QDarts: A quantum dot array transition simulator for finding charge transitions in the presence of finite tunnel couplings, non-constant charging energies and sensor dots
Jan A. Krzywda, Weikun Liu, Evert van Nieuwenburg, Oswin Krause
We present QDarts, an efficient simulator for realistic charge stability diagrams of quantum dot array (QDA) devices in equilibrium states. It allows for pinpointing the location of concrete charge states and their transitions in a high-dimensional voltage space (via arbitrary two-dimensional cuts through it), and includes effects of finite tunnel coupling, non-constant charging energy and a simulation of noisy sensor dots. These features enable close matching of various experimental results in the literature, and the package hence provides a flexible tool for testing QDA experiments, as well as opening the avenue for developing new methods of device tuning.
We present QDarts, an efficient simulator for realistic charge stability diagrams of quantum dot array (QDA) devices in equilibrium states. It allows for pinpointing the location of concrete charge states and their transitions in a high-dimensional voltage space (via arbitrary two-dimensional cuts through it), and includes effects of finite tunnel coupling, non-constant charging energy and a simulation of noisy sensor dots. These features enable close matching of various experimental results in the literature, and the package hence provides a flexible tool for testing QDA experiments, as well as opening the avenue for developing new methods of device tuning.
Semiconductor quantum-dot arrays are a compelling platform for scalable quantum technologies, yet their practical operation is hindered by the complexity of tuning large-scale devices. Existing automation tools rely on simplified physical models---such as constant-capacitance approximations and equilibrium Hubbard models---which assume instantaneous relaxation to a steady state. These frameworks fail in experimentally critical regimes where measurement rates exceed tunneling dynamics, necessitating more sophisticated non-equilibrium control strategies. To bridge this gap, we introduce QArray+, an extension of the QArray framework that incorporates gate-dependent tunnel coupling and a quantum open-system description of dissipative processes. This approach enables the unified simulation of coherent interdot charge-state hybridization and the non-equilibrium latching dynamics essential for training robust machine-learning models for automated device operation. Implemented in JAX with GPU acceleration, QArray+ scales across GPUs and multi-node systems. For example, a charge stability diagram for a 100X100 grid of gate voltages over 64 dots can be computed in ∼0.17s on multiple GPUs. Since interdot interactions are short-ranged and the corresponding tuning corrections are local, simulations at these scales capture the physics relevant to even larger devices. These capabilities support high-throughput dataset generation for automated device tuning.
Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a 100 × 100 100 × 100 pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.
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).
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 industrial-grade silicon quantum dot bilinear arrays, we develop a theoretical framework to mitigate the effect of cross-capacitances in 2x2 arrays of quantum dots and extend it to 2xN and NxN arrays. The method is based on extracting the gradients in gate-voltage space of different charge transitions in multiple two-dimensional charge stability diagrams to determine the system's virtual gates. To automate the process, we train an ensemble of regression models to extract the gradients from a Hough transformation of charge stability diagrams and validate the algorithm on simulated and experimental data of a 2x2 quantum dot array. Our method provides a completely automated tool to mitigate cross-capacitance effects in arrays of QDs which could be utilised to study variability in device electrostatics across large arrays.
Serial triple quantum dot (STQD) systems have received extensive attention in the past decade, not only because quantum dot scaling up is an indispensable ingredient for integrations, but also due to the fact that specific charge states of STQD can be employed to achieve fast full-electrical manipulation of spin qubits. For the latter, a comprehensive understanding of the relationship between neighboring charge occupancy states of STQD is essential for three-electron exchange-only spin qubit-based quantum computations. Charge stability diagram is usually employed to map out the charge occupation states about the plunger gate voltages of STQDs and to study the degeneracy among charge occupation states. Experimentally, two- rather than three-dimensional charge stability diagram was obtained in a lot of early studies by keeping one of plunger gates unchanged to reduce complexity. The obtained two-dimensional diagram can only provide limited information and is subject to blurred boundary of charge occupation states due to the low tunneling current and the energy level broading effects. It is, therefore, challenge to searching for the working points where quantum manipulation can be performed promptly and accurately. In principle, three-dimensional charge occupation stability diagram can be efficiently constructed by numerical simulations based on constant interaction (CI) model. In this study, we calculate the electrochemical potential of STQD about three plunger gate voltages by using the CI model-based capacitance network to reproduce any desired two-dimensional charge stability diagram. The simulated diagram not only well accords with the diagrams obtained from the early experimental data of STQD, but also provides high clarity of the charge state boundaries with tunable parameters. The systematical study of two-dimensional charge stability diagram reviews the energy degeneracy triple and quadruple points of STQD charge occupation states and concludes the energy degeneracy points in three types to compare with experimental data. For each of the energy degeneracy points, we discuss both the electron and hole transport by using the electrochemical potential alignment schematics. We reveal the common and unique triple points of STQD in comparison with those of double quantum dot. The quadruple points of STQD are also addressed in the manipulation of quantum cellular automata and quantum logical gate. The comprehensive understanding of these energy degeneracy points can efficiently guide experiments to build an optimal working point of the STQD system for quantum computations and simulations.
Spins in semiconductor quantum dots offer a scalable approach to quantum computing; however, precise control and efficient readout of large quantum dot arrays remain challenging, mainly due to the hyperdimensional voltage space required for tuning multiple gates per dot. To automate this process, large datasets are required for testing and training autotuning algorithms. To address the demand for such large datasets, we introduce RF-Squad, a physics-based simulator designed to realistically replicate radiofrequency (RF) reflectometry measurements of quantum dot arrays, with the ability to go beyond the Constant Interaction Model (CIM) and simulate physical phenomena such as tunnel coupling, tunnel rates, and quantum confinement. Implemented in JAX, an accelerated linear algebra library, RF-Squad achieves high computational speed, enabling the simulation of a 100x100 pixel charge stability diagram of a double quantum dot (DQD) in 52.1 $\pm$0.2 milliseconds at the CIM level. Using optimization algorithms, combined with it's layered architecture, RF-Squad allows users to balance physical accuracy with computational speed, scaling from simple to highly detailed models.