RF-Squad: A radiofrequency simulator for quantum dot arrays

TL;DR

RF-Squad is a fast, physics-based RF reflectometry simulator for quantum dot arrays that goes beyond the Constant Interaction Model by modularly including tunnel coupling, quantum confinement, voltage-dependent effects, and finite tunnel rates. Implemented in JAX, it enables millisecond-scale generation of realistic charge stability diagrams, supporting large-scale data generation for autotuning and digital-twin workflows. The paper demonstrates benchmarking across system size and model complexity, and validates key RF features against experimental data, highlighting strong potential for dataset synthesis and device design. This work provides a flexible tool to balance physical fidelity and speed, facilitating automated tuning, rapid prototyping, and scalable quantum-dot device analysis via RF measurements.

Abstract

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.

Figures (10)

• Figure 1: Schematic of a double quantum dot (DQD) in the CIM framework. The two QDs, labelled $D_1$ and $D_2$, are controlled by gate voltages $V_1$ and $V_2$. The relevant capacitance elements forming the CIM capacitance matrices are indicated: red terms represent dot-to-gate capacitance, while blue terms denote dot-to-dot capacitance. The mutual capacitance between the QDs is denoted as $C_m$ and corresponds to the elements $C_\text{{dg}, 12 (21)}$.
• Figure 2: Illustration of the layered architecture of RF-Squad, demonstrating how each layer progressively incorporates additional physical effects to better replicate the experimental charge stability diagram (CSD) of a DQD, shown in (h). (a) The base layer is modelled using the Constant Interaction Model (CIM). (b) Incorporates tunnel coupling by solving the eigenvalue problem in Eq \ref{['eqn:hamiltonian']}, introducing curvature at charge transitions. (c) Includes quantum confinement effects, leading to periodic variations in honeycomb sizes due to additional energy contributions as described in Eq \ref{['eqn:fd_energy']}. (d) Applies the Wentzel-Kramers-Brillouin (WKB) approximation to tunnel coupling, capturing the voltage-driven transition from a double to a single QD. (e) Models capacitance matrices as voltage-dependent functions, leading to non-repeating honeycomb patterns. (f) Simulates RF reflectometry using Eq \ref{['eqn:BIG']}, focusing on capacitance variations induced by an oscillatory gate voltage. (g) Adds Gaussian and $1/f$ noise to replicate experimental imperfections. (h) Presents the experimentally measured CSD, serving as the benchmark for comparison. For a full list of parameters used, see Appendix \ref{['app:parameters']}.
• Figure 3: Effect of tunnel-rate weighting on the CSD of a DQD. (a) Baseline without tunnel-rate effects. (b) ICT-dominated regime: $t_c \sim \hbar \omega_f$ and $\gamma_{\text{dot}} \ll \hbar \omega_f$, showing only interdot transitions. (c) DRT-dominated regime (dot 1): $\gamma_{\text{dot1}} \sim \hbar \omega_f$ and $t_c \ll \hbar \omega_f$, yielding only dot 1 reservoir features. (d) Voltage-dependent tunnel rates (WKB): both ICT and DRT tunnel rates vary exponentially with gate voltages, as given by Eq. \ref{['eqn:wkb']}. For a full list of parameters used, see Appendix \ref{['app:parameters']}.
• Figure 4: Dependence of the mean squared error (MSE) on the maximum Fock depth in the reduced Fock basis approach. Increasing the maximum Fock depth systematically improves simulation accuracy by reducing artefacts, but at the cost of longer computation times. Each point corresponds to a 100$\times$100-pixel CSD simulation performed using the full Fock basis, including voltage-dependent tunnel couplings and quantum confinement effects. The corresponding reduced simulations were performed with adaptive Fock depths (MFD = 1–5), and the MSE was computed relative to the full Fock state reference to quantify the resulting error efficiency trade-off.
• Figure 5: The average time required to run the base layer of RF-Squad, the CIM, as a function of the number of QDs. The average was determined by simulating the occupancy diagrams with $100 \times 100$ pixels for one hundred random QD arrays ranging in size by increasing the size of the capacitance matrix $M$. The maximum QD occupancy ranged from one to three.