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arXiv:2608.28263

Rapid Charge Stability Diagram Generation from Device-level Modeling of Semiconductor Quantum Dots

Ron Nodel, David W. Kanaar, Connor Nasseraddin, Tim J. Wilson, Hong-Wen Jiang, Jason R. Petta, Chris Anderson, Mark F. Gyure

cond-mat.mes-hallquant-phSubmitted Aug 28, 2026• Announced Aug 31, 2026
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Abstract

Self-consistent Schrödinger-Poisson calculations are a powerful tool for predicting the behavior of layered semiconductor quantum dot devices. However, characterization of charge stability diagrams through fully simulated gate-voltage sweeps is computationally expensive. Combining a Multi-Domain Multi-Model (MDMM) approach with an automated tuning routine, we identify gate voltages associated with selected charge configurations. This small set of self-consistent simulations can be augmented with Full Configuration Interaction (FCI) energy calculations to extract charging energies, lever arms, and interdot Coulomb interactions to directly parameterize a Hubbard model for rapid charge stability diagram generation. For an Intel Tunnel Falls Si/SiGe device, we demonstrate the Hubbard model's ability to reproduce charge stability diagrams at a fraction of the computational cost in comparison to voltage bias sweeps. We further compare the simulated diagrams to experimental data and demonstrate qualitative agreement. Our result represents a step towards predictive digital twin models for semiconductor quantum dot devices. Finally, we apply this workflow towards lever arm engineering in a second device, demonstrating that the method extends to multiple architectures.

Comments
15 pages, 9 figures

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•Jan 1, 2025•0 citations
Self-consistent Schrödinger-Poisson calculations are a powerful tool for predicting the behavior of layered semiconductor quantum dot devices. However, characterization of charge stability diagrams through fully simulated gate-voltage sweeps is computationally expensive. Combining a Multi-Domain Multi-Model (MDMM) approach with an automated tuning routine, we identify gate voltages associated with selected charge configurations. This small set of self-consistent simulations can be augmented with Full Configuration Interaction (FCI) energy calculations to extract charging energies, lever arms, and interdot Coulomb interactions to directly parameterize a Hubbard model for rapid charge stability diagram generation. For an Intel Tunnel Falls Si/SiGe device, we demonstrate the Hubbard model's ability to reproduce charge stability diagrams at a fraction of the computational cost in comparison to voltage bias sweeps. We further compare the simulated diagrams to experimental data and demonstrate qualitative agreement. Our result represents a step towards predictive digital twin models for semiconductor quantum dot devices. Finally, we apply this workflow towards lever arm engineering in a second device, demonstrating that the method extends to multiple architectures.
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We predict large regions of the charge stability diagram using a multiband and multielectron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with N=3N=3N=3 electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.
As quantum dot (QD)-based spin qubits advance toward larger, more complex device architectures, rapid, automated device characterization and data analysis tools become critical. The orientation and spacing of transition lines in a charge stability diagram (CSD) contain a fingerprint of a QD device's capacitive environment, making these measurements useful tools for device characterization. However, manually interpreting these features is time-consuming, error-prone, and impractical at scale. Here, we present an automated protocol for extracting underlying capacitive properties from CSDs. Our method integrates machine learning, image processing, and object detection to identify and track charge transitions across large datasets without manual labeling. We demonstrate this method using experimentally measured data from a strained-germanium single-quantum-well (planar) and a strained-germanium double-quantum-well (bilayer) QD device. Unlike for planar QD devices, CSDs in bilayer germanium heterostructure exhibit a larger set of transitions, including interlayer tunneling and distinct loading lines for the vertically stacked QDs, making them a powerful testbed for automation methods. By analyzing the properties of many CSDs, we can statistically estimate physically relevant quantities, like relative lever arms and capacitive couplings. Thus, our protocol enables rapid extraction of useful, nontrivial information about QD devices.
Gate-defined semiconductor quantum dots require an appropriate number of electrons to function as qubits. The number of electrons is usually tuned by analyzing charge stability diagrams, in which charge transitions manifest as edges. Therefore, to fully automate qubit tuning, it is necessary to recognize these edges automatically and reliably. This paper investigates possible detection methods, describes their training with simulated data from the SimCATS framework, and performs a quantitative comparison with a future hardware implementation in mind. Furthermore, we investigated the quality of the optimized approaches on experimentally measured data from a GaAs and a SiGe qubit sample.
Discrete charge fluctuations, routinely observed in semiconductor quantum dot devices, may contribute significantly to device drift and errors resulting from qubit miscalibration. Understanding the nature and origins of these discrete charge fluctuations may provide insights into material improvements or means of mitigating charge noise in semiconductor quantum dot devices. In this work, we measure multi-level charge fluctuations present in a Si/SiGe double quantum dot device over a range of device operating voltages and temperatures. To characterize the parameter-dependent dynamics of the underlying fluctuating degrees of freedom, we perform a detailed analysis of the measured noise timeseries. We perform algorithmically assisted drift detection and change point detection to detrend the data and remove a slow fluctuator component, as a preprocessing step. We perform model comparison on the post-processed time series between different nnn-level fluctuator (nnnLF) factorial hidden Markov models (FHMMs), finding that although at most sweep values the independent pair of 2LFs model would be preferred, in a particular region of voltage space the 4LF model outperforms the other models, indicating a conditional rate dependence between the two fluctuators. By tracking fluctuator transition rates, biases, and weights over a range of different device configurations, we estimate gate voltage and conductivity sensitivity. In particular, we fit a phenomenological, detailed balance model to the extracted independent 2LFs rate data, yielding lever arm estimates in the range of −2μ-2 μ−2μeV/mV up to 4μ4 μ4μeV/mV between the two 2LFs and nearby gate electrodes. We expect that these characterization results may aid in subsequent spatial triangulation of the charge fluctuators.
Reliable detection of charge transitions in charge stability diagrams (CSDs) is a key requirement for the full automation of quantum dot device control. Performing this task directly at the cryogenic stage reduces data transfer and supports scalability. To provide the large labeled datasets required for developing and evaluating detection methods, we introduced SimCATS [1], a simulator that generates realistic CSDs including sensor responses and distortions. We optimize both traditional and machine-learning-based detection methods using simulated data and benchmark them on simulated and experimental measurements from GaAs and SiGe qubit devices. We also investigate the potential of model compression and find its performance closely tied to task complexity, which can be alleviated by sensor dot compensation. In fact, we find that sensor compensation allows machine-learning approaches to be reduced in size by up to two orders of magnitude while maintaining, or even improving, detection quality. Together with high-quality measurements, this enables robust and scalable (ray-based) charge transition detection. Finally, we estimate the cryogenic power budget for applying this approach to large-scale systems with up to one million qubits. [1] F. Hader et al., "Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)", IEEE Transactions on Quantum Engineering, DOI: 10.1109/TQE.2024.3445967 (2024).