The Sport of Tuning Quantum Dot Arrays: How the QDarts Simulator is Changing the Game

Introducing QDarts 

In the fast-paced arena of quantum computing, researchers from the University of Copenhagen and the University of Leiden have achieved a major victory with their latest development: Quantum Dot Array Transition Simulator (QDarts), SciPost [1]. QDarts is a simulation software package aimed at enabling fast generation of charge stability diagrams for arbitrary quantum dot networks. The development of this tool simulator as supported by Quantum Machines in the bridge project of the Digital Research Centre of Denmark (DIREC) [2]. 

Building effective spin-based quantum computers is like preparing for a championship game – every detail counts. One of the biggest hurdles is developing fully automatic tuning algorithms. Just as a coach needs to adapt strategies based on player performance, researchers must navigate the quirks introduced by manufacturing imprecisions and environmental factors. Each quantum chip behaves differently, which means a tailored approach is essential for success. However, nowadays most researchers only have access to single chips and thus it becomes difficult to test automated procedures and argue that they will also work on new devices.  

Joining the Game 

Enter QDarts, a simulator designed to streamline this complex process. You can think of it as a digital coach that helps researchers find their optimal tuning algorithms by going through many possible scenarios. QDarts simulates realistic charge stability diagrams, which identify the voltage settings that ensure the right number of electrons reside on each quantum dot and the voltage changes that allow electrons to tunnel between the dots. You can find more info and codes on the QDarts github [3].

Example of configuring the parameters for the QDarts simulator:

capacitance_config = {
        "C_DD" : C_DD, #dot-dot capacitance matrix
        "C_Dg" : C_DG, #dot-gate capacitance matrix
        "ks" : 4,      #distortion of Coulomb peaks. 
}

tunneling_config = {
        "tunnel_couplings": tunnel_couplings,  #tunnel coupling matrix
        "temperature": 0.1,                    #temperature in Kelvin
        "energy_range_factor": 5,              #energy scale for the Hamiltonian generation.
}

sensor_config = {
        "sensor_dot_indices": [4,5],           #Indices of the sensor dots
        "sensor_detunings": [-0.0005,-0.0005], #Detuning of the sensor dots
        "noise_amplitude": {"fast_noise": 0.8*1e-6, "slow_noise": 1e-8}, #Noise amplitude for the sensor dots in eV
        "peak_width_multiplier": 15,           #Width of the sensor peaks in the units of thermal broadening m *kB*T/0.61.
}

Example of simulating a charge stability diagram (CSD) experiment with the QDarts simulator:

# Create the experiment object from the configuration files

experiment = Experiment(capacitance_config, tunneling_config, sensor_config)
     xexp, yexp, _, polytopesexp, sensor_signalexp, _ = experiment.generate_CSD(
     plane_axes = np.array([[0,0,-1,1,0,0],[1,-1,0,0,0,0]]), # vectors spanning the cut in voltage space
     target_state = [3,2,3,2,5,5],  # target state for transition
     target_transition = [-1,1,-1,1,0,0], #target transition from target state, here transition to [2,3,2,3,5,5]
     x_voltages=np.linspace(-0.0022, 0.0018, 100), #voltage range for x-axis
     y_voltages=np.linspace(-0.0021, 0.0019, 100), #voltage range for y-axis
     compute_polytopes = True, #compute the corners of constant occupation
     compensate_sensors=True, #compensate the sensor signals
     use_virtual_gates=True, #use the virtual gates
     use_sensor_signal=True) #use the sensor signals

In quantum experiments, the control parameters are voltages set for example by the QDAC-II / QDAC-II Compact and OPX1000, and the readout parameter could be a demodulated sensor signal from an RF reflectometry setup read by the OPX1000. Currently, this tuning often relies on expert intuition and hands-on adjustments, but simulators like QDarts aim to change that. By providing qualitatively realistic looking simulations based on a number of realistic device parameters, it will significantly increase the amount of training data for new tuning algorithms.

And for anyone looking to extend their training data sets, there are now many datasets and simulation platforms to explore, next to QDarts. Ranging from NIST’s QFlow datasets [4], to the Delft University of Technology QDsim simulation package [5], to the University of Oxford QArray simulation package [6], there are now a full range of opportunities to build up a large amount of training data.

Next to the increased access to simulated datasets, Quantum Machines also ensures that it is becoming increasingly easier and faster to measure stability diagrams. Using the modular video mode architecture allows a truly interactive quantum dot array tune-up environment to scan through their large parameter spaces. You can read more about this video mode implementation on our quantum control solutions for spin qubits page.

How QDarts hits the bullseye:

• Intermediate-sized Quantum Dot Arrays: Capable of simulating up to 10 quantum dots.
• Charge Position Tracking: Simulates the position of charges within the array.
• Tunneling Effects: Models how electrons tunnel between dots.
• Realistic Sensor Signals: Incorporates noise models for 1D and 2D parameter scans, helping to refine strategies.
• Automatic Parameter Discovery: Identifies control parameters of interest.
• Optimizations and Caching: Ensures rapid simulations.
• Device Imperfections: Accounts for changes in capacitances under the movement of electrons and changes in the sensor peak shapes.

Figure 1: Example of a charge stability diagram created by the QDarts simulator (left) which can be used for analysis, for example finding the size of the honeycomb patterns as a function of the number of electrons (right). Data courtesy of Dr. Jan Krzywda from Leiden University.

And the developers of QDarts will keep the ball rolling, as they already have plans to implement more features in the future. For example, they aim to add the possibility to simulate electron time dynamics, allowing the simulation of slow transitions and of quantum dots without direct access to an electron reservoir.

In the thrilling game of quantum innovation, QDarts is helping research teams across the globe to take a shot at new automated tuning algorithms. So, gear up and get ready — this is just the beginning of an exciting journey into the future of automating the tuning of quantum dot arrays!

References

[1] Krzywda, Jan A., et al. “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.” SciPost Physics Codebases (2025): 043.
[2] https://direc.dk/automatic-tuning-of-spin-qubit-arrays
[3] https://github.com/condensedAI/QDarts
[4] https://data.nist.gov/od/id/66492819760D3FF6E05324570681BA721894
[5] Gualtieri, V., Renshaw-Whitman, C., Hernandes, V., & Greplova, E. (2024). QDsim: An user-friendly toolbox for simulating large-scale quantum dot device. arXiv preprint arXiv:2404.02712.
[6] van Straaten, B., Hickie, J., Schorling, L., Schuff, J., Fedele, F., & Ares, N. (2024). QArray: a GPU-accelerated constant capacitance model simulator for large quantum dot arrays. arXiv preprint arXiv:2404.04994.