Fidelity benchmarks for two-qubit gates in silicon

On the feasibility of a quantum sensing protocol designed with electrically controlled spins in silicon quantum dots

Though electron spins in electrically defined silicon (Si) quantum dot systems have been extensively employed for physical realization of quantum processing units, their application to quantum sensing has not been active compared to the case of photonic qubits and nitrogen-vacancy spins in diamonds. This work presents a comprehensive study on the feasibility of Si quantum dot structures as a physical platform for implementation of a sensing protocol for magnetic fields. To examine sensing operations at a systematic level, we adopt in-house device simulations taking a Si double quantum dot (DQD) system as a target device where the confinement of electron spins is controlled with electrical biases in a Si/Si-germanium heterostructure. Simulation results demonstrate the fairly nice utility of the Si DQD platform for detecting externally presented static magnetic fields, and, more notably, reveal that sensing operations are not quite vulnerable to charge noise that is omnipresent in solid materials. As a rare study that presents in-depth discussion on operations of quantum sensing units at a device-level based on computational modeling, this work can deliver practical insights for potential designs of sensing units with electron spins in Si devices.

SWAP Gate for Spin Qubits Based on Silicon Devices Integrated with a Micromagnet

In our toolbox of quantum gates for spin qubits, the SWAP-family gates based on Heisenberg exchange coupling are quite versatile: the SWAP gate can help solve the connectivity problem by realizing both short- and long-range spin state transfer, while the S W A P gate is a basic two-qubit entangling gate. Here we demonstrate a SWAP gate in a double quantum dot in isotopically enriched silicon in the presence of a micromagnet. We achieve a two-orders-of-magnitude adjustable ratio between the exchange coupling J and the Zeeman energy difference ΔEz, overcoming a major obstacle for a high-fidelity SWAP gate. We also calibrate the single-qubit local phases, evaluate the logical-basis fidelity of the SWAP gate, and further analyze the dominant error sources. These results pave the way for high-fidelity SWAP gates and processes based on them, such as quantum communication on chip and quantum simulation.

12-Spin-Qubit Arrays Fabricated on a 300 mm Semiconductor Manufacturing Line

Intel's efforts to build a practical quantum computer are focused on developing a scalable spin-qubit platform leveraging industrial high-volume semiconductor manufacturing expertise and 300 mm fabrication infrastructure. Here, we provide an overview of the design, fabrication, and demonstration of a new customized quantum test chip, which contains 12-quantum-dot spin-qubit linear arrays, code named Tunnel Falls. These devices are fabricated using immersion and extreme ultraviolet lithography (EUV), along with other standard high-volume manufacturing (HVM) processes as well as production-level process control. We present key device features and fabrication details as well as qubit characterization results confirming device functionality. These results corroborate our fabrication methods and are a crucial step toward scaling of extensible 2D qubit array schemes.

Measurement of Enhanced Spin-Orbit Coupling Strength for Donor-Bound Electron Spins in Silicon

While traditionally considered a deleterious effect in quantum dot spin qubits, the spin-orbit interaction is recently being revisited as it allows for rapid coherent control by on-chip AC electric fields. For electrons in bulk silicon, spin-orbit coupling (SOC) is intrinsically weak, however, it can be enhanced at surfaces and interfaces, or through atomic placement. Here it is showed that the strength of the spin-orbit coupling can be locally enhanced by more than two orders of magnitude in the manybody wave functions of multi-donor quantum dots compared to a single donor, reaching strengths so far only reported for holes or two-donor system with certain symmetry. These findings may provide a pathway toward all-electrical control of donor-bound spins in silicon using electric dipole spin resonance (EDSR).

Tomography of entangling two-qubit logic operations in exchange-coupled donor electron spin qubits

Scalable quantum processors require high-fidelity universal quantum logic operations in a manufacturable physical platform. Donors in silicon provide atomic size, excellent quantum coherence and compatibility with standard semiconductor processing, but no entanglement between donor-bound electron spins has been demonstrated to date. Here we present the experimental demonstration and tomography of universal one- and two-qubit gates in a system of two weakly exchange-coupled electrons, bound to single phosphorus donors introduced in silicon by ion implantation. We observe that the exchange interaction has no effect on the qubit coherence. We quantify the fidelity of the quantum operations using gate set tomography (GST), and we use the universal gate set to create entangled Bell states of the electrons spins, with fidelity 91.3 ± 3.0%, and concurrence 0.87 ± 0.05. These results form the necessary basis for scaling up donor-based quantum computers.

