Rapid gate-based spin read-out in silicon using an on-chip resonator

Demonstration of Microwave Resonators and Double Quantum Dots on Optimized Reverse-Graded Ge/SiGe Heterostructures

One of the most promising platforms for the realization of spin-based quantum computing are planar germanium quantum wells embedded between silicon-germanium barriers. To achieve comparably thin stacks with little surface roughness, this type of heterostructure can be grown using the so-called reverse linear grading approach, where the growth starts with a virtual germanium substrate followed by a graded silicon-germanium alloy with an increasing silicon content. However, the compatibility of such reverse-graded heterostructures with superconducting microwave resonators has not yet been demonstrated. Here, we report on the successful realization of well-controlled double quantum dots and high-quality coplanar waveguide resonators on the same reverse-graded Ge/SiGe heterostructure.

Electric Dipole Coupling of a Bilayer Graphene Quantum Dot to a High-Impedance Microwave Resonator

We implement circuit quantum electrodynamics (cQED) with quantum dots in bilayer graphene, a maturing material platform that can host long-lived spin and valley states. Our device combines a high-impedance (Zr ≈ 1 kΩ) superconducting microwave resonator with a double quantum dot electrostatically defined in a graphene-based van der Waals heterostructure. Electric dipole coupling between the subsystems allows the resonator to sense the electric susceptibility of the double quantum dot from which we reconstruct its charge stability diagram. We achieve sensitive and fast detection of the interdot transition with a signal-to-noise ratio of 3.5 within 1 μs integration time. The charge-photon interaction is quantified in the dispersive and resonant regimes by comparing the resonator response to input-output theory, yielding a coupling strength of g/2π = 49.7 MHz. Our results introduce cQED as a probe for quantum dots in van der Waals materials and indicate a path toward coherent charge-photon coupling with bilayer graphene quantum dots.

Controllable Single Cooper Pair Splitting in Hybrid Quantum Dot Systems

Cooper pair splitters hold utility as a platform for investigating the entanglement of electrons in Cooper pairs, but probing splitters with voltage-biased Ohmic contacts prevents the retention of electrons from split pairs since they can escape to the drain reservoirs. We report the ability to controllably split and retain single Cooper pairs in a multi-quantum-dot device isolated from lead reservoirs, and separately demonstrate a technique for detecting the electrons emerging from a split pair. First, we identify a coherent Cooper pair splitting charge transition using dispersive gate sensing at GHz frequencies. Second, we utilize a double quantum dot as an electron parity sensor to detect parity changes resulting from electrons emerging from a superconducting island.

Performance of high impedance resonators in dirty dielectric environments

High-impedance resonators are a promising contender for realizing long-distance entangling gates between spin qubits. Often, the fabrication of spin qubits relies on the use of gate dielectrics which are detrimental to the quality of the resonator. Here, we investigate loss mechanisms of high-impedance NbTiN resonators in the vicinity of thermally grown SiO2 and Al2O3 fabricated by atomic layer deposition. We benchmark the resonator performance in elevated magnetic fields and at elevated temperatures and find that the internal quality factors are limited by the coupling between the resonator and two-level systems of the employed oxides. Nonetheless, the internal quality factors of high-impedance resonators exceed 103 in all investigated oxide configurations which implies that the dielectric configuration would not limit the performance of resonators integrated in a spin-qubit device. Because these oxides are commonly used for spin qubit device fabrication, our results allow for straightforward integration of high-impedance resonators into spin-based quantum processors. Hence, these experiments pave the way for large-scale, spin-based quantum computers.

Probing the Jaynes-Cummings Ladder with Spin Circuit Quantum Electrodynamics

We report observations of transitions between excited states in the Jaynes-Cummings ladder of circuit quantum electrodynamics with electron spins (spin circuit QED). We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multiphoton transitions by increasing the probe power and using two-tone spectroscopy. This ability to probe the Jaynes-Cummings ladder is enabled by improvements in the coupling-to-decoherence ratio, and shows an increase in the maturity of spin circuit QED as an interesting platform for studying quantum phenomena.

