README.md

Automatic virtual voltage extraction of a 2×N array of quantum dots with machine learning:

Implementation of the paper:

arxiv preprint

Due to the size of the regression models, they can be found at this Google drive folder The experimental data instead can be downloaded from here:

Simulating a 2xN array of QDs:

The Mosquito project has been making silicon QD arrays by modifying current transistor technology as least as possible, resulting in a 2xN architecture. As a result, the random_c function takes this geometry into account, as the parameter ratio is used to determine the relationship between the mutual and cross capacitances perpendicular, parallel or diagonally across the nanowire. The matrix CC has the gate capacitors of each QD on the main diagonal and the cross capacitors off-diagonal, which allows to speed up the calculation via vectorization. The function stability_diagram then calculates the corresponding stability diagram taking inspiration from Wiel, W. G. Van Der. (2003). Electron transport through double quantum dots.

For a more detailed example, see the Jupyter notebook

Automatically extracting the gradients of a DQD:

We have developed an algorithm designed to extract the virtual voltages from a stability diagram when applying voltages along two of the gates, without human intervention. This is done by using a Hough transform on thresholded data to obtain a histogram of the best fit $\theta$ values. However, due to the presence of more peaks than expected and experimental noise, it is relatively hard to interpret. As a result, a neural network has been trained to extract the required gradients on theoretical data. An outline of the different steps is highlighted below and more information can be found on the Jupyter notebook

Number of measurements required:

To reconstruct the G transformation matrix, if only nearest neighbours are taken into account, 5N-4 stability diagrams are required to be measured. We apply two gate voltages at a time in the low electron regime, such that the system behaves similar to a DQD. The algorithm developed to extract the gradients can be easily implemented. As the different measurements are taken, the G transformation matrix can be constructed and thus allowing us to change our basis from gate voltage to virtual voltage space as shown for a 2x2 array of QDs: