Modular Autonomous Virtualization System for Two-Dimensional Semiconductor Quantum Dot Arrays

TL;DR

MAViS tackles gate crosstalk in dense gate-defined quantum dot arrays by building a modular five-layer virtualization stack that converts raw gate voltages and sensor readouts into orthogonal, virtual gates. It combines ML-based feature extraction from 2D charge stability diagrams with regression and CV techniques (notably the Hough transform) to estimate cross-capacitances and construct linear and nonlinear barrier compensations, including $K_j = J_j + \sum_m [\alpha^{ON}_{j,m} N_m^2 + \beta^{ON}_{j,m} N_m]$ for ON-regime operation. Demonstrated on a 10-QD Ge/SiGe device, MAViS achieves autonomous, real-time virtualization of sensor, plunger, and barrier gates, completing the full stack in about 5 hours and maintaining stable charge configurations across large barrier modulations. The framework is device-agnostic and modular, enabling scalable control of large quantum dot registers and offering a path toward applying similar virtualization strategies to other qubit platforms and exchange-coupled operations.

Abstract

Arrays of gate-defined semiconductor quantum dots are among the leading candidates for building scalable quantum processors. High-fidelity initialization, control, and readout of spin qubit registers require exquisite and targeted control over key Hamiltonian parameters that define the electrostatic environment. However, due to the tight gate pitch, capacitive crosstalk between gates hinders independent tuning of chemical potentials and interdot couplings. While virtual gates offer a practical solution, determining all the required cross-capacitance matrices accurately and efficiently in large quantum dot registers is an open challenge. Here, we establish a modular automated virtualization system (MAViS) -- a general and modular framework for autonomously constructing a complete stack of multilayer virtual gates in real time. Our method employs machine learning techniques to rapidly extract features from two-dimensional charge stability diagrams. We then utilize computer vision and regression models to self-consistently determine all relative capacitive couplings necessary for virtualizing plunger and barrier gates in both low- and high-tunnel-coupling regimes. Using MAViS, we successfully demonstrate accurate virtualization of a dense two-dimensional array comprising ten quantum dots defined in a high-quality Ge/SiGe heterostructure. Our work offers an elegant and practical solution for the efficient control of large-scale semiconductor quantum dot systems.

Figures (5)