Quantum Interference and Coherent Population Trapping in a Double Quantum Dot

Quantum interference is a natural consequence of wave-particle duality in quantum mechanics, and is widely observed at the atomic scale. One interesting manifestation of quantum interference is coherent population trapping (CPT), first proposed in three-level driven atomic systems and observed in quantum optical experiments. Here, we demonstrate CPT in a gate-defined semiconductor double quantum dot (DQD), with some unique twists as compared to the atomic systems. Specifically, we observe CPT in both driven and nondriven situations. We further show that CPT in a driven DQD could be used to generate adiabatic state transfer. Moreover, our experiment reveals a nontrivial modulation to the CPT caused by the longitudinal driving field, yielding an odd-even effect and a tunable CPT. Our results broaden the field of CPT, and open up the possibility of quantum simulation and quantum computation based on adiabatic passage in quantum dot systems.

Valley-Free Silicon Fins Caused by Shear Strain

Electron spins confined in silicon quantum dots are promising candidates for large-scale quantum computers. However, the degeneracy of the conduction band of bulk silicon introduces additional levels dangerously close to the window of computational energies, where the quantum information can leak. The energy of the valley states-typically 0.1 meV-depends on hardly controllable atomistic disorder and still constitutes a fundamental limit to the scalability of these architectures. In this work, we introduce designs of complementary metal-oxide-semiconductor (CMOS)-compatible silicon fin field-effect transistors that enhance the energy gap to noncomputational states by more than one order of magnitude. Our devices comprise realistic silicon-germanium nanostructures with a large shear strain, where troublesome valley degrees of freedom are completely removed. The energy of noncomputational states is therefore not affected by unavoidable atomistic disorder and can further be tuned in situ by applied electric fields. Our design ideas are directly applicable to a variety of setups and will offer a blueprint toward silicon-based large-scale quantum processors.

Spatially Resolved Dielectric Loss at the Si/SiO_{2} Interface

The Si/SiO_{2} interface is populated by isolated trap states that modify its electronic properties. These traps are of critical interest for the development of semiconductor-based quantum sensors and computers, as well as nanoelectronic devices. Here, we study the electric susceptibility of the Si/SiO_{2} interface with nm spatial resolution using frequency-modulated atomic force microscopy. The sample measured here is a patterned dopant delta layer buried 2 nm beneath the silicon native oxide interface. We show that charge organization timescales of the Si/SiO_{2} interface range from 1-150 ns, and increase significantly around interfacial traps. We conclude that under time-varying gate biases, dielectric loss in metal-insulator-semiconductor capacitor devices is in the frequency range of MHz to sub-MHz, and is highly spatially heterogeneous over nm length scales.

Anisotropic exchange interaction of two hole-spin qubits

Semiconductor spin qubits offer the potential to employ industrial transistor technology to produce large-scale quantum computers. Silicon hole spin qubits benefit from fast all-electrical qubit control and sweet spots to counteract charge and nuclear spin noise. However, the demonstration of a two-qubit interaction has remained an open challenge. One missing factor is an understanding of the exchange coupling in the presence of a strong spin-orbit interaction. Here we study two hole-spin qubits in a silicon fin field-effect transistor, the workhorse device of today's semiconductor industry. We demonstrate electrical tunability of the exchange splitting from above 500 MHz to close-to-off and perform a conditional spin-flip in 24 ns. The exchange is anisotropic because of the spin-orbit interaction. Upon tunnelling from one quantum dot to the other, the spin is rotated by almost 180 degrees. The exchange Hamiltonian no longer has the Heisenberg form and can be engineered such that it enables two-qubit controlled rotation gates without a trade-off between speed and fidelity. This ideal behaviour applies over a wide range of magnetic field orientations, rendering the concept robust with respect to variations from qubit to qubit, indicating that it is a suitable approach for realizing a large-scale quantum computer.

High-fidelity spin qubit operation and algorithmic initialization above 1 K

The encoding of qubits in semiconductor spin carriers has been recognized as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale1-10. However, the operation of the large number of qubits required for advantageous quantum applications11-13 will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 K, at which the cooling power is orders of magnitude higher14-18. Here we tune up and operate spin qubits in silicon above 1 K, with fidelities in the range required for fault-tolerant operations at these temperatures19-21. We design an algorithmic initialization protocol to prepare a pure two-qubit state even when the thermal energy is substantially above the qubit energies and incorporate radiofrequency readout to achieve fidelities up to 99.34% for both readout and initialization. We also demonstrate single-qubit Clifford gate fidelities up to 99.85% and a two-qubit gate fidelity of 98.92%. These advances overcome the fundamental limitation that the thermal energy must be well below the qubit energies for the high-fidelity operation to be possible, surmounting a main obstacle in the pathway to scalable and fault-tolerant quantum computation.

