Quantum error correction with silicon spin qubits.

Future large-scale quantum computers will rely on quantum error correction (QEC) to protect the fragile quantum information during computation1,2. Among the possible candidate platforms for realizing quantum computing devices, the compatibility with mature nanofabrication technologies of silicon-based spin qubits offers promise to overcome the challenges in scaling up device sizes from the prototypes of today to large-scale computers3-5. Recent advances in silicon-based qubits have enabled the implementations of high-quality one-qubit and two-qubit systems6-8. However, the demonstration of QEC, which requires three or more coupled qubits1, and involves a three-qubit gate9-11 or measurement-based feedback, remains an open challenge. Here we demonstrate a three-qubit phase-correcting code in silicon, in which an encoded three-qubit state is protected against any phase-flip error on one of the three qubits. The correction to this encoded state is performed by a three-qubit conditional rotation, which we implement by an efficient single-step resonantly driven iToffoli gate. As expected, the error correction mitigates the errors owing to one-qubit phase-flip, as well as the intrinsic dephasing mainly owing to quasi-static phase noise. These results show successful implementation of QEC and the potential of a silicon-based platform for large-scale quantum computing.

Fast universal quantum gate above the fault-tolerance threshold in silicon.

Fault-tolerant quantum computers that can solve hard problems rely on quantum error correction1. One of the most promising error correction codes is the surface code2, which requires universal gate fidelities exceeding an error correction threshold of 99 per cent3. Among the many qubit platforms, only superconducting circuits4, trapped ions5 and nitrogen-vacancy centres in diamond6 have delivered this requirement. Electron spin qubits in silicon7-15 are particularly promising for a large-scale quantum computer owing to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent owing to the slow operation16. Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate universal gate fidelity beyond the fault-tolerance threshold and may enable scalable silicon quantum computers.

Observation of the Kondo screening cloud.

When a magnetic impurity exists in a metal, conduction electrons form a spin cloud that screens the impurity spin. This basic phenomenon is called the Kondo effect1,2. Unlike electric-charge screening, the spin-screening cloud3-6 occurs quantum coherently, forming spin-singlet entanglement with the impurity. Although the spins interact locally around the impurity, the Kondo cloud can theoretically spread out over several micrometres. The cloud has not so far been detected, and so its physical existence-a fundamental aspect of the Kondo effect-remains controversial7,8. Here we present experimental evidence of a Kondo cloud extending over a length of micrometres, comparable to the theoretical length ξK. In our device, a Kondo impurity is formed in a quantum dot2,9-11, coupling on one side to a quasi-one-dimensional channel12 that houses a Fabry-Pérot interferometer of various gate-defined lengths L exceeding one micrometre. When we sweep a voltage on the interferometer end gate-separated by L from the quantum dot-to induce Fabry-Pérot oscillations in conductance we observe oscillations in the measured Kondo temperature TK, which is a signature of the Kondo cloud at distance L. When L is less than ξK the TK oscillation amplitude becomes larger as L becomes smaller, obeying a scaling function of a single parameter L/ξK, whereas when L is greater than ξK the oscillation is much weaker. Our results reveal that ξK is the only length parameter associated with the Kondo effect, and that the cloud lies mostly within a length of ξK. Our experimental method offers a way of detecting the spatial distribution of exotic non-Fermi liquids formed by multiple magnetic impurities or multiple screening channels13-16 and of studying spin-correlated systems.

Optically Driven Rotation of Exciton-Polariton Condensates.

