Automatic virtual voltage extraction of a 2x2 array of quantum dots with machine learning

Abstract

Spin qubits in quantum dots are a compelling platform for fault-tolerant quantum computing due to the potential to fabricate dense two-dimensional arrays with nearest neighbour couplings, a requirement to implement the surface code. However, due to the proximity of the surface gate electrodes cross-coupling capacitances can be substantial, making it difficult to control each quantum dot independently. Increasing the number of quantum dots increases the complexity of the calibration process, which becomes impractical to do heuristically. Inspired by recent demonstrations of industrialgrade silicon quantum dot bilinear arrays, we develop a theoretical framework to cancel the effect of cross-capacitances in a 2×N array of quantum dots, based on the gradients in gate voltage space of different charge transitions that can be measured in multiple two-dimensional charge stability diagrams. To automate the process, we successfully train a neural network to extract the gradients from a Hough transformation of a stability diagram and test the algorithm on simulated and experimental data of a 2×2 quantum dot array.

Learning Coulomb Diamonds in Large Quantum Dot Arrays

“…Changing the gate voltages and measuring the quantum dot occupations in the systems ground state leads to a so-called charge-stability diagram (CSD), mapping the high-dimensional voltage space to that of the number of electrons on each dot. Constructing a CSD is typically done by performing many two-dimensional raster scans of pairs of gate voltages [3,6]. Based on these raster scans higher-precision line-scans are performed around areas where the QD occupations change to estimate the normal of the charge transition.…”

“…Moreover, since the number of control voltages grows linearly with the number of quantum dots, hand-tuning their values becomes more and more challenging due to cross-talk between the dots. Only recently did we see the emergence of automatic tuning algorithms, often implemented using machine-learning [6][7][8][9][10][11][12]. These approaches were used only for small arrays, and still lag behind the results achievable via manual tuning.…”

Learning Coulomb Diamonds in Large Quantum Dot Arrays

“…Changing the gate voltages and measuring the quantum dot occupations in the systems ground state leads to a so-called charge-stability diagram (CSD), mapping the highdimensional voltage space to that of the number of electrons on each dot. Constructing a CSD is typically done by performing many two-dimensional raster scans of pairs of gate voltages [3,6]. Based on these raster scans higher-precision line-scans are performed around areas where the QD occupations change to estimate the normal of the charge transition.…”

“…Moreover, since the number of control voltages grows linearly with the number of quantum dots, hand-tuning their values becomes more and more challenging due to cross-talk between the dots. Only recently did we see the emergence of automatic tuning algorithms, often implemented using machinelearning [6][7][8][9][10][11][12]. These approaches were used only for small arrays, and still lag behind the results achievable via manual tuning.…”

An automated approach for consecutive tuning of quantum dot arrays

“…3a and 3b). The slopes of the charge transition lines are used to compute the cross-capacitance matrix 𝑪 cross 38,45,46 , with which the correspondence between virtual and physical gates can be established. The cross-capacitance causes physical gates to influence not only the electrochemical potential of corresponding QDs but also those of nearby QDs.…”