Manipulating Coherent Exciton Dynamics in CsPbI3 Perovskite Quantum Dots Using Magnetic Field

Lead halide perovskite quantum dots (QDs) have recently emerged as a promising material platform for quantum information processing owing to their strong light-matter interaction and relatively long-lived optical and spin coherences. In particular, the coherence of the fine-structure bright excitons is sustainable up to room temperature and can be observed even at an ensemble level. Here modulation of the polarization of these excitons in CsPbI3 QDs and manipulation of their time-domain coherent dynamics using a longitudinal magnetic field are demonstrated. The manipulation is realized using femtosecond quantum beat spectroscopy performed with both circularly- and linearly-polarized pulses. The results are well captured by the density of matrix simulation and are picturized using a Bloch sphere. This study forms the basis for preparing arbitrary coherent superpositions of excitons in perovskite QDs for an array of quantum technologies under near-ambient conditions.

An atomic-scale multi-qubit platform

Individual electron spins in solids are promising candidates for quantum science and technology, where bottom-up assembly of a quantum device with atomically precise couplings has long been envisioned. Here, we realized atom-by-atom construction, coherent operations, and readout of coupled electron-spin qubits using a scanning tunneling microscope. To enable the coherent control of "remote" qubits that are outside of the tunnel junction, we complemented each electron spin with a local magnetic field gradient from a nearby single-atom magnet. Readout was achieved by using a sensor qubit in the tunnel junction and implementing pulsed double electron spin resonance. Fast single-, two-, and three-qubit operations were thereby demonstrated in an all-electrical fashion. Our angstrom-scale qubit platform may enable quantum functionalities using electron spin arrays built atom by atom on a surface.

Dangling Bonds as Possible Contributors to Charge Noise in Silicon and Silicon-Germanium Quantum Dot Qubits

Spin qubits based on Si and Si1-xGex quantum dot architectures exhibit among the best coherence times of competing quantum computing technologies, yet they still suffer from charge noise that limit their qubit gate fidelities. Identifying the origins of these charge fluctuations is therefore a critical step toward improving Si quantum-dot-based qubits. Here, we use hybrid functional calculations to investigate possible atomistic sources of charge noise, focusing on charge trapping at Si and Ge dangling bonds (DBs). We evaluate the role of global and local environment in the defect levels associated with DBs in Si, Ge, and Si1-xGex alloys, and consider their trapping and excitation energies within the framework of configuration coordinate diagrams. We additionally consider the influence of strain and oxidation in charge-trapping energetics by analyzing Si and GeSi DBs in SiO2 and strained Si layers in typical Si1-xGex quantum dot heterostructures. Our results identify that Ge dangling bonds are more problematic charge-trapping centers both in typical Si1-xGex alloys and associated oxidation layers, and they may be exacerbated by compositional inhomogeneities. These results suggest the importance of alloy homogeneity and possible passivation schemes for DBs in Si-based quantum dot qubits and are of general relevance to mitigating possible trap levels in other Si, Ge, and Si1-xGex-based metal-oxide-semiconductor stacks and related devices.

Ultrafast and Electrically Tunable Rabi Frequency in a Germanium Hut Wire Hole Spin Qubit

Hole spin qubits based on germanium (Ge) have strong tunable spin-orbit interaction (SOI) and ultrafast qubit operation speed. Here we report that the Rabi frequency (f_Rabi) of a hole spin qubit in a Ge hut wire (HW) double quantum dot (DQD) is electrically tuned through the detuning energy (ϵ) and middle gate voltage (V_M). f_Rabi gradually decreases with increasing ϵ; on the contrary, f_Rabi is positively correlated with V_M. We attribute our results to the change of electric field on SOI and the contribution of the excited state in quantum dots to f_Rabi. We further demonstrate an ultrafast f_Rabi exceeding 1.2 GHz, which indicates the strong SOI in our device. The discovery of an ultrafast and electrically tunable f_Rabi in a hole spin qubit has potential applications in semiconductor quantum computing.

Collective Microwave Response for Multiple Gate-Defined Double Quantum Dots

We fabricate and characterize a hybrid quantum device that consists of five gate-defined double quantum dots (DQDs) and a high-impedance NbTiN transmission resonator. The controllable interactions between DQDs and the resonator are spectroscopically explored by measuring the microwave transmission through the resonator in the detuning parameter space. Utilizing the high tunability of the system parameters and the high cooperativity (C_total > 17.6) interaction between the qubit ensemble and the resonator, we tune the charge-photon coupling and observe the collective microwave response changing from linear to nonlinear. Our results present the maximum number of DQDs coupled to a resonator and manifest a potential platform for scaling up qubits and studying collective quantum effects in semiconductor-superconductor hybrid cavity quantum electrodynamics systems.

