiconductor spin qubits offer advantages such as high scalability and compatibility with existing semiconductor technologies. However, as the number of qubits increases, manual qubit tuning becomes infeasible, motivating automated tuning approaches. In this study, we use U-Net, a neural network method for object detection, to identify charge transition lines in experimental charge stability diagrams. The extracted charge transition lines are analyzed using the Hough transform to determine their positions and angles. Based on this analysis, we obtain the transformation matrix to virtual gates. Furthermore, we identify the single-electron regime by clustering the Hough transform outputs. We also show the single-electron regime within the virtual gate space. These sequential processes are performed automatically. This approach will advance automated control technologies for large-scale quantum devices.

💡 Research Summary

The paper addresses a critical bottleneck in scaling semiconductor spin‑qubit processors: the manual tuning of gate voltages to isolate a single electron in each quantum dot. As the number of dots grows to the thousands or millions required for fault‑tolerant quantum computing, an automated pipeline for extracting charge transition lines (CT‑lines) from charge stability diagrams (CSDs), defining virtual gates, and locating the single‑electron regime (SER) becomes indispensable.

To this end, the authors develop a four‑stage workflow. First, they train a U‑Net convolutional neural network to perform pixel‑wise segmentation of experimental CSD images. The training set consists of 11 CSDs from different devices, from which 182 101 patches (48 × 48 px, down‑scaled to 43 × 43 px) are extracted. Data augmentation includes random inversion of line colour and random gamma‑correction to make the model robust against variations in sensor contrast and line polarity. After training, the U‑Net outputs a probability map for “CT‑line” versus background; a simple argmax binarization yields a clean binary image that isolates the transition lines. Dice similarity scores of ≈0.96 demonstrate that the network outperforms conventional binarization methods (Gaussian pre‑processing, Otsu thresholding, Canny edge detection), which suffer from noise‑induced artefacts.

Second, the binary image is fed to the HoughLines algorithm (OpenCV implementation). The transform returns for each detected line a pair (ρ, θ), where ρ is the perpendicular distance from the origin and θ the line’s orientation. In a double‑dot system, two families of lines appear: nearly vertical and nearly horizontal. By averaging θ within each family, the authors construct a 2 × 2 transformation matrix G that maps the physical plunger‑gate voltages V to virtual‑gate coordinates U = G·V. Applying G to the original CSD re‑orients the diagram so that the two line families become orthogonal, greatly simplifying subsequent analysis.

Third, because the Hough transform often yields multiple detections for a single physical CT‑line, the authors apply density‑based spatial clustering of applications with noise (DBSCAN) to the standardized (ρ, θ) data. DBSCAN automatically discovers clusters without a predefined number of clusters and discards isolated points as noise. Within each cluster, the mean ρ and θ are taken as the representative line. When a cluster produces an extra line (e.g., due to duplicate detection), the line whose θ deviates most from the overall mean is removed. This clustering‑and‑merging step successfully reduces the over‑segmented Hough output to a set of distinct, parallel CT‑lines for both vertical‑like and horizontal‑like families.

Finally, the SER is identified by locating the intersection of the leftmost vertical line and the bottommost horizontal line in the clustered set. This point corresponds to the (n, m) = (1, 1) charge configuration, i.e., the regime where each dot contains exactly one electron. The authors overlay a green rectangle on both the raw CSD and the virtual‑gate‑transformed CSD to visually confirm the SER.

The entire pipeline is validated on two datasets: the authors’ own measurements and a publicly available CSD from another research group. In both cases the workflow automatically produces a clean binary segmentation, accurate virtual‑gate axes, and a correctly identified SER, demonstrating robustness to different device designs and measurement conditions.

Key contributions include: (1) a noise‑resilient U‑Net segmentation model tailored for CT‑line extraction; (2) a systematic use of the Hough transform to obtain precise geometric parameters; (3) an unsupervised DBSCAN clustering scheme that eliminates duplicate line detections without manual tuning; (4) a closed‑form construction of the virtual‑gate matrix directly from the averaged line angles; and (5) a fully automated identification of the single‑electron regime.

Limitations are acknowledged: very weak lines in low‑signal regions may be missed, and the current two‑family (vertical/horizontal) assumption must be extended for multi‑dot arrays where additional line orientations appear. Nonetheless, the presented methodology constitutes a practical step toward autonomous tuning of large‑scale quantum‑dot processors, paving the way for scalable semiconductor quantum computers.