Colloquium: Advances in automation of quantum dot devices control

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

Multi-Dimensional Quantum Capacitance of the Two-Site Hubbard Model: The Role of Tunable Interdot Tunneling

Few-electron states confined in quantum-dot arrays are key objects in quantum computing. The discrimination between these states is essential for the readout of a (multi-)qubit state, and can be achieved through a measurement of the quantum capacitance within the gate-reflectometry approach. For a system controlled by several gates, the dependence of the measured capacitance on the direction of the oscillations in the voltage space is captured by the quantum capacitance matrix. Herein, we apply this tool to study a double quantum dot coupled to three gates, which enable the tuning of both the bias and the tunneling between the two dots. Analytical solutions for the two-electron case are derived within a Hubbard model, showing the overall dependence of the quantum capacitance matrix on the applied gate voltages. In particular, we investigate the role of the tunneling gate and reveal the possibility of exploiting interdot coherences in addition to charge displacements between the dots. Our results can be directly applied to double-dot experimental setups, and pave the way for further applications to larger arrays of quantum dots.

Novel Nanotube Multiquantum Dot Devices

Addressable quantum states well isolated from the environment are of considerable interest for quantum information science and technology. Carbon nanotubes are an appealing system, since a perfect crystal can be grown without any missing atoms and its cylindrical structure prevents ill-defined atomic arrangement at the surface. Here, we develop a reliable process to fabricate compact multielectrode circuits that can sustain the harsh conditions of the nanotube growth. Nanotubes are suspended over multiple gate electrodes, which are themselves structured over narrow dielectric ridges to reduce the effect of the charge fluctuators of the substrate. We measure high-quality double- and triple-quantum dot charge stability diagrams. Transport measurements through the triple-quantum dot indicate long-range tunneling of single electrons between the left and right quantum dots. This work paves the way to the realization of a new generation of condensed-matter devices in an ultraclean environment, including spin qubits, mechanical qubits, and quantum simulators.

Ramped measurement technique for robust high-fidelity spin qubit readout

State preparation and measurement of single-electron spin qubits typically rely on spin-to-charge conversion where a spin-dependent charge transition of the electron is detected by a coupled charge sensor. For high-fidelity, fast readout, this process requires that the qubit energy is much larger than the temperature of the system limiting the temperature range for measurements. Here, we demonstrate an initialization and measurement technique that involves voltage ramps rather than static voltages allowing us to achieve state-to-charge readout fidelities above 99% for qubit energies almost half that required by traditional methods. This previously unidentified measurement technique is highly relevant for achieving high-fidelity electron spin readout at higher temperature operation and offers a number of pragmatic benefits compared to traditional energy-selective readout such as real-time dynamic feedback and minimal alignment procedures.

Fingerprints of Qubit Noise in Transient Cavity Transmission

Noise affects the coherence of qubits and thereby places a bound on the performance of quantum computers. We theoretically study a generic two-level system with fluctuating control parameters in a photonic cavity and find that basic features of the noise spectral density are imprinted in the transient transmission through the cavity. We obtain analytical expressions for generic noise and proceed to study the cases of quasistatic, white and 1/f^{α} noise in more detail. Additionally, we propose a way of extracting the noise power spectral density in a frequency band only bounded by the range of the qubit-cavity detuning and with an exponentially decaying error due to finite measurement times. Our results suggest that measurements of the time-dependent transmission probability represent a novel way of extracting noise characteristics.

Parametric Amplifiers Based on Quantum Dots

Josephson parametric amplifiers (JPAs) approaching quantum-limited noise performance have been instrumental in enabling high fidelity readout of superconducting qubits and, recently, semiconductor quantum dots (QDs). We propose that the quantum capacitance arising in electronic two-level systems (the dual of Josephson inductance) can provide an alternative dissipationless nonlinear element for parametric amplification. We experimentally demonstrate phase-sensitive parametric amplification using a QD-reservoir electron transition in a CMOS nanowire split-gate transistor embedded in a 1.8 GHz superconducting lumped-element microwave cavity, achieving parametric gains of -3 to +3  dB, limited by Sisyphus dissipation. Using a semiclassical model, we find an optimized design within current technological capabilities could achieve gains and bandwidths comparable to JPAs, while providing complementary specifications with respect to integration in semiconductor platforms or operation at higher magnetic fields.

Quantum logic with spin qubits crossing the surface code threshold

High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance-the ability to correct errors faster than they occur1. The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual threshold depends on many details, a common target is the approximately 1% error threshold of the well-known surface code2,3. Reaching two-qubit gate fidelities above 99% has been a long-standing major goal for semiconductor spin qubits. These qubits are promising for scaling, as they can leverage advanced semiconductor technology4. Here we report a spin-based quantum processor in silicon with single-qubit and two-qubit gate fidelities, all of which are above 99.5%, extracted from gate-set tomography. The average single-qubit gate fidelities remain above 99% when including crosstalk and idling errors on the neighbouring qubit. Using this high-fidelity gate set, we execute the demanding task of calculating molecular ground-state energies using a variational quantum eigensolver algorithm5. Having surpassed the 99% barrier for the two-qubit gate fidelity, semiconductor qubits are well positioned on the path to fault tolerance and to possible applications in the era of noisy intermediate-scale quantum devices.

