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Once called a "classically non-describable two-valuedness" by Pauli , the electron spin is a natural resource for long-lived quantum information since it is mostly impervious to electric fluctuations and can be replicated in large arrays using silicon quantum dots, which offer high-fidelity control. Paradoxically, one of the most convenient control strategies is the integration of nanoscale magnets to artificially enhance the coupling between spins and electric field, which in turn hampers the spin's noise immunity and adds architectural complexity. Here we demonstrate a technique that enables a \emph{switchable} interaction between spins and orbital motion of electrons in silicon quantum dots, without the presence of a micromagnet. The naturally weak effects of the relativistic spin-orbit interaction in silicon are enhanced by more than three orders of magnitude by controlling the energy quantisation of electrons in the nanostructure, enhancing the orbital motion. Fast electrical control is demonstrated in multiple devices and electronic configurations, highlighting the utility of the technique. Using the electrical drive we achieve coherence time $T_{2,{\rm Hahn}}\approx50 \mu$s, fast single-qubit gates with ${T_{\pi/2}=3}$ ns and gate fidelities of 99.93 % probed by randomised benchmarking. The higher gate speeds and better compatibility with CMOS manufacturing enabled by on-demand electric control improve the prospects for realising scalable silicon quantum processors.

The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom “flip-flop” qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.

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., Nature Communications, 12 (1), ISSN:2041-1723

One of the key pathways towards scalability of spin-based quantum computing systems lies in achieving long-range interactions between electrons and increasing their inter-connectivity. Coherent spin transport is one of the most promising strategies to achieve this architectural advantage. Experimental results have previously demonstrated high fidelity transportation of spin qubits between two quantum dots in silicon and identified possible sources of error. In this theoretical study, we investigate these errors and analyze the impact of tunnel coupling, magnetic field and spin-orbit effects on the spin transfer process. The interplay between these effects gives rise to double dot configurations that include regimes of enhanced decoherence that should be avoided for quantum information processing. These conclusions permit us to extrapolate previous experimental conclusions and rationalize the future design of large scale quantum processors., 18 pages, 9 figures

Recent days have witnessed significant interests in applying quantum-enhanced techniques for solving a variety of machine learning tasks. Variational methods that use quantum resources of imperfect quantum devices with the help of classical computing techniques are popular for supervised learning. Variational quantum classification (VQC) is one of such methods with possible quantum advantage in using quantum-enhanced features that are hard to compute by classical methods. Its performance depends on the mapping of classical features into a quantum-enhanced feature space. Although there have been many quantum-mapping functions proposed so far, there is little discussion on efficient mapping of discrete features, such as age group, zip code, and others, which are often significant for classifying datasets of interest. We first introduce the use of quantum random-access coding (QRAC) to map such discrete features efficiently into limited number of qubits for VQC. In numerical simulations, we present a range of encoding strategies and demonstrate their limitations and capabilities. We experimentally show that QRAC can help speeding up the training of VQC by reducing its parameters via saving on the number of qubits for the mapping. We confirm the effectiveness of the QRAC in VQC by experimenting on classification of real-world datasets with both simulators and real quantum devices.

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). 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). 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. We coherently control the qubits using electrically driven spin resonance in isotopically enriched silicon. 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. 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. 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.

Nuclear spins were among the first physical platforms to be considered for quantum information processing

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.

Wide-field magnetometry can be realized by imaging the optically-detected magnetic resonance of diamond nitrogen vacancy (NV) center ensembles. However, NV ensemble inhomogeneities significantly limit the magnetic-field sensitivity of these measurements. We demonstrate a double-double quantum (DDQ) driving technique to facilitate wide-field magnetic imaging of dynamic magnetic fields at a micron scale. DDQ imaging employs four-tone radio frequency pulses to suppress inhomogeneity-induced variations of the NV resonant response. As a proof-of-principle, we use the DDQ technique to image the dc magnetic field produced by individual magnetic-nanoparticles tethered by single DNA molecules to a diamond sensor surface. This demonstrates the efficacy of the diamond NV ensemble system in high-frame-rate magnetic microscopy, as well as single-molecule biophysics applications.