The rotational response of quantum condensed fluids is strikingly distinct from rotating classical fluids, especially notable for the excitation and ordering of quantized vortex ensembles. Although widely studied in conservative systems, the dynamics of rotating open-dissipative superfluids such as exciton-polariton condensates remains largely unexplored, as it requires high-frequency rotation while avoiding resonantly driving the condensate. We create a rotating polariton condensate at gigahertz frequencies by off-resonantly pumping with a rotating optical stirrer composed of the time-dependent interference of two frequency-offset, structured laser modes. Acquisition of angular momentum exceeding the critical 1ℏ/particle is directly measured, accompanied by the deterministic nucleation and capture of quantized vortices with a handedness controlled by the pump rotation direction. The demonstration of controlled optical rotation of a spontaneously formed polariton condensate enables new opportunities for the study of open dissipative superfluidity, ordering of non-Hermitian quantized vortex matter, and topological states in a highly nonlinear, photonic platform.

Real-Time Observation of Charge-Spin Cooperative Dynamics Driven by a Nonequilibrium Phonon Environment.

We report on experimental observations of charge-spin cooperative dynamics of two-electron states in a GaAs double quantum dot located in a nonequilibrium phonon environment. When the phonon energy exceeds the lowest excitation energy in the quantum dot, the spin-flip rate of a single electron strongly enhances. In addition, originated from the spatial gradient of phonon density between the dots, the parallel spin states become more probable than the antiparallel ones. These results indicate that spin is essential for further demonstrations of single-electron thermodynamic systems driven by phonons, which will greatly contribute to understanding of the fundamental physics of thermoelectric devices.

Quasiparticle Trapping at Vortices Producing Josephson Supercurrent Enhancement.

The Josephson junction of a strong spin-orbit material under a magnetic field is a promising Majorana fermion candidate. Supercurrent enhancement by a magnetic field has been observed in the InAs nanowire Josephson junctions and assigned to a topological transition. In this work we observe a similar phenomenon but discuss the nontopological origin by considering the trapping of quasiparticles by vortices that penetrate the superconductor under a finite magnetic field. This assignment is supported by the observed hysteresis of the switching current when sweeping up and down the magnetic field. Our experiment shows the importance of quasiparticles in superconducting devices with a magnetic field, which can provide important insights for the design of qubits using superconductors.

Charge Neutral Current Generation in a Spontaneous Quantum Hall Antiferromagnet.

The intrinsic Hall effect allows for the generation of a nondissipative charge neutral current, such as a pure spin current generated via the spin Hall effect. Breaking of the spatial inversion or time reversal symmetries, or the spin-orbit interaction is generally considered necessary for the generation of such a charge neutral current. Here, we challenge this general concept and present generation and detection of a charge neutral current in a centrosymmetric material with little spin-orbit interaction. We employ bilayer graphene, and find enhanced nonlocal transport in the quantum Hall antiferromagnetic state, where spontaneous symmetry breaking occurs due to the electronic correlation.

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.

Robust Single-Shot Spin Measurement with 99.5% Fidelity in a Quantum Dot Array.

We demonstrate a new method for projective single-shot measurement of two electron spin states (singlet versus triplet) in an array of gate-defined lateral quantum dots in GaAs. The measurement has very high fidelity and is robust with respect to electric and magnetic fluctuations in the environment. It exploits a long-lived metastable charge state, which increases both the contrast and the duration of the charge signal distinguishing the two measurement outcomes. This method allows us to evaluate the charge measurement error and the spin-to-charge conversion error separately. We specify conditions under which this method can be used, and project its general applicability to scalable quantum dot arrays in GaAs or silicon.

Electrons surfing on a sound wave as a platform for quantum optics with flying electrons.

Electrons in a metal are indistinguishable particles that interact strongly with other electrons and their environment. Isolating and detecting a single flying electron after propagation, in a similar manner to quantum optics experiments with single photons, is therefore a challenging task. So far only a few experiments have been performed in a high-mobility two-dimensional electron gas in which the electron propagates almost ballistically. In these previous works, flying electrons were detected by means of the current generated by an ensemble of electrons, and electron correlations were encrypted in the current noise. Here we demonstrate the experimental realization of high-efficiency single-electron source and detector for a single electron propagating isolated from the other electrons through a one-dimensional channel. The moving potential is excited by a surface acoustic wave, which carries the single electron along the one-dimensional channel at a speed of 3 µm ns(-1). When this quantum channel is placed between two quantum dots several micrometres apart, a single electron can be transported from one quantum dot to the other with quantum efficiencies of emission and detection of 96% and 92%, respectively. Furthermore, the transfer of the electron can be triggered on a timescale shorter than the coherence time T(2)* of GaAs spin qubits. Our work opens new avenues with which to study the teleportation of a single electron spin and the distant interaction between spatially separated qubits in a condensed-matter system.