Jellybean Quantum Dots in Silicon for Qubit Coupling and On-Chip Quantum Chemistry

The small size and excellent integrability of silicon metal-oxide-semiconductor (SiMOS) quantum dot spin qubits make them an attractive system for mass-manufacturable, scaled-up quantum processors. Furthermore, classical control electronics can be integrated on-chip, in-between the qubits, if an architecture with sparse arrays of qubits is chosen. In such an architecture qubits are either transported across the chip via shuttling or coupled via mediating quantum systems over short-to-intermediate distances. This paper investigates the charge and spin characteristics of an elongated quantum dot-a so-called jellybean quantum dot-for the prospects of acting as a qubit-qubit coupler. Charge transport, charge sensing, and magneto-spectroscopy measurements are performed on a SiMOS quantum dot device at mK temperature and compared to Hartree-Fock multi-electron simulations. At low electron occupancies where disorder effects and strong electron-electron interaction dominate over the electrostatic confinement potential, the data reveals the formation of three coupled dots, akin to a tunable, artificial molecule. One dot is formed centrally under the gate and two are formed at the edges. At high electron occupancies, these dots merge into one large dot with well-defined spin states, verifying that jellybean dots have the potential to be used as qubit couplers in future quantum computing architectures.

Terahertz nanospectroscopy of plasmon polaritons for the evaluation of doping in quantum devices

Terahertz (THz) waves are a highly sensitive probe of free carrier concentrations in semiconducting materials. However, most experiments operate in the far-field, which precludes the observation of nanoscale features that affect the material response. Here, we demonstrate the use of nanoscale THz plasmon polaritons as an indicator of surface quality in prototypical quantum devices properties. Using THz near-field hyperspectral measurements, we observe polaritonic features in doped silicon near a metal-semiconductor interface. The presence of the THz surface plasmon polariton indicates the existence of a thin film doped layer on the device. Using a multilayer extraction procedure utilising vector calibration, we quantitatively probe the doped surface layer and determine its thickness and complex permittivity. The recovered multilayer characteristics match the dielectric conditions necessary to support the THz surface plasmon polariton. Applying these findings to superconducting resonators, we show that etching of this doped layer leads to an increase of the quality factor as determined by cryogenic measurements. This study demonstrates that THz scattering-type scanning near-field optical microscopy (s-SNOM) is a promising diagnostic tool for characterization of surface dielectric properties of quantum devices.

Material-Inherent Noise Sources in Quantum Information Architecture

NISQ is a representative keyword at present as an acronym for "noisy intermediate-scale quantum", which identifies the current era of quantum information processing (QIP) technologies. QIP science and technologies aim to accomplish unprecedented performance in computation, communications, simulations, and sensing by exploiting the infinite capacity of parallelism, coherence, and entanglement as governing quantum mechanical principles. For the last several decades, quantum computing has reached to the technology readiness level 5, where components are integrated to build mid-sized commercial products. While this is a celebrated and triumphant achievement, we are still a great distance away from quantum-superior, fault-tolerant architecture. To reach this goal, we need to harness technologies that recognize undesirable factors to lower fidelity and induce errors from various sources of noise with controllable correction capabilities. This review surveys noisy processes arising from materials upon which several quantum architectures have been constructed, and it summarizes leading research activities in searching for origins of noise and noise reduction methods to build advanced, large-scale quantum technologies in the near future.

The Use of Exchange Coupled Atom Qubits as Atomic-Scale Magnetic Field Sensors

Phosphorus atoms in silicon offer a rich quantum computing platform where both nuclear and electron spins can be used to store and process quantum information. While individual control of electron and nuclear spins has been demonstrated, the interplay between them during qubit operations has been largely unexplored. This study investigates the use of exchange-based operation between donor bound electron spins to probe the local magnetic fields experienced by the qubits with exquisite precision at the atomic scale. To achieve this, coherent exchange oscillations are performed between two electron spin qubits, where the left and right qubits are hosted by three and two phosphorus donors, respectively. The frequency spectrum of exchange oscillations shows quantized changes in the local magnetic fields at the qubit sites, corresponding to the different hyperfine coupling between the electron and each of the qubit-hosting nuclear spins. This ability to sense the hyperfine fields of individual nuclear spins using the exchange interaction constitutes a unique metrology technique, which reveals the exact crystallographic arrangements of the phosphorus atoms in the silicon crystal for each qubit. The detailed knowledge obtained of the local magnetic environment can then be used to engineer hyperfine fields in multi-donor qubits for high-fidelity two-qubit gates.

