Spin qubits in semiconducting quantum dots are currently limited by slow readout processes, which are orders of magnitude slower than gate operations. In contrast, Andreev spin qubits benefit from fast measurement schemes enabled by the large resonator couplings of superconducting qubits but suffer from reduced coherence during qubit operations. Here, we propose fast and high-fidelity measurement protocols based on an electrically-tunable coupling between quantum dot and Andreev spin qubits. In realistic devices, this coupling can be made sufficiently strong to enable high-fidelity readout well below microseconds, potentially enabling mid-circuit measurements. Crucially, the electrical tunability of our coupler permits to switch it off during idle periods, minimizing crosstalk and measurement back-action. Our approach is fully compatible with germanium-based devices and paves the way for scalable quantum computing architectures by leveraging the advantages of heterogeneous qubit implementations.

Efficiently characterizing quantum dot (QD) devices is a critical bottleneck when scaling quantum processors based on confined spins. Measuring high-resolution charge stability diagrams (or CSDs, data maps which crucially define the occupation of QDs) is time-consuming, particularly in emerging architectures where CSDs must be acquired with remote sensors that cannot probe the charge of the relevant dots directly. In this work, we present a generative approach to accelerate acquisition by reconstructing full CSDs from sparse measurements, using a conditional diffusion model. We evaluate our approach using two experimentally motivated masking strategies: uniform grid-based sampling, and line-cut sweeps. Our lightweight architecture, trained on approximately 9,000 examples, successfully reconstructs CSDs, maintaining key physically important features such as charge transition lines, from as little as 4% of the total measured data. We compare the approach to interpolation methods, which fail when the task involves reconstructing large unmeasured regions. Our results demonstrate that generative models can significantly reduce the characterization overhead for quantum devices, and provides a robust path towards an experimental implementation.

The ability to physically move qubits within a register allows the design of hardware-specific error-correction codes, which can achieve fault-tolerance while respecting other constraints. In particular, recent advancements have demonstrated the shuttling of electron and hole spin qubits through a quantum dot array with high fidelity. It is therefore timely to explore error correction architectures consisting merely of two parallel quantum dot arrays, an experimentally validated architecture compatible with classical wiring and control constraints. Upon such an architecture, we develop a suite of heuristic methods for compiling any Calderbank-Shor-Steane (CSS) error-correcting code's syndrome-extraction circuit to run with a reduced number of shuttling operations. We demonstrate how column-regular qLDPC codes can be compiled in a provably minimal number of shuttles that is exactly equal to the column weight of the code when Shor-style syndrome extraction is used. We provide tables stating the number of required shuttles for many contemporary codes of interest. In addition, we provide a proof of the NP hardness of minimizing the number of shuttle operations for general codes, even when using Shor syndrome extraction. We also discuss how one could get around this by placing blanks in the ancilla array to achieve minimal shuttles with Shor syndrome extraction on any CSS code, at the cost of longer ancilla arrays.

Hybrid superconductor-semiconductor systems provide a versatile platform for quantum technologies, ranging from superconducting-spin interfaces to topological quantum devices. Progress toward scalable implementations requires superconductors that exhibit high critical fields ($>1$T) at accessible temperatures integrated with low-disorder semiconductor heterostructures. Here we demonstrate a superconducting platinum iridium germanosilicide (PtIrSiGe), with critical out-of-plane magnetic field up to $B_{\perp} = 1.9$T and critical temperature of $T_c\sim 1.85$K, integrated with planar germanium with mobility $μ= 1.3\times 10^6$cm$^{2}$/Vs via top-down lithography fabrication. We show that the integrity of the germanium quantum well and mobility and density of the 2D hole gas are preserved despite annealing at $500°$C, a temperature comparable to that used for strained germanium epitaxy. We further demonstrate proximitisation of a buried germanium quantum well in a gate-defined Josephson junction/SQUID on a Ge/SiGe heterostructure.