Designs for a two-dimensional Si quantum dot array with spin qubit addressability

Electron spins in Si are an attractive platform for quantum computation, backed with their scalability and fast, high-fidelity quantum logic gates. Despite the importance of two-dimensional integration with efficient connectivity between qubits for medium- to large-scale quantum computation, however, a practical device design that guarantees qubit addressability is yet to be seen. Here, we propose a practical 3 × 3 quantum dot device design and a larger-scale design as a longer-term target. The design goal is to realize qubit connectivity to the four nearest neighbors while ensuring addressability. We show that a 3 × 3 quantum dot array can execute four-qubit Grover’s algorithm more efficiently than the one-dimensional counterpart. To scale up the two-dimensional array beyond 3 × 3, we propose a novel structure with ferromagnetic gate electrodes. Our results showcase the possibility of medium-sized quantum processors in Si with fast quantum logic gates and long coherence times.

Electron cascade for distant spin readout

The spin of a single electron in a semiconductor quantum dot provides a well-controlled and long-lived qubit implementation. The electron charge in turn allows control of the position of individual electrons in a quantum dot array, and enables charge sensors to probe the charge configuration. Here we show that the Coulomb repulsion allows an initial charge transition to induce subsequent charge transitions, inducing a cascade of electron hops, like toppling dominoes. A cascade can transmit information along a quantum dot array over a distance that extends by far the effect of the direct Coulomb repulsion. We demonstrate that a cascade of electrons can be combined with Pauli spin blockade to read out distant spins and show results with potential for high fidelity using a remote charge sensor in a quadruple quantum dot device. We implement and analyse several operating modes for cascades and analyse their scaling behaviour. We also discuss the application of cascade-based spin readout to densely-packed two-dimensional quantum dot arrays with charge sensors placed at the periphery. The high connectivity of such arrays greatly improves the capabilities of quantum dot systems for quantum computation and simulation.

Readout of remote spins in quantum dot arrays is a challenge for future quantum computing architectures. Here, the authors implement electron cascade for spin readout on quantum dots far away from a charge sensor in a quadruple quantum dot device and discuss its applicability to large-scale arrays.

A single-hole spin qubit

Qubits based on quantum dots have excellent prospects for scalable quantum technology due to their compatibility with standard semiconductor manufacturing. While early research focused on the simpler electron system, recent demonstrations using multi-hole quantum dots illustrated the favourable properties holes can offer for fast and scalable quantum control. Here, we establish a single-hole spin qubit in germanium and demonstrate the integration of single-shot readout and quantum control. We deplete a planar germanium double quantum dot to the last hole, confirmed by radio-frequency reflectrometry charge sensing. To demonstrate the integration of single-shot readout and qubit operation, we show Rabi driving on both qubits. We find remarkable electric control over the qubit resonance frequencies, providing great qubit addressability. Finally, we analyse the spin relaxation time, which we find to exceed one millisecond, setting the benchmark for hole quantum dot qubits. The ability to coherently manipulate a single hole spin underpins the quality of strained germanium and defines an excellent starting point for the construction of quantum hardware.

While most results so far in semiconductor spin-based quantum computation use electron spins, devices based on hole spins may have more favourable properties for quantum applications. Here, the authors demonstrate single-shot readout and coherent control of a qubit made from a single hole spin.

Conditional teleportation of quantum-dot spin states

Among the different platforms for quantum information processing, individual electron spins in semiconductor quantum dots stand out for their long coherence times and potential for scalable fabrication. The past years have witnessed substantial progress in the capabilities of spin qubits. However, coupling between distant electron spins, which is required for quantum error correction, presents a challenge, and this goal remains the focus of intense research. Quantum teleportation is a canonical method to transmit qubit states, but it has not been implemented in quantum-dot spin qubits. Here, we present evidence for quantum teleportation of electron spin qubits in semiconductor quantum dots. Although we have not performed quantum state tomography to definitively assess the teleportation fidelity, our data are consistent with conditional teleportation of spin eigenstates, entanglement swapping, and gate teleportation. Such evidence for all-matter spin-state teleportation underscores the capabilities of exchange-coupled spin qubits for quantum-information transfer.

