Scaling Quantum-Dot-Qubit Systems
Even the most compelling experiment can become boring when repeated dozens of times. Therefore, rather than using artificial intelligence to automate the creative and insightful aspects of science and engineering, automation should focus instead on improving the productivity of researchers. In that vein, Justyna Zwolak of the National Institute of Standards and Technology in Maryland and her colleagues have demonstrated software for automating standard parts of experiments on semiconductor quantum-dot qubits [1]. The feat is a step toward the fully automated calibration of quantum processors. Larger and more challenging spin and quantum computing experiments will likely also benefit from it [2].
Semiconductor technology enables the fabrication of quantum-mechanical devices with unparalleled control [3], performance [4], reproducibility [5], and large-scale integration [6]—exactly what is needed for a highly scalable quantum computer. Classical digital logic represents bits as localized volumes of high or low electric potential, and the semiconductor industry has developed efficient ways to control such potentials—exactly what is needed for the operation of qubits based on quantum dots. Silicon or germanium are nearly ideal semiconductors to host qubits encoded in the spin state of electrons or electron vacancies (holes) confined in an electric potential formed in a quantum dot by transistor-like gate electrodes.
Voltages applied to metal gate electrodes patterned on a semiconductor allow for the confinement and control of single electrons or holes in a quantum dot and for the manipulation of their spin state. There are two main types of gates: Plunger gates control the amount of charge in a dot, whereas barrier gates control the quantum-mechanical tunneling of charges in the quantum-dot system. Dots defined by such gates offer in situ dynamical control over each dot’s charge state and its excited-state spectrum, interdot couplings, and even some of the system’s magnetic properties. This manipulation is achieved by applying direct-current voltages and trains of voltage pulses called baseband pulses to the system. Precise control of a qubit encoded in a dot’s spins requires precise control of single charges in the dot, though this alone is not sufficient.
Until recently, experiments with more than a handful of quantum dots were impractical because of the complexity and nonuniformity of such quantum-dot systems. The complexity requires experimenters to meticulously set many control parameters in order to reach the desired system configuration. Each quantum dot has multiple plunger and barrier gate electrodes for controlling its charge occupation, confinement, and coupling to neighboring dots. And in an array of dots, significant irreducible capacitive crosstalk must be mitigated. Nonuniformity arises because fabrication variations and disorder make each quantum dot unique. An iterative process is therefore needed to find the appropriate voltages for each gate electrode. Only then can the spins be controlled through applied radio-frequency magnetic fields, radio-frequency electrical pulses in a magnetic gradient, or baseband pulses.
Zwolak and her colleagues have demonstrated a new and faster way to perform the initial calibration of an array of quantum dots. Using a completely automated “virtualization” scheme, they calibrated an array of ten quantum dots in only five hours, including both data acquisition and postprocessing. Manually calibrating each of the 25 gate electrodes in the device could have taken days. Virtualization establishes a set of “virtual gates” where each virtual plunger gate modulates only the charge occupation of the dot directly beneath it, and each virtual barrier gate affects only the nearby tunnel barriers without changing charge occupation. Researchers can then plan experiments using virtual gate voltages, which can be translated into “real” gate voltages in the appropriate ratios to enable independent charge or spin control for quantum simulation or computing [7].
Zwolak and her colleagues built what they call a modular automated virtualization system (MAViS), which automates calibration of these virtual gates in several iterations. The software tracks gate voltages through several transformations, each one compensating for capacitive crosstalk in a subset of the device. MAViS first compensates for changes in a local charge sensor and then fixes the total charge in each dot through virtualization of the plunger gates. Finally, virtualization of the barrier gates enables modulation of tunnel couplings between dots in a fixed charge state.
All capacitances in the system are inferred through the motion of charges into, out of, and between dots in response to voltages applied to the plunger and barrier gates. Each interdot charge transition results in a change in charge-sensor current, typically represented as a 2D charge-stability plot comparing the effect of two gate electrodes. For interpreting this complex set of dependencies [8] from the pixels of charge-sensor data, Zwolak and her colleagues developed a machine-learning-based charge-transition identifier. As each capacitance is determined and the gate virtualization improves, increasingly sophisticated tracking routines use the charge-transition identifier to estimate the linear and quadratic virtualization terms between plunger and barrier gates.
Although MAViS aims to establish virtual, independent control over the charge state of the dots, many other aspects of quantum-dot qubits remain to be fully automated. Going beyond MAViS, virtualization of tunnel couplings to barrier gates would unlock additional parallelism, allowing multiple barrier gates to change simultaneously even with capacitive crosstalk. Producing the same virtual, independent control with reduced data demand through physics-informed tuning [9] would increase the speed of characterizing and calibrating large quantum-dot arrays.
In this new world of virtualization, automation is a dialogue between what the fabrication team can produce and what the software developers should expect. Improved automation comes both from improved software and physics insight, but equally from improved fabrication, which depends on scale and process control [10]. Future results for spin simulation, quantum error correction, and quantum computing algorithms depend on these developments progressing together.
References
- A. S. Rao et al., “Modular autonomous virtualization system for two-dimensional semiconductor quantum dot arrays,” Phys. Rev. X 15, 021034 (2025).
- J. P. Zwolak and J. M. Taylor, “Colloquium: Advances in automation of quantum dot devices control,” Rev. Mod. Phys. 95, 011006 (2023).
- A. J. Weinstein et al., “Universal logic with encoded spin qubits in silicon,” Nature 615, 817 (2023).
- T. Tanttu et al., “Assessment of the errors of high-fidelity two-qubit gates in silicon quantum dots,” Nat. Phys. 20, 1804 (2024).
- S. Neyens et al., “Probing single electrons across 300-mm spin qubit wafers,” Nature 629, 80 (2024).
- A. M. J. Zwerver et al., “Qubits made by advanced semiconductor manufacturing,” Nat. Electron. 5, 184 (2022).
- T. Hensgens et al., “Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array,” Nature 548, 70 (2017).
- O. Krause et al., “Estimation of convex polytopes for automatic discovery of charge state transitions in quantum dot arrays,” Electronics 11, 2327 (2022).
- J. Ziegler et al., “Tuning arrays with rays: Physics-informed tuning of quantum dot charge states,” Phys. Rev. Appl. 20, 034067 (2023).
- H. C. George et al., “12-Spin-qubit arrays fabricated on a 300 mm semiconductor manufacturing line,” Nano Lett. 25, 793 (2024).