Semiconductor quantum dots (QDs) are a promising platform for multiple different qubit implementations, all of which are voltage controlled by programmable gate electrodes. However, as the QD arrays grow in size and complexity, tuning procedures that can fully autonomously handle the increasing number of control parameters are becoming essential for enabling scalability. We propose a bootstrapping algorithm for initializing a depletion-mode QD device in preparation for subsequent phases of tuning. During bootstrapping, the QD device functionality is validated, all gates are characterized, and the QD charge sensor is made operational. We demonstrate the bootstrapping protocol in conjunction with a coarse-tuning module, showing that the combined algorithm can efficiently and reliably take a cooled-down QD device to a desired global-state configuration in under 8 min, with a success rate of 96%. Finally, by following heuristic approaches to QD device initialization and combining the efficient ray-based measurement with the rapid radio-frequency reflectometry measurements, the proposed algorithm establishes a reference in terms of performance, reliability, and efficiency against which alternative algorithms can be benchmarked.

We present and experimentally implement a real-time protocol for calibrating the frequency of a resonantly driven qubit, achieving exponential scaling in calibration precision with the number of measurements, up to the limit imposed by decoherence. The real-time processing capabilities of a classical controller dynamically generate adaptive probing sequences for qubit-frequency estimation. Each probing evolution time and drive frequency are calculated to divide the prior probability distribution into two branches, following a locally optimal strategy that mimics a conventional binary search. The scheme does not require repeated measurements at the same setting, as it accounts for state preparation and measurement errors. Its use of a parametrized probability distribution favors numerical accuracy and computational speed. We show the efficacy of the algorithm by stabilizing a flux-tunable transmon qubit, leading to improved coherence and gate fidelity. As benchmarked by gate-set tomography, the field-programmable gate array (FPGA) powered control electronics partially mitigates non-Markovian noise, which is detrimental to quantum error correction. The mitigation is achieved by dynamically updating and feeding forward the qubit frequency. Our protocol highlights the importance of feedback in improving the calibration and stability of qubits subject to drift and can be readily applied to other qubit platforms.

We investigate automated optimization of the potential landscape in a quantum point contact device, using a 3 × 3 gate array patterned atop the constriction. Optimization is performed using the covariance matrix adaptation evolutionary strategy, for which we introduce a metric for how “steplike” the conductance is as the channel becomes constricted. We first perform the optimization of the gate voltages in a tight-binding simulation and show how such tuning can be used to mitigate a random disorder potential. The optimization is then performed in a physical device in experiment, where we also observe a marked improvement in the quantization of the conductance resulting from the optimization procedure.

As one of the few group IV materials with the potential to host superconductor–semiconductor hybrid devices, planar germanium hosting proximitized quantum dots is a compelling platform to achieve and combine topological superconductivity with existing and new qubit modalities. We demonstrate a quantum dot in a Ge/SiGe heterostructure proximitized by a platinum germanosilicide (PtSiGe) superconducting lead, forming a superconducting lead–quantum dot–superconducting lead junction. We show tunability of the coupling strength between the quantum dot and the superconducting lead, and gate control of the ratio of charging energy and the induced gap, and we tune the ground state of the system between even and odd parity. Furthermore, we characterize critical magnetic field strengths, finding a critical out-of-plane field of 0.90 ± 0.04 T. Finally, we explore sub-gap spin splitting, observing rich physics in the resulting spectra, that we model using a zero-bandwidth model in the Yu–Shiba–Rusinov limit. Our findings open up the physics of alternative spin and superconducting qubits, and the physics of Josephson junction arrays, in germanium. The authors achieve gate-controlled proximitization of a quantum dot in a planar germanium heterostructure, an isotopically purifiable group IV material. A patterned Pt germanosilicide superconductor is introduced via a thermally activated reaction.

Gate-defined quantum dots are a promising candidate system for realizing scalable, coupled qubit systems and serving as a fundamental building block for quantum computers. However, present-day quantum dot devices suffer from imperfections that must be accounted for, which hinders the characterization, tuning, and operation process. Moreover, with an increasing number of quantum dot qubits, the relevant parameter space grows sufficiently to make heuristic control infeasible. Thus, it is imperative that reliable and scalable autonomous tuning approaches are developed. This meeting report outlines current challenges in automating quantum dot device tuning and operation with a particular focus on datasets, benchmarking, and standardization. We also present insights and ideas put forward by the quantum dot community on how to overcome them. We aim to provide guidance and inspiration to researchers invested in automation efforts.