Suppressing quantum errors by scaling a surface code logical qubit

Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10-6 logical error per cycle floor set by a single high-energy event (1.6 × 10-7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.

Non-adiabatic quantum control of quantum dot arrays with fixed exchange using Cartan decomposition

In semiconductor spin qubits which typically interact through short-range exchange coupling, shuttling of spin is a practical way to generate quantum operations between distant qubits. Although the exchange is often tunable through voltages applied to gate electrodes, its minimal value can be significantly large, which hinders the applicability of existing shuttling protocols to such devices, requiring a different approach. In this work, we extend our previous results for double- and triple-dot systems, and describe a method for implementing spin state transfer in long chains of singly occupied quantum dots in a non-adiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems in a systematic way, and use dynamical invariants to design smooth non-adiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we discuss the extensibility of our results to directed shuttling of spin states on two-dimensional lattices of quantum dots with fixed coupling. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

A single hole spin with enhanced coherence in natural silicon

Semiconductor spin qubits based on spin-orbit states are responsive to electric field excitations, allowing for practical, fast and potentially scalable qubit control. Spin electric susceptibility, however, renders these qubits generally vulnerable to electrical noise, which limits their coherence time. Here we report on a spin-orbit qubit consisting of a single hole electrostatically confined in a natural silicon metal-oxide-semiconductor device. By varying the magnetic field orientation, we reveal the existence of operation sweet spots where the impact of charge noise is minimized while preserving an efficient electric-dipole spin control. We correspondingly observe an extension of the Hahn-echo coherence time up to 88 μs, exceeding by an order of magnitude existing values reported for hole spin qubits, and approaching the state-of-the-art for electron spin qubits with synthetic spin-orbit coupling in isotopically purified silicon. Our finding enhances the prospects of silicon-based hole spin qubits for scalable quantum information processing.

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.

A coherent quantum link between distant quantum processors is desirable for scaling up of quantum computation. Noiri et al. demonstrate a strategy to link distant quantum processors in silicon, by implementing a shuttling-based two-qubit gate between spin qubits in a Si/SiGe triple quantum dot.

Optical measurement of electron spins in quantum dots: quantum Zeno effects

We describe theoretically the effects of the quantum back action under the continuous optical measurement of electron spins in quantum dots. We consider the system excitation by elliptically polarized light close to the trion resonance, which allows for simultaneous spin orientation and measurement. We microscopically demonstrate that the nuclei-induced spin relaxation can be both suppressed and accelerated by the continuous spin measurement due to the quantum Zeno and anti-Zeno effects, respectively. Our theoretical predictions can be directly compared with the future experimental results and straightforwardly generalized for pump-probe experiments.

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.

Efficient Gating of Magnons by Proximity Superconductors

Electrostatic gating confines and controls the transport of electrons in integrated circuits. Magnons, the quanta of spin waves of the magnetic order, are promising alternative information carriers, but difficult to gate. Here we report that superconducting strips on top of thin magnetic films can totally reflect magnons by their diamagnetic response to the magnon stray fields. The induced large frequency shifts unidirectionally block the magnons propagating normal to the magnetization. Two superconducting gates parallel to the magnetization create a magnonic cavity. The option to gate coherent magnons adds functionalities to magnonic devices, such as reprogrammable logical devices and increased couplings to other degrees of freedom.

Devitalizing noise-driven instability of entangling logic in silicon devices with bias controls

The quality of quantum bits (qubits) in silicon is highly vulnerable to charge noise that is omnipresent in semiconductor devices and is in principle hard to be suppressed. For a realistically sized quantum dot system based on a silicon-germanium heterostructure whose confinement is manipulated with electrical biases imposed on top electrodes, we computationally explore the noise-robustness of 2-qubit entangling operations with a focus on the controlled-X (CNOT) logic that is essential for designs of gate-based universal quantum logic circuits. With device simulations based on the physics of bulk semiconductors augmented with electronic structure calculations, we not only quantify the degradation in fidelity of single-step CNOT operations with respect to the strength of charge noise, but also discuss a strategy of device engineering that can significantly enhance noise-robustness of CNOT operations with almost no sacrifice of speed compared to the single-step case. Details of device designs and controls that this work presents can establish practical guideline for potential efforts to secure silicon-based quantum processors using an electrode-driven quantum dot platform.