The performance requirements for fault-tolerant quantum computing are very stringent. Qubits must be manipulated, coupled, and measured with error rates well below 1%. For semiconductor implementations, silicon quantum dot spin qubits have demonstrated average single-qubit Clifford gate error rates that approach this threshold, notably with error rates of 0.14% in isotopically enriched $^{28}$Si/SiGe devices. This gate performance, together with high-fidelity two-qubit gates and measurements, is only known to meet the threshold for fault-tolerant quantum computing in some architectures when assuming that the noise is incoherent, and still lower error rates are needed to reduce overhead. Here we experimentally show that pulse engineering techniques, widely used in magnetic resonance, improve average Clifford gate error rates for silicon quantum dot spin qubits to 0.043%,a factor of 3 improvement on previous best results for silicon quantum dot devices. By including tomographically complete measurements in randomised benchmarking, we infer a higher-order feature of the noise called the unitarity, which measures the coherence of noise. This in turn allows us to theoretically predict that average gate error rates as low as 0.026% may be achievable with further pulse improvements. These fidelities are ultimately limited by Markovian noise, which we attribute to charge noise emanating from the silicon device structure itself, or the environment.

We present an imaging modality that enables detection of magnetic moments and their resulting stray magnetic fields. We use wide-field magnetic imaging that employs a diamond-based magnetometer and has combined magneto-optic detection (e.g. magneto-optic Kerr effect) capabilities. We employ such an instrument to image magnetic (stripe) domains in multilayered ferromagnetic structures., 7 pages

Combatting noise on the platform The potential of quantum computers to solve problems that are intractable for classical computers has driven advances in hardware fabrication. In practice, the main challenge in realizing quantum computers is that general, many-particle quantum states are highly sensitive to noise, which inevitably causes errors in quantum algorithms. Some noise sources are inherent to the current materials platforms. de Leon et al. review some of the materials challenges for five platforms for quantum computers and propose directions for their solution. Science , this issue p. eabb2823

The introduction of stable isotopes in the fabrication of semiconductor nanowires provides an additional degree of freedom to manipulate their basic properties, design an entirely new class of devices, and highlight subtle but important nanoscale and quantum phenomena. With this perspective, we report on phonon engineering in metal-catalyzed silicon nanowires with tailor-made isotopic compositions grown using isotopically enriched silane precursors 28SiH4, 29SiH4, and 30SiH4 with purity better than 99.9%. More specifically, isotopically mixed nanowires 28Six30Si1–x with a composition close to the highest mass disorder (x ∼ 0.5) were investigated. The effect of mass disorder on the phonon behavior was elucidated and compared to that in isotopically pure 29Si nanowires having a similar reduced mass. We found that the disorder-induced enhancement in phonon scattering in isotopically mixed nanowires is unexpectedly much more significant than in bulk crystals of close isotopic compositions. This effect is explained by a nonuniform distribution of 28Si and 30Si isotopes in the grown isotopically mixed nanowires with local compositions ranging from x = ∼0.25 to 0.70. Moreover, we also observed that upon heating, phonons in 28Six30Si1–x nanowires behave remarkably differently from those in 29Si nanowires suggesting a reduced thermal conductivity induced by mass disorder. Using Raman nanothermometry, we found that the thermal conductivity of isotopically mixed 28Six30Si1–x nanowires is ∼30% lower than that of isotopically pure 29Si nanowires in agreement with theoretical predictions., O.M. acknowledges funding from NSERC-Canada (Discovery Grants) and Canada Research Chair, Fondation de l’École Polytechnique de Montréal. The work at Keio was supported in part by the Grant-in-Aid for Scientific Research by MEXT, in part by NanoQuine, in part by FIRST, and in part by JSPS Core-to-Core Program. J.A. acknowledges the funding from the Generalitat de Catalunya 2014 SGR 1638. M.d.l.M. thanks the CSIC Jae-Predoc program. J.A. and M.d.l.M. thank funding from Spanish MINECO MAT2014-51480-ERC.