Optimal control of qubits requires the ability to adapt continuously to their ever-changing environment. We demonstrate a real-time control protocol for a two-electron singlet-triplet qubit with two fluctuating Hamiltonian parameters. Our approach leverages single-shot readout classification and dynamic waveform generation, allowing full Hamiltonian estimation to dynamically stabilize and optimize the qubit performance. Powered by a field-programmable gate array (FPGA), the quantum control electronics estimates the Overhauser field gradient between the two electrons in real time, enabling controlled Overhauser-driven spin rotations and thus bypassing the need for micromagnets or nuclear polarization protocols. It also estimates the exchange interaction between the two electrons and adjusts their detuning, resulting in extended coherence of Hadamard rotations when correcting for fluctuations of both qubit axes. Our study highlights the role of feedback in enhancing the performance and stability of quantum devices affected by quasistatic noise.

Environmental fluctuations degrade the performance of solid-state qubits but can in principle be mitigated by real-time Hamiltonian estimation down to time scales set by the estimation efficiency. We implement a physics-informed and an adaptive Bayesian estimation strategy and apply them in real time to a semiconductor spin qubit. The physics-informed strategy propagates a probability distribution inside the quantum controller according to the Fokker-Planck equation, appropriate for describing the effects of nuclear spin diffusion in gallium-arsenide. Evaluating and narrowing the anticipated distribution by a predetermined qubit probe sequence enables improved dynamical tracking of the uncontrolled magnetic field gradient within the singlet-triplet qubit. The adaptive strategy replaces the probe sequence by a small number of qubit probe cycles, with each probe time conditioned on the previous measurement outcomes, thereby further increasing the estimation efficiency. The combined real-time estimation strategy efficiently tracks low-frequency nuclear spin fluctuations in solid-state qubits, and can be applied to other qubit platforms by tailoring the appropriate update equation to capture their distinct noise sources.

Silicon quantum devices are maturing from academic single- and two-qubit devices to industrially-fabricated dense quantum-dot (QD) arrays, increasing operational complexity and the need for better pulsed-gate and readout techniques. We perform gate-voltage pulsing and gate-based reflectometry measurements on a dense 2$\times$2 array of silicon quantum dots fabricated in a 300-mm-wafer foundry. Utilizing the strong capacitive couplings within the array, it is sufficient to monitor only one gate electrode via high-frequency reflectometry to establish single-electron occupation in each of the four dots and to detect single-electron movements with high bandwidth. A global top-gate electrode adjusts the overall tunneling times, while linear combinations of side-gate voltages yield detailed charge stability diagrams. To test for spin physics and Pauli spin blockade at finite magnetic fields, we implement symmetric gate-voltage pulses that directly reveal bidirectional interdot charge relaxation as a function of the detuning between two dots. Charge sensing within the array can be established without the involvement of adjacent electron reservoirs, important for scaling such split-gate devices towards longer 2$\times$N arrays. Our techniques may find use in the scaling of few-dot spin-qubit devices to large-scale quantum processors.

Many important phenomena in quantum devices are dynamic, meaning that they cannot be studied using time-averaged measurements alone. Experiments that measure such transient effects are collectively known as fast readout. One of the most useful techniques in fast electrical readout is radio-frequency reflectometry, which can measure changes in impedance (both resistive and reactive) even when their duration is extremely short, down to a microsecond or less. Examples of reflectometry experiments, some of which have been realised and others so far only proposed, include projective measurements of qubits and Majorana devices for quantum computing, real-time measurements of mechanical motion and detection of non-equilibrium temperature fluctuations. However, all of these experiments must overcome the central challenge of fast readout: the large mismatch between the typical impedance of quantum devices (set by the resistance quantum) and of transmission lines (set by the impedance of free space). Here, we review the physical principles of radio-frequency reflectometry and its close cousins, measurements of radio-frequency transmission and emission. We explain how to optimise the speed and sensitivity of a radio-frequency measurement, and how to incorporate new tools such as superconducting circuit elements and quantum-limited amplifiers into advanced radio-frequency experiments. Our aim is three-fold: to introduce the readers to the technique, to review the advances to date and to motivate new experiments in fast quantum device dynamics. Our intended audience includes experimentalists in the field of quantum electronics who want to implement radio-frequency experiments or improve them, together with physicists in related fields who want to understand how the most important radio-frequency measurements work.