Universal control of a six-qubit quantum processor in silicon

Future quantum computers capable of solving relevant problems will require a large number of qubits that can be operated reliably1. However, the requirements of having a large qubit count and operating with high fidelity are typically conflicting. Spins in semiconductor quantum dots show long-term promise2,3 but demonstrations so far use between one and four qubits and typically optimize the fidelity of either single- or two-qubit operations, or initialization and readout4-11. Here, we increase the number of qubits and simultaneously achieve respectable fidelities for universal operation, state preparation and measurement. We design, fabricate and operate a six-qubit processor with a focus on careful Hamiltonian engineering, on a high level of abstraction to program the quantum circuits, and on efficient background calibration, all of which are essential to achieve high fidelities on this extended system. State preparation combines initialization by measurement and real-time feedback with quantum-non-demolition measurements. These advances will enable testing of increasingly meaningful quantum protocols and constitute a major stepping stone towards large-scale quantum computers.

The functions of a reservoir offset voltage applied to physically defined p-channel Si quantum dots

We propose and define a reservoir offset voltage as a voltage commonly applied to both reservoirs of a quantum dot and study the functions in p-channel Si quantum dots. By the reservoir offset voltage, the electrochemical potential of the quantum dot can be modulated. In addition, when quantum dots in different channels are capacitively coupled, the reservoir offset voltage of one of the QDs can work as a gate voltage for the others. Our results show that the technique will lead to reduction of the number of gate electrodes, which is advantageous for future qubit integration.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Valley Splitting in Silicon from the Interference Pattern of Quantum Oscillations

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined in silicon metal oxide semiconductor Hall-bar transistors. These silicon metal oxide semiconductor Hall bars are made by advanced semiconductor manufacturing on 300 mm silicon wafers and support a two-dimensional electron gas of high quality with a maximum mobility of 17.6×10^{3}  cm^{2}/Vs and minimum percolation density of 3.45×10^{10}  cm^{-2}. Because of the low disorder, we observe beatings in the Shubnikov-de Haas oscillations that arise from the energy splitting of the two low-lying conduction band valleys. From the analysis of the oscillations beating patterns up to T=1.7  K, we estimate a maximum valley splitting of ΔE_{VS}=8.2  meV at a density of 6.8×10^{12}  cm^{-2}. Furthermore, the valley splitting increases with density at a rate consistent with theoretical predictions for a near-ideal semiconductor-oxide interface.

Two-qubit silicon quantum processor with operation fidelity exceeding 99

Silicon spin qubits satisfy the necessary criteria for quantum information processing. However, a demonstration of high-fidelity state preparation and readout combined with high-fidelity single- and two-qubit gates, all of which must be present for quantum error correction, has been lacking. We use a two-qubit Si/SiGe quantum processor to demonstrate state preparation and readout with fidelity greater than 97%, combined with both single- and two-qubit control fidelities exceeding 99%. The operation of the quantum processor is quantitatively characterized using gate set tomography and randomized benchmarking. Our results highlight the potential of silicon spin qubits to become a dominant technology in the development of intermediate-scale quantum processors.

A silicon singlet-triplet qubit driven by spin-valley coupling

Spin–orbit effects, inherent to electrons confined in quantum dots at a silicon heterointerface, provide a means to control electron spin qubits without the added complexity of on-chip, nanofabricated micromagnets or nearby coplanar striplines. Here, we demonstrate a singlet–triplet qubit operating mode that can drive qubit evolution at frequencies in excess of 200 MHz. This approach offers a means to electrically turn on and off fast control, while providing high logic gate orthogonality and long qubit dephasing times. We utilize this operational mode for dynamical decoupling experiments to probe the charge noise power spectrum in a silicon metal-oxide-semiconductor double quantum dot. In addition, we assess qubit frequency drift over longer timescales to capture low-frequency noise. We present the charge noise power spectral density up to 3 MHz, which exhibits a 1/f^α dependence consistent with α ~ 0.7, over 9 orders of magnitude in noise frequency.

Spin-orbit coupling in gate-defined quantum dots in silicon metal-oxide semiconductors provides a promising route for electrical control of spin qubits. Here, the authors demonstrate that intervalley spin–orbit interaction enables fast singlet–triplet qubit rotations in this platform, at frequencies exceeding 200MHz.

Precision tomography of a three-qubit donor quantum processor in silicon

Nuclear spins were among the first physical platforms to be considered for quantum information processing^1,2, because of their exceptional quantum coherence³ and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted ³¹P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin⁴, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)⁵, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors⁶. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons^7-9 or physically shuttled across different locations^10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

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 silicon^7-15 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.

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.