Critical Current Scaling in Long Diffusive Graphene-Based Josephson Junctions.

We present transport measurements on long, diffusive, graphene-based Josephson junctions. Several junctions are made on a single-domain crystal of CVD graphene and feature the same contact width of ∼9 µm but vary in length from 400 to 1000 nm. As the carrier density is tuned with the gate voltage, the critical current in these junctions ranges from a few nanoamperes up to more than 5 µA, while the Thouless energy, ETh, covers almost 2 orders of magnitude. Over much of this range, the product of the critical current and the normal resistance ICRN is found to scale linearly with ETh, as expected from theory. However, the value of the ratio ICRN/ETh is found to be 0.1-0.2, which much smaller than the predicted ∼10 for long diffusive SNS junctions.

Injection of a single electron from static to moving quantum dots.

We study the injection mechanism of a single electron from a static quantum dot into a moving quantum dot. The moving quantum dots are created with surface acoustic waves (SAWs) in a long depleted channel. We demonstrate that the injection process is characterized by an activation law with a threshold that depends on the SAW amplitude and on the dot-channel potential gradient. By sufficiently increasing the SAW modulation amplitude, we can reach a regime where the transfer has unity probability and is potentially adiabatic. This study points to the relevant regime to use moving dots in quantum information protocols.

Electron States of Uniaxially Strained Graphene.

We report an experimental study of electron states and the resulting electronic transport properties of uniaxially strained graphene. For this study we developed a novel strain application method that is compatible with the planar device technology. We identify the value of the strain induced in graphene by Raman spectroscopy and show with atomic force microscopy that its topography consists of wrinkles up to 4 nm height aligned along the direction of the applied strain. Transport experiments reveal a broadening of the charge neutrality region and the convergence of Landau levels to multiple Dirac points in Landau-fan diagrams. These observations are consistent with large fluctuations of the scalar potential via the strain-induced wrinkles, which is experimentally observed for the first time.

Quantum Manipulation of Two-Electron Spin States in Isolated Double Quantum Dots.

We studied experimentally the dynamics of the exchange interaction between two antiparallel electron spins in an isolated double quantum dot where coupling to the electron reservoirs can be ignored. We demonstrate that the level of control of such a double dot is higher than in conventional double dots. In particular, it allows us to couple coherently two electron spins in an efficient manner following a scheme initially proposed by Loss and DiVincenzo [Phys. Rev. A 57, 120 (1998)]. The present study demonstrates that isolated quantum dots are a possible route to increase the number of coherently coupled quantum dots.

Straining graphene using thin film shrinkage methods.

Theoretical works suggest the possibility and usefulness of strain engineering of graphene by predicting remarkable properties, such as Dirac cone merging, bandgap opening and pseudo magnetic field generation. However, most of these predictions have not yet been confirmed because it is experimentally difficult to control the magnitude and type (e.g., uniaxial, biaxial, and so forth) of strain in graphene devices. Here we report two novel methods to apply strain without bending the substrate. We employ thin films of evaporated metal and organic insulator deposited on graphene, which shrink after electron beam irradiation or heat application. These methods make it possible to apply both biaxial strain and in-plane isotropic compressive strain in a well-controlled manner. Raman spectroscopy measurements show a clear splitting of the degenerate states of the G-band in the case of biaxial strain, and G-band blue shift without splitting in the case of in-plane isotropic compressive strain. In the case of biaxial strain application, we find out the ratio of the strain component perpendicular to the stretching direction is at least three times larger than what was previously observed, indicating that shrinkage of the metal or organic insulator deposited on graphene induces both tensile and compressive strain in this atomically thin material. Our studies present for the first time a viable way to apply strain to graphene without the need to bend the substrate.