Quantum dot arrays possess ground states governed by Coulomb energies, utilized prominently by singly occupied quantum dots, each implementing a spin qubit. For such quantum processors, the controlled transitions between ground states are of operational significance, as these allow the control of quantum information within the array such as qubit initialization and entangling gates. For few-dot arrays, ground states are traditionally mapped out by performing dense raster-scan measurements in control-voltage space. These become impractical for larger arrays due to the large number of measurements needed to sample the high-dimensional gate-voltage hypercube and the comparatively little information extracted. We develop a hardware-triggered detection method based on reflectometry, to acquire measurements directly corresponding to transitions between ground states. These measurements are distributed sparsely within the high-dimensional voltage space by executing line searches proposed by a learning algorithm. Our autonomous software-hardware algorithm accurately estimates the polytope of Coulomb blockade boundaries, experimentally demonstrated in a 2$\times$2 array of silicon quantum dots.

In spin based quantum dot arrays, material or fabrication imprecisions affect the behaviour of the device, which must be taken into account when controlling it. This requires measuring the shape of specific convex polytopes. We present an algorithm that automatically discovers count, shape and size of the facets of a convex polytope from measurements by alternating a phase of model-fitting with a phase of querying new measurements, based on the fitted model. We evaluate the algorithm on simulated polytopes and devices, as well as a real 2 × 2 spin qubit array. Results show that we can reliably find the facets of the convex polytopes, including small facets with sizes on the order of the measurement precision.

We introduce an algorithm that is able to find the facets of Coulomb diamonds in quantum dot arrays. We simulate these arrays using the constant-interaction model, and rely only on one-dimensional raster scans (rays) to learn a model of the device using regularized maximum likelihood estimation. This allows us to determine, for a given charge state of the device, which transitions exist and what the compensated gate voltages for these are. For smaller devices the simulator can also be used to compute the exact boundaries of the Coulomb diamonds, which we use to assess that our algorithm correctly finds the vast majority of transitions with high precision.

In many physical approaches to quantum computation, error-correction schemes assume the ability to form two-dimensional qubit arrays with nearest-neighbor couplings and parallel operations at multiple qubit sites. While semiconductor spin qubits exhibit long coherence times relative to their operation speed and single-qubit fidelities above error correction thresholds, multiqubit operations in two-dimensional arrays have been limited by fabrication, operation, and readout challenges. We present a two-by-two array of four singlet-triplet qubits in gallium arsenide and show simultaneous coherent operations and four-qubit measurements via exchange oscillations and frequency-multiplexed single-shot measurements. A larger multielectron quantum dot is fabricated in the center of the array as a tunable interqubit link, which we utilize to demonstrate coherent spin exchange with selected qubits. Our techniques are extensible to other materials, indicating a path towards quantum processors with gate-controlled spin qubits.

In the past decade, semiconducting qubits have made great strides in overcoming decoherence, improving the prospects for scalability and have become one of the leading contenders for the development of large-scale quantum circuits. In this Review, we describe the current state of the art in semiconductor charge and spin qubits based on gate-controlled semiconductor quantum dots, shallow dopants and colour centres in wide-bandgap materials. We frame the relative strengths of the different semiconductor qubit implementations in the context of applications such as quantum simulation, computing, sensing and networks. By highlighting the status and future perspectives of the basic types of semiconductor qubits, this Review aims to serve as a technical introduction for non-specialists and a forward-looking reference for scientists intending to work in this field. Semiconductor qubits are expected to have diverse future quantum applications. This Review discusses semiconductor qubit implementations from the perspective of an ecosystem of applications, such as quantum simulation, sensing, computation and communication.

The implementation of large-scale fault-tolerant quantum computers calls for the integration of millions of physical qubits with very low error rates. This outstanding engineering challenge may benefit from emerging qubits that are protected from dominating noise sources in the qubits' environment. In addition to different noise reduction techniques, protective approaches typically encode qubits in global or local decoherence-free subspaces, or in dynamical sweet spots of driven systems. We exemplify such protected qubits by reviewing the state-of-art in protected solid-state qubits based on semiconductors, superconductors, and hybrid devices.