Gate-based single-shot readout of spins in silicon

Fast Thermodynamic Study on a Silicon Nanotransistor at Cryogenic Temperatures

Cryogenic temperatures are crucial for the operation of semiconductor quantum electronic devices, yet the heating effects induced by microwave or laser signals used for quantum state manipulation can lead to significant temperature variations at the nanoscale. Therefore, probing the temperature of individual devices in working conditions and understanding the thermodynamics are paramount for designing and operating large-scale quantum computing systems. In this study, we demonstrate high-sensitivity fast thermometry in a silicon nanotransistor at cryogenic temperatures using RF reflectometry. Through this method, we explore the thermodynamic processes of the nanotransistor during and after a laser pulse and determine the dominant heat dissipation channels in the few-kelvin temperature range. These insights are important to understand thermal budgets in quantum circuits, with our techniques being compatible with microwave and laser radiation, offering a versatile approach for studying other quantum electronic devices in working conditions.

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.

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.

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.

Variable-Barrier Quantum Coulomb Blockade Effect in Nanoscale Transistors

Current-voltage characteristics of a quantum dot in double-barrier configuration, as formed in the nanoscale channel of silicon transistors, were analyzed both experimentally and theoretically. Single electron transistors (SET) made in a SOI-FET configuration using silicon quantum dot as well as phosphorus donor quantum dots were experimentally investigated. These devices exhibited a quantum Coulomb blockade phenomenon along with a detectable effect of variable tunnel barriers. To replicate the experimental results, we developed a generalized formalism for the tunnel-barrier dependent quantum Coulomb blockade by modifying the rate-equation approach. We qualitatively replicate the experimental results with numerical calculation using this formalism for two and three energy levels participated in the tunneling transport. The new formalism supports the features of most of the small-scaled SET devices.

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.

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.

Charge-noise spectroscopy of Si/SiGe quantum dots via dynamically-decoupled exchange oscillations

Electron spins in silicon quantum dots are promising qubits due to their long coherence times, scalable fabrication, and potential for all-electrical control. However, charge noise in the host semiconductor presents a major obstacle to achieving high-fidelity single- and two-qubit gates in these devices. In this work, we measure the charge-noise spectrum of a Si/SiGe singlet-triplet qubit over nearly 12 decades in frequency using a combination of methods, including dynamically-decoupled exchange oscillations with up to 512 π pulses during the qubit evolution. The charge noise is colored across the entire frequency range of our measurements, although the spectral exponent changes with frequency. Moreover, the charge-noise spectrum inferred from conductance measurements of a proximal sensor quantum dot agrees with that inferred from coherent oscillations of the singlet-triplet qubit, suggesting that simple transport measurements can accurately characterize the charge noise over a wide frequency range in Si/SiGe quantum dots.

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.

Microwaves in Quantum Computing

Quantum information processing systems rely on a broad range of microwave technologies and have spurred development of microwave devices and methods in new operating regimes. Here we review the use of microwave signals and systems in quantum computing, with specific reference to three leading quantum computing platforms: trapped atomic ion qubits, spin qubits in semiconductors, and superconducting qubits. We highlight some key results and progress in quantum computing achieved through the use of microwave systems, and discuss how quantum computing applications have pushed the frontiers of microwave technology in some areas. We also describe open microwave engineering challenges for the construction of large-scale, fault-tolerant quantum computers.

Universality of Entanglement Transitions from Stroboscopic to Continuous Measurements

Measurement-driven transitions between extensive and subextensive scaling of the entanglement entropy receive interest as they illuminate the intricate physics of thermalization and control in open interacting quantum systems. While this transition is well established for stroboscopic measurements in random quantum circuits, a crucial link to physical settings is its extension to continuous observations, where for an integrable model it has been shown that the transition changes its nature and becomes immediate. Here, we demonstrate that the entanglement transition at finite coupling persists if the continuously measured system is randomly nonintegrable, and show that it is smoothly connected to the transition in the stroboscopic models. This provides a bridge between a wide range of experimental settings and the wealth of knowledge accumulated for the latter systems.

Microwave Photon Detectors Based on Semiconducting Double Quantum Dots

Detectors of microwave photons find applications in different fields ranging from security to cosmology. Due to the intrinsic difficulties related to the detection of vanishingly small energy quanta ℏ ω , significant portions of the microwave electromagnetic spectrum are still uncovered by suitable techniques. No prevailing technology has clearly emerged yet, although different solutions have been tested in different contexts. Here, we focus on semiconductor quantum dots, which feature wide tunability by external gate voltages and scalability for large architectures. We discuss possible pathways for the development of microwave photon detectors based on photon-assisted tunneling in semiconducting double quantum dot circuits. In particular, we consider implementations based on either broadband transmission lines or resonant cavities, and we discuss how developments in charge sensing techniques and hybrid architectures may be beneficial for the development of efficient photon detectors in the microwave range.

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.