An Operation Guide of Si-MOS Quantum Dots for Spin Qubits

In the last 20 years, silicon quantum dots have received considerable attention from academic and industrial communities for research on readout, manipulation, storage, near-neighbor and long-range coupling of spin qubits. In this paper, we introduce how to realize a single spin qubit from Si-MOS quantum dots. First, we introduce the structure of a typical Si-MOS quantum dot and the experimental setup. Then, we show the basic properties of the quantum dot, including charge stability diagram, orbital state, valley state, lever arm, electron temperature, tunneling rate and spin lifetime. After that, we introduce the two most commonly used methods for spin-to-charge conversion, i.e., Elzerman readout and Pauli spin blockade readout. Finally, we discuss the details of how to find the resonance frequency of spin qubits and show the result of coherent manipulation, i.e., Rabi oscillation. The above processes constitute an operation guide for helping the followers enter the field of spin qubits in Si-MOS quantum dots.

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 circuits^2,3, 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 times^6-8, high-fidelity all-electrical control^9-13, high-temperature operation^14,15 and quantum entanglement of two spin qubits^9,11,12. 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.

Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field

Decoherence of Rabi oscillation in a two-level quantum system consists of two components, a simple exponential decay and a damped oscillation. In dense-ensemble spin systems like negatively charged nitrogen-vacancy (NV⁻) centers in diamond, fast quantum state decoherence often obscures clear observation of the Rabi nutation. On the other hand, the simple exponential decay (or baseline decay) of the oscillation in such spin systems can be readily detected but has not been thoroughly explored in the past. This study investigates in depth the baseline decay of dense spin ensembles in diamond under continuously driving microwave (MW). It is found that the baseline decay times of NV⁻ spins decrease with the increasing MW field strength and the MW detuning dependence of the decay times shows a Lorentzian-like spectrum. The experimental findings are in good agreement with simulations based on the Bloch formalism for a simple two-level system in the low MW power region after taking into account the effect of inhomogeneous broadening. This combined investigation provides new insight into fundamental spin relaxation processes under continuous driving electromagnetic fields and paves ways to better understanding of this underexplored phenomena using single NV⁻ centers, which have shown promising applications in quantum computing and quantum metrology.

Single-electron spin resonance in a nanoelectronic device using a global field

Spin-based silicon quantum electronic circuits offer a scalable platform for quantum computation, combining the manufacturability of semiconductor devices with the long coherence times afforded by spins in silicon. Advancing from current few-qubit devices to silicon quantum processors with upward of a million qubits, as required for fault-tolerant operation, presents several unique challenges, one of the most demanding being the ability to deliver microwave signals for large-scale qubit control. Here, we demonstrate a potential solution to this problem by using a three-dimensional dielectric resonator to broadcast a global microwave signal across a quantum nanoelectronic circuit. Critically, this technique uses only a single microwave source and is capable of delivering control signals to millions of qubits simultaneously. We show that the global field can be used to perform spin resonance of single electrons confined in a silicon double quantum dot device, establishing the feasibility of this approach for scalable spin qubit control.

A High-Sensitivity Charge Sensor for Silicon Qubits above 1 K

Recent studies of silicon spin qubits at temperatures above 1 K are encouraging demonstrations that the cooling requirements for solid-state quantum computing can be considerably relaxed. However, qubit readout mechanisms that rely on charge sensing with a single-island single-electron transistor (SISET) quickly lose sensitivity due to thermal broadening of the electron distribution in the reservoirs. Here we exploit the tunneling between two quantized states in a double-island single-electron transistor (SET) to demonstrate a charge sensor with an improvement in the signal-to-noise ratio by an order of magnitude compared to a standard SISET, and a single-shot charge readout fidelity above 99% up to 8 K at a bandwidth greater than 100 kHz. These improvements are consistent with our theoretical modeling of the temperature-dependent current transport for both types of SETs. With minor additional hardware overhead, these sensors can be integrated into existing qubit architectures for a high-fidelity charge readout at few-kelvin temperatures.

Exponential suppression of bit or phase errors with cyclic error correction

Realizing the potential of quantum computing requires sufficiently low logical error rates¹. Many applications call for error rates as low as 10⁻¹⁵ (refs. ^2–9), but state-of-the-art quantum platforms typically have physical error rates near 10⁻³ (refs. ^10–14). Quantum error correction^15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device^18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

Repetition codes running many cycles of quantum error correction achieve exponential suppression of errors with increasing numbers of qubits.

Coherent spin qubit transport in silicon

A fault-tolerant quantum processor may be configured using stationary qubits interacting only with their nearest neighbours, but at the cost of significant overheads in physical qubits per logical qubit. Such overheads could be reduced by coherently transporting qubits across the chip, allowing connectivity beyond immediate neighbours. Here we demonstrate high-fidelity coherent transport of an electron spin qubit between quantum dots in isotopically-enriched silicon. We observe qubit precession in the inter-site tunnelling regime and assess the impact of qubit transport using Ramsey interferometry and quantum state tomography techniques. We report a polarization transfer fidelity of 99.97% and an average coherent transfer fidelity of 99.4%. Our results provide key elements for high-fidelity, on-chip quantum information distribution, as long envisaged, reinforcing the scaling prospects of silicon-based spin qubits.