• Figure 1: Device architecture and virtualization workflow. (a) Layout of a ten-QD array based on a 3-4-3 geometry. Holes are trapped in gate-defined germanium QDs controlled by a set of barrier (dark blue), plunger (magenta), and screening (cyan) gates. (b) Schematic displaying the approximate potential landscape and position of the QDs in the array, with D$_n$, for $n\in[1,\dots,10]$, indicating each dot and S$_N$, S$_E$, S$_S$, and S$_W$ indicating the north, east, south, and west charge sensor, respectively. (c) A typical 2D CSD of a double QD measured via the rf-reflectometry charge sensing on S$_N$. (d) The workflow of the ML model: Each pixel is assigned a probability to be part of a horizontal, vertical, and interdot transition (diagonal and no transition classes not shown). (e) Probability distribution of each pixel to be a horizontal (left) or vertical (right) transition class. (f) Probability distribution of each pixel to be an interdot class. (g) A Gaussian fit to the log-transformed probability distribution for the interdot class. (h) Extracted coordinates of the interdot centers of mass based on dynamic thresholding.
• Figure 2: Plunger gates orthogonalization and normalization. (a) Exemplary charge stability diagram spanned by the sensor-virtualized gates $\mathrm{vP}_7$ and $\mathrm{vP}_3$. In red, we overlay the output of the pixel classifier module for vertical transitions. The region circled in green indicates a single transition segment, while the blue dashed line indicates the composite line averaged over the three segments of the D$_7$ transition line on the left-hand side of the image. The red line in the center of the image has been erroneously marked by the classifier. (b) The Hough transform of the ML model output. The individual transitions become thin bands, which overlap at a single point corresponding to the composite line (marked in blue). The three additional peaks (marked in green) correspond to the individual transitions on the left-hand side. Each pixel has a width of $0.17$ mV and a height of $0.35$ mV. (c) The sum of the squares of the Hough transform, forming a bimodal distribution corresponding to the composite and individual transitions. (d) Inverse of the virtual matrix $M_2$ obtained from the Hough transforms (left) and a 2D CSD acquired with orthogonalized virtual plunger gates (right). (e) Inverse of the normalized virtual plunger matrix $M_3$ (left) and 2D CSD acquired with normalized virtual plunger gates. In the space spanned by $\mathrm{N}_7$ and $\mathrm{N}_3$, the charging voltages for the specific charge state are constant (20 mV), allowing for uniform $x$ and $y$ axes.
• Figure 3: Barrier coarse virtualization (OFF regime). (a) Sequence of N$_3$ vs N$_7$ CSDs as a function of barrier v$\mathrm{B}_6$ stepped in the range $[-10, 10]$ mV with respect to the starting dc voltage. (b) Sequence of N$_3$ vs N$_7$ CSDs as a function of the virtualized barrier J$_6$. The cyan points in (a) and (b) indicate the positions of the interdots returned by the ML module and the magenta diamonds indicate the center of the tracked honeycomb. (c), (d) Concise presentations of the evolution of the charge sector (interdots and center of the diamond) extracted from (a) and (b), respectively, showing the effective virtualization of J$_6$, which when varied maintains a constant charge state. (e) The fit to the center of the honeycomb positions for plunger gates N$_3$ and N$_7$ as a function of barrier gate v$\mathrm{B}_6$ showing a linear dependence. (f) The distribution of the pairwise distances between all identified interdots between consecutive 2D CSD. The center of this distribution provides the rate of change of interdot position with barrier strength, i.e., the cross-capacitances. The dashed box encloses points used to determine the crosstalk coefficients. Points lying outside of this box are considered outliers. (g) The resulting capacitive-crosstalk matrix with N$_3$ vs J$_6$ and N$_7$ vs J$_6$ highlighted.
• Figure 4: Barrier fine virtualization (ON regime). (a) Sequence of CSDs N$_5$ vs N$_8$ as a function of J$_8$ in the range $[-110, 5]$ mV with respect to the dc reference point. (b) Sequence of CSDs N$_5$ vs N$_8$ as a function of K$_8$ in the same range. The cyan points in (a) and (b) indicate the position of the interdots returned by the ML module and the magenta diamonds indicate the center of the tracked honeycomb. The shift in the (N$_8$, N$_5$) space of the central charge sector in (a) reveals imperfect virtualization over the large voltage range (115 mV). Panel (b), where the finely virtualized gate K$_8$ is adopted, shows a decreased susceptibility to the barrier gate voltage change. (c), (d) Concise presentation of the evolution of the charge state while stepping J$_8$ and K$_8$, respectively. The finely calibrated K$_8$ preserves the position of the charge state. (e) The fit to the center of the honeycomb positions for plunger gates N$_5$ and N$_8$ as a function of barrier gate J$_8$ indicating a beyond-linear dependence for N$_5$. (f), (g) The quadratic coefficient $\sqrt{\alpha}$ and linear compensation coefficient $\beta$, respectively, with K$_8$ vs N$_5$ and vs N$_8$ highlighted.
• Figure 5: Simulated barrier virtualization in the ON regime, showing the widening of the interdot region and the quadratic shift in the charge state center. (a), (b) Simulated charge stability diagrams illustrating the shift in interdot transitions (cyan dots) and the center of the $(1, 1)$ charge state (magenta diamonds) as a function of the virtualized barrier in the OFF ($\mathrm{B}$) and ON ($\mathrm{J}$) regimes, respectively. (c), (d) Overlaid positions of the interdot transitions (cyan) and the [1, 1] charge state center (purple) as functions of $\mathrm{J}$ and $\mathrm{K}$. (e) The quadratic fit to the position of the $(1, 1)$ charge state center as a function of $\mathrm{J}$ and $\mathrm{K}$.