Operation of a silicon quantum processor unit cell above one kelvin

Quantum computers are expected to outperform conventional computers in several important applications, from molecular simulation to search algorithms, once they can be scaled up to large numbers-typically millions-of quantum bits (qubits)^1-3. For most solid-state qubit technologies-for example, those using superconducting circuits or semiconductor spins-scaling poses a considerable challenge because every additional qubit increases the heat generated, whereas the cooling power of dilution refrigerators is severely limited at their operating temperature (less than 100 millikelvin)^4-6. Here we demonstrate the operation of a scalable silicon quantum processor unit cell comprising two qubits confined to quantum dots at about 1.5 kelvin. We achieve this by isolating the quantum dots from the electron reservoir, and then initializing and reading the qubits solely via tunnelling of electrons between the two quantum dots^7-9. We coherently control the qubits using electrically driven spin resonance^10,11 in isotopically enriched silicon^{12 28}Si, attaining single-qubit gate fidelities of 98.6 per cent and a coherence time of 2 microseconds during 'hot' operation, comparable to those of spin qubits in natural silicon at millikelvin temperatures^13-16. Furthermore, we show that the unit cell can be operated at magnetic fields as low as 0.1 tesla, corresponding to a qubit control frequency of 3.5 gigahertz, where the qubit energy is well below the thermal energy. The unit cell constitutes the core building block of a full-scale silicon quantum computer and satisfies layout constraints required by error-correction architectures^8,17. Our work indicates that a spin-based quantum computer could be operated at increased temperatures in a simple pumped ⁴He system (which provides cooling power orders of magnitude higher than that of dilution refrigerators), thus potentially enabling the integration of classical control electronics with the qubit array^18,19.

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.

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

Silicon spin qubits are one of the leading platforms for quantum computation^1,2. As with any qubit implementation, a crucial requirement is the ability to measure individual quantum states rapidly and with high fidelity. Since the signal from a single electron spin is minute, the different spin states are converted to different charge states^3,4. Charge detection, so far, has mostly relied on external electrometers^5-7, which hinders scaling to two-dimensional spin qubit arrays^2,8,9. Alternatively, gate-based dispersive read-out based on off-chip lumped element resonators has been demonstrated^10-13, but integration times of 0.2-2 ms were required to achieve single-shot read-out^14-16. Here, we connect an on-chip superconducting resonant circuit to two of the gates that confine electrons in a double quantum dot. Measurement of the power transmitted through a feedline coupled to the resonator probes the charge susceptibility, distinguishing whether or not an electron can oscillate between the dots in response to the probe power. With this approach, we achieve a signal-to-noise ratio of about six within an integration time of only 1 μs. Using Pauli's exclusion principle for spin-to-charge conversion, we demonstrate single-shot read-out of a two-electron spin state with an average fidelity of >98% in 6 μs. This result may form the basis of frequency-multiplexed read-out in dense spin qubit systems without external electrometers, therefore simplifying the system architecture.

Gate-based high fidelity spin readout in a CMOS device

The engineering of a compact qubit unit cell that embeds all quantum functionalities is mandatory for large-scale integration. In addition, these functionalities should present the lowest error rate possible to successfully implement quantum error correction protocols¹. Electron spins in silicon quantum dots are particularly promising because of their high control fidelity^2-5 and their potential compatibility with complementary metal-oxide-semiconductor industrial platforms^6,7. However, an efficient and scalable spin readout scheme is still missing. Here we demonstrate a high fidelity and robust spin readout based on gate reflectometry in a complementary metal-oxide-semiconductor device that consists of a qubit dot and an ancillary dot coupled to an electron reservoir. This scalable method allows us to read out a spin in a single-shot manner with an average fidelity above 98% for a 0.5 ms integration time. To achieve such a fidelity, we combine radio-frequency gate reflectometry with a latched spin blockade mechanism that requires electron exchange between the ancillary dot and the reservoir. We show that the demonstrated high readout fidelity is fully preserved up to 0.5 K. This result holds particular relevance for the future cointegration of spin qubits and classical control electronics.

Gate-reflectometry dispersive readout and coherent control of a spin qubit in silicon

Silicon spin qubits have emerged as a promising path to large-scale quantum processors. In this prospect, the development of scalable qubit readout schemes involving a minimal device overhead is a compelling step. Here we report the implementation of gate-coupled rf reflectometry for the dispersive readout of a fully functional spin qubit device. We use a p-type double-gate transistor made using industry-standard silicon technology. The first gate confines a hole quantum dot encoding the spin qubit, the second one a helper dot enabling readout. The qubit state is measured through the phase response of a lumped-element resonator to spin-selective interdot tunneling. The demonstrated qubit readout scheme requires no coupling to a Fermi reservoir, thereby offering a compact and potentially scalable solution whose operation may be extended above 1 K.

Semiconductor quantum computation

Semiconductors, a significant type of material in the information era, are becoming more and more powerful in the field of quantum information. In recent decades, semiconductor quantum computation was investigated thoroughly across the world and developed with a dramatically fast speed. The research varied from initialization, control and readout of qubits, to the architecture of fault-tolerant quantum computing. Here, we first introduce the basic ideas for quantum computing, and then discuss the developments of single- and two-qubit gate control in semiconductors. Up to now, the qubit initialization, control and readout can be realized with relatively high fidelity and a programmable two-qubit quantum processor has even been demonstrated. However, to further improve the qubit quality and scale it up, there are still some challenges to resolve such as the improvement of the readout method, material development and scalable designs. We discuss these issues and introduce the forefronts of progress. Finally, considering the positive trend of the research on semiconductor quantum devices and recent theoretical work on the applications of quantum computation, we anticipate that semiconductor quantum computation may develop fast and will have a huge impact on our lives in the near future.