Despite recent demonstrations of coherent spin-state transfer in arrays of spin qubits via exchange interaction, all-matter spin-state teleportation is still out of reach. Here the authors provide evidence for conditional teleportation of quantum-dot spin states, entanglement swapping, and gate teleportation.

Fast Gate-Based Readout of Silicon Quantum Dots Using Josephson Parametric Amplification

Spins in silicon quantum devices are promising candidates for large-scale quantum computing. Gate-based sensing of spin qubits offers a compact and scalable readout with high fidelity, however, further improvements in sensitivity are required to meet the fidelity thresholds and measurement timescales needed for the implementation of fast feedback in error correction protocols. Here, we combine radio-frequency gate-based sensing at 622 MHz with a Josephson parametric amplifier, that operates in the 500-800 MHz band, to reduce the integration time required to read the state of a silicon double quantum dot formed in a nanowire transistor. Based on our achieved signal-to-noise ratio, we estimate that singlet-triplet single-shot readout with an average fidelity of 99.7% could be performed in 1  μs, well below the requirements for fault-tolerant readout and 30 times faster than without the Josephson parametric amplifier. Additionally, the Josephson parametric amplifier allows operation at a lower radio-frequency power while maintaining identical signal-to-noise ratio. We determine a noise temperature of 200 mK with a contribution from the Josephson parametric amplifier (25%), cryogenic amplifier (25%) and the resonator (50%), showing routes to further increase the readout speed.

Radio-Frequency-Detected Fast Charge Sensing in Undoped Silicon Quantum Dots

Spin qubits in silicon quantum dots offer a promising platform for a quantum computer as they have a long coherence time and scalability. The charge sensing technique plays an essential role in reading out the spin qubit as well as tuning the device parameters, and therefore, its performance in terms of measurement bandwidth and sensitivity is an important factor in spin qubit experiments. Here we demonstrate fast and sensitive charge sensing by radio frequency reflectometry of an undoped, accumulation-mode Si/SiGe double quantum dot. We show that the large parasitic capacitance in typical accumulation-mode gate geometries impedes reflectometry measurements. We present a gate geometry that significantly reduces the parasitic capacitance and enables fast single-shot readout. The technique allows us to distinguish between the singly- and doubly occupied two-electron states under the Pauli spin blockade condition in an integration time of 0.8 μs, the shortest value ever reported in silicon, by the signal-to-noise ratio of 6. These results provide a guideline for designing silicon spin qubit devices suitable for the fast and high-fidelity readout.

Single-spin qubits in isotopically enriched silicon at low magnetic field

Single-electron spin qubits employ magnetic fields on the order of 1 Tesla or above to enable quantum state readout via spin-dependent-tunnelling. This requires demanding microwave engineering for coherent spin resonance control, which limits the prospects for large scale multi-qubit systems. Alternatively, singlet-triplet readout enables high-fidelity spin-state measurements in much lower magnetic fields, without the need for reservoirs. Here, we demonstrate low-field operation of metal-oxide-silicon quantum dot qubits by combining coherent single-spin control with high-fidelity, single-shot, Pauli-spin-blockade-based ST readout. We discover that the qubits decohere faster at low magnetic fields with [Formula: see text] μs and [Formula: see text] μs at 150 mT. Their coherence is limited by spin flips of residual 29Si nuclei in the isotopically enriched 28Si host material, which occur more frequently at lower fields. Our finding indicates that new trade-offs will be required to ensure the frequency stabilization of spin qubits, and highlights the importance of isotopic enrichment of device substrates for the realization of a scalable silicon-based quantum processor.

Fast Charge Sensing of Si/SiGe Quantum Dots via a High-Frequency Accumulation Gate

Quantum dot arrays are a versatile platform for the implementation of spin qubits, as high-bandwidth sensor dots can be integrated with single-, double-, and triple-dot qubits yielding fast and high-fidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the two-dimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surface-mount resonant circuit to the plunger gate of a high-impedance sensor, we realized a fast charge sensing technique that is compatible with resistive 2DEGs. We demonstrate this by acquiring at high speed charge stability diagrams of double- and triple-dot arrays in Si/SiGe heterostructures as well as pulsed-gate single-shot charge and spin readout with integration times as low as 2.4 μs.