Phase engineering of anomalous Josephson effect derived from Andreev molecules.

A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.

Phase-dependent Andreev molecules and superconducting gap closing in coherently-coupled Josephson junctions.

The Josephson junction (JJ) is an essential element of superconducting (SC) devices for both fundamental and applied physics. The short-range coherent coupling of two adjacent JJs forms Andreev molecule states (AMSs), which provide a new ingredient to engineer exotic SC phenomena such as topological SC states and Andreev qubits. Here we provide tunneling spectroscopy measurements on a device consisting of two electrically controllable planar JJs sharing a single SC electrode. We discover that Andreev spectra in the coupled JJ are highly modulated from those in the single JJs and possess phase-dependent AMS features reproduced in our numerical calculation. Notably, the SC gap closing due to the AMS formation is experimentally observed. Our results help in understanding SC transport derived from the AMS and promoting the use of AMS physics to engineer topological SC states and quantum information devices.

Full counting statistics for orbital-degenerate impurity Anderson model with Hund's rule exchange coupling.

We study nonequilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling J, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling, and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value F(b)=(9M+6)/(5M+4) determined by the orbital degeneracy M. We also investigate the crossover between the small and large J limits in the two-orbital case M=2, using the numerical renormalization group approach.

A shuttling-based two-qubit logic gate for linking distant silicon quantum processors.

Control of entanglement between qubits at distant quantum processors using a two-qubit gate is an essential function of a scalable, modular implementation of quantum computation. Among the many qubit platforms, spin qubits in silicon quantum dots are promising for large-scale integration along with their nanofabrication capability. However, linking distant silicon quantum processors is challenging as two-qubit gates in spin qubits typically utilize short-range exchange coupling, which is only effective between nearest-neighbor quantum dots. Here we demonstrate a two-qubit gate between spin qubits via coherent spin shuttling, a key technology for linking distant silicon quantum processors. Coherent shuttling of a spin qubit enables efficient switching of the exchange coupling with an on/off ratio exceeding 1000, while preserving the spin coherence by 99.6% for the single shuttling between neighboring dots. With this shuttling-mode exchange control, we demonstrate a two-qubit controlled-phase gate with a fidelity of 93%, assessed via randomized benchmarking. Combination of our technique and a phase coherent shuttling of a qubit across a large quantum dot array will provide feasible path toward a quantum link between distant silicon quantum processors, a key requirement for large-scale quantum computation.

Quantum tomography of an entangled three-qubit state in silicon.

Quantum entanglement is a fundamental property of coherent quantum states and an essential resource for quantum computing1. In large-scale quantum systems, the error accumulation requires concepts for quantum error correction. A first step toward error correction is the creation of genuinely multipartite entanglement, which has served as a performance benchmark for quantum computing platforms such as superconducting circuits2,3, trapped ions4 and nitrogen-vacancy centres in diamond5. Among the candidates for large-scale quantum computing devices, silicon-based spin qubits offer an outstanding nanofabrication capability for scaling-up. Recent studies demonstrated improved coherence times6-8, high-fidelity all-electrical control9-13, high-temperature operation14,15 and quantum entanglement of two spin qubits9,11,12. Here we generated a three-qubit Greenberger-Horne-Zeilinger state using a low-disorder, fully controllable array of three spin qubits in silicon. We performed quantum state tomography16 and obtained a state fidelity of 88.0%. The measurements witness a genuine Greenberger-Horne-Zeilinger class quantum entanglement that cannot be separated into any biseparable state. Our results showcase the potential of silicon-based spin qubit platforms for multiqubit quantum algorithms.