Bell-state tomography in a silicon many-electron artificial molecule

An error-corrected quantum processor will require millions of qubits, accentuating the advantage of nanoscale devices with small footprints, such as silicon quantum dots. However, as for every device with nanoscale dimensions, disorder at the atomic level is detrimental to quantum dot uniformity. Here we investigate two spin qubits confined in a silicon double quantum dot artificial molecule. Each quantum dot has a robust shell structure and, when operated at an occupancy of 5 or 13 electrons, has single spin-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}$$\end{document}12 valence electron in its p- or d-orbital, respectively. These higher electron occupancies screen static electric fields arising from atomic-level disorder. The larger multielectron wavefunctions also enable significant overlap between neighbouring qubit electrons, while making space for an interstitial exchange-gate electrode. We implement a universal gate set using the magnetic field gradient of a micromagnet for electrically driven single qubit gates, and a gate-voltage-controlled inter-dot barrier to perform two-qubit gates by pulsed exchange coupling. We use this gate set to demonstrate a Bell state preparation between multielectron qubits with fidelity 90.3%, confirmed by two-qubit state tomography using spin parity measurements.

Multielectron quantum dots offer a promising platform for high-performance spin qubits; however, previous demonstrations have been limited to single-qubit operation. Here, the authors report a universal gate set and two-qubit Bell state tomography in a high-occupancy double quantum dot in silicon.

CMOS-based cryogenic control of silicon quantum circuits

The most promising quantum algorithms require quantum processors that host millions of quantum bits when targeting practical applications¹. A key challenge towards large-scale quantum computation is the interconnect complexity. In current solid-state qubit implementations, an important interconnect bottleneck appears between the quantum chip in a dilution refrigerator and the room-temperature electronics. Advanced lithography supports the fabrication of both control electronics and qubits in silicon using technology compatible with complementary metal oxide semiconductors (CMOS)². When the electronics are designed to operate at cryogenic temperatures, they can ultimately be integrated with the qubits on the same die or package, overcoming the 'wiring bottleneck'^3-6. Here we report a cryogenic CMOS control chip operating at 3 kelvin, which outputs tailored microwave bursts to drive silicon quantum bits cooled to 20 millikelvin. We first benchmark the control chip and find an electrical performance consistent with qubit operations of 99.99 per cent fidelity, assuming ideal qubits. Next, we use it to coherently control actual qubits encoded in the spin of single electrons confined in silicon quantum dots^7-9 and find that the cryogenic control chip achieves the same fidelity as commercial instruments at room temperature. Furthermore, we demonstrate the capabilities of the control chip by programming a number of benchmarking protocols, as well as the Deutsch-Josza algorithm¹⁰, on a two-qubit quantum processor. These results open up the way towards a fully integrated, scalable silicon-based quantum computer.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Probing hole spin transport of disorder quantum dots via Pauli spin-blockade in standard silicon transistors

Single hole transport and spin detection is achievable in standard p-type silicon transistors owing to the strong orbital quantization of disorder based quantum dots. Through the use of the well acting as a pseudo-gate, we discover the formation of a double-quantum dot system exhibiting Pauli spin-blockade and investigate the magnetic field dependence of the leakage current. This enables attributes that are key to hole spin state control to be determined, where we calculate a tunnel couplingt_cof 57μeV and a short spin-orbit lengthl_SOof 250 nm. The demonstrated strong spin-orbit interaction at the interface when using disorder based quantum dots supports electric-field mediated control. These results provide further motivation that a readily scalable platform such as industry standard silicon technology can be used to investigate interactions which are useful for quantum information processing.

Radio-frequency single electron transistors in physically defined silicon quantum dots with a sensitive phase response

Radio-frequency reflectometry techniques are instrumental for spin qubit readout in semiconductor quantum dots. However, a large phase response is difficult to achieve in practice. In this work, we report radio-frequency single electron transistors using physically defined quantum dots in silicon-on-insulator. We study quantum dots which do not have the top gate structure considered to hinder radio frequency reflectometry measurements using physically defined quantum dots. Based on the model which properly takes into account the parasitic components, we precisely determine the gate-dependent device admittance. Clear Coulomb peaks are observed in the amplitude and the phase of the reflection coefficient, with a remarkably large phase signal of ∼45°. Electrical circuit analysis indicates that it can be attributed to a good impedance matching and a detuning from the resonance frequency. We anticipate that our results will be useful in designing and simulating reflectometry circuits to optimize qubit readout sensitivity and speed.