Towards autonomous time-calibration of large quantum-dot devices: Detection, real-time feedback, and noise spectroscopy

TL;DR

This work tackles drift and charge-noise in large semiconductor quantum-dot qubit arrays by introducing TERNS, an autonomous framework that uses the full network of charge-transition lines in charge stability diagrams as a multidimensional electrostatic probe. By tracking the center of charge-state cells in time and across multiple DQDs, TERNS enables real-time drift detection, compensating feedback, and frequency-domain noise spectroscopy, yielding insight into both global and local noise processes. The method is demonstrated on a densely packed 10-QD germanium device, revealing slow $1/f^2$-type drift, dominant two-level fluctuators, and a mean spatial correlation length of $188\pm38$ nm, while achieving sub-millivolt stabilization accuracy and robust performance under engineered perturbations and simulated noise. These capabilities provide a scalable pathway for autonomous calibration and continuous stabilization in large QD quantum processors, with direct access to dot-specific noise diagnostics essential for high-fidelity, long-duration qubit operation.

Abstract

The performance and scalability of semiconductor quantum-dot (QD) qubits are limited by electrostatic drift and charge noise that shift operating points and destabilize qubit parameters. As systems expand to large one- and two-dimensional arrays, manual recalibration becomes impractical, creating a need for autonomous stabilization frameworks. Here, we introduce a method that uses the full network of charge-transition lines in repeatedly acquired double-quantum-dot charge stability diagrams (CSDs) as a multidimensional probe of the local electrostatic environment. By accurately tracking the motion of selected transitions in time, we detect voltage drifts, identify abrupt charge reconfigurations, and apply compensating updates to maintain stable operating conditions. We demonstrate our approach on a 10-QD device, showing robust stabilization and real-time diagnostic access to dot-specific noise processes. The high acquisition rate of radio-frequency reflectometry CSD measurements also enables time-domain noise spectroscopy, allowing the extraction of noise power spectral densities, the identification of two-level fluctuators, and the analysis of spatial noise correlations across the array. From our analysis, we find that the background noise at 100~$μ$\si{\hertz} is dominated by drift with a power law of $1/f^2$, accompanied by a few dominant two-level fluctuators and an average linear correlation length of $(188 \pm 38)$~\si{\nano\meter} in the device. These capabilities form the basis of a scalable, autonomous calibration and characterization module for QD-based quantum processors, providing essential feedback for long-duration, high-fidelity qubit operations.

Figures (4)

• Figure 1: (a) Layout of a 3-4-3 QD device in germanium with 10 plungers and 12 barriers studied in this work. From Ref. Rao24-MAViS. (b) Cartoon of a double QD system formed within a heterostructure with the electrostatic potential shown in white and a single spin qubit shown inside this potential. The potential is altered by spurious interactions (green) with defects (white arrows), leading to drift in the optimal operating point (voltages, tunnel coupling, qubit frequency, etc.). (c) We monitor the CSD of each DQD in (2+1) space and time dimensions by extracting the center of the charge state cell and tracking its drift over time. (d) For each charge state cell of interest, we track for two days the locations of the four interdots at $30$ intervals. The state at $t=0$ h is marked with stars and at $t=48$ h with diamonds.
• Figure 2: Time-evolution of ten QD in a planar QD device over two days. (a) Extracted mean-normalized trajectory of the center of the $(n_i,n_j)$ charge state under a few selected plungers. In all plunger gate voltages, we observe a gradual drift, highest in magnitude under N$_2$ where the charge stability center shifts by almost $5$ mV over two days. A similar trend is observed for N$_4$ extracted from two different DQD CSD series. (b) Time domain stability analysis using Allan variance with averaging time plotted in log-log scale for the same trajectory. Each row corresponds to the Allan variance of a specific plunger and is normalized to be within (0,1). The trajectory of the charge state under most plungers follows a power-law type noise. Plunger N$_2$, N$_4$, and N$_8$ reveal a distinct peak in the center (red circles) of the Allan variance indicative of non-power law or Lorentzian-type noise, suggesting stronger coupling to a single TLF. (c) PSD for all QDs from the trajectory of the center of the corresponding CSD, showing that most plungers experience drift with noise that decays faster than $1/f$. Black (red) dotted lines correspond to the $f^{-2}$ ($f^{-1}$). (d) Extracted noise amplitude $\sqrt{S_0}$ at $100$ µHz (colorbrs) for all ten QDs and the fitted exponents (black error bars) from the power spectral density. We see that the system is dominated by Red noise ($1/f^2$) at these low frequencies ($100$ µhertz). Most plungers show a noise amplitude $(2 \text{ to } 5) \text{ mV}/\sqrt{\text{Hz}}$. There isn't a strictly linear trend across the plunger index, suggesting that the local environment or the specific tuning of each virtual gate affects the noise coupling differently. (e) The Pearson correlation coefficients (dimensionless) for all plunger pairs. (f) Pearson correlation coefficients as a function of distance between plungers, revealing that the correlation decays rapidly with little to no linear correlation beyond $150$ nm. The solid red line represents the best-fit model, with a predicted mean correlation length of $(180\pm38)$ nm. The shaded regions indicate values within the $95~\%$ confidence interval.
• Figure 3: Detection of engineered drift on the QD array. (a) Results of the charge cell center tracking when pulses of different strengths are applied to normalized plunger N$_{7}$ every 5 s, showing the quadrilateral corners and the resulting cell centers determined through TERNS. (b) The cell corners identified via the MAViS interdot classifier model, with the top-left corner of the cell consistently missing. (c) The pulses applied to N$_{7}$ (red) and the corresponding detected change in positions of the charge cell center (black), showing perfect correlations. (Inset) A linear fit to the amplitude of the detected shift vs applied shift, giving $R^2\approx 1$. Simulated trajectory of the center of the charge state cell with (purple) and without (black) real-time feedback applied to a map subject to (d) linear drift and (e) random jumps. The error signal is shown in red with the feedback threshold and gain factor set to $(F_g, \epsilon) = (3.4, 0.02)$ respectively.
• Figure 4: Performance of TERNS on simulated data. (a) The distribution of the mean detected error for different levels of signal-to-noise ratio (SNR). For each combination of white noise and telegraph noise levels, the error is calculated across 10 realizations. We find that as the SNR decreases, the performance of the detection algorithm deteriorates. At about white noise-induced SNR levels of $\approx 0.7$, the simulated charge stability maps become completely noisy. (b) A single realization of a charge stability map with noise levels corresponding to the labels in (a), along with the predicted interdots (magenta) and the center of the central charge state (teal). (b) Example experimental datasets that we study in this paper.