The quantum coherence and gate fidelity of electron spin qubits in semiconductors is often limited by noise arising from coupling to a bath of nuclear spins. Isotopic enrichment of spin-zero nuclei such as $^{28}$Si has led to spectacular improvements of the dephasing time $T_2^*$ which, surprisingly, can extend two orders of magnitude beyond theoretical expectations. Using a single-atom $^{31}$P qubit in enriched $^{28}$Si, we show that the abnormally long $T_2^*$ is due to the controllable freezing of the dynamics of the residual $^{29}$Si nuclei close to the donor. Our conclusions are supported by a nearly parameter-free modeling of the $^{29}$Si nuclear spin dynamics, which reveals the degree of back-action provided by the electron spin as it interacts with the nuclear bath. This study clarifies the limits of ergodic assumptions in analyzing many-body spin-problems under conditions of strong, frequent measurement, and provides novel strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors., 11 pages, 5 figures

We report detection and coherent control of a single proton nuclear spin using an electronic spin of the nitrogen-vacancy (NV) center in diamond as a quantum sensor. In addition to determining the NV-proton hyperfine parameters by employing multipulse sequences, we polarize and coherently rotate the single proton spin, and detect an induced free precession. Observation of free induction decays is an essential ingredient for high resolution proton nuclear magnetic resonance, and the present work extends it to the atomic scale. We also discuss the origin of the proton as incorporation during chemical vapor deposition growth, which provides an opportunity to use protons in diamond as built-in quantum memories coupled with the NV center., 6 pages, 4 figures. Published in Applied Physics Letters

Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of $^{31}$P donors implanted in silicon. The coupling strength, $J = 32.06 \pm 0.06$ MHz, is measured spectroscopically with unprecedented precision. Since the coupling is weaker than the electron-nuclear hyperfine coupling $A \approx 90$ MHz which detunes the two electrons, a native two-qubit Controlled-Rotation gate can be obtained via a simple electron spin resonance pulse. This scheme is insensitive to the precise value of $J$, which makes it suitable for the scale-up of donor-based quantum computers in silicon that exploit the Metal-Oxide-Semiconductor fabrication protocols commonly used in the classical electronics industry., 10 pages, 5 figures, plus Supplementary Information. v2 contains additional references, and a simpler explanation of two-qubit CROT gates for donors in silicon

Quantum gates between spin qubits can be implemented leveraging the natural Heisenberg exchange interaction between two electrons in contact with each other. This interaction is controllable by electrically tailoring the overlap between electronic wavefunctions in quantum dot systems, as long as they occupy neighbouring dots. An alternative route is the exploration of superexchange - the coupling between remote spins mediated by a third idle electron that bridges the distance between quantum dots. We experimentally demonstrate direct exchange coupling and provide evidence for second neighbour mediated superexchange in a linear array of three single-electron spin qubits in silicon, inferred from the electron spin resonance frequency spectra. We confirm theoretically through atomistic modeling that the device geometry only allows for sizeable direct exchange coupling for neighbouring dots, while next nearest neighbour coupling cannot stem from the vanishingly small tail of the electronic wavefunction of the remote dots, and is only possible if mediated., 20 pages, 1.4MB, 4 figures

We characterize single nitrogen-vacancy (NV) centers created by 10-keV N+ ion implantation into diamond via thin SiO$_2$ layers working as screening masks. Despite the relatively high acceleration energy compared with standard ones (< 5 keV) used to create near-surface NV centers, the screening masks modify the distribution of N$^+$ ions to be peaked at the diamond surface [Ito et al., Appl. Phys. Lett. 110, 213105 (2017)]. We examine the relation between coherence times of the NV electronic spins and their depths, demonstrating that a large portion of NV centers are located within 10 nm from the surface, consistent with Monte Carlo simulations. The effect of the surface on the NV spin coherence time is evaluated through noise spectroscopy, surface topography, and X-ray photoelectron spectroscopy., 10 pages, 8 figures. To appear in Journal of Applied Physics (Special Topics on Materials for Quantum Technologies: Computing, Information, and Sensing)

Electron spins confined in quantum dots are an attractive system to realize high-fidelity qubits owing to their long coherence time. With the prolonged spin coherence time, however, the control fidelity can be limited by systematic errors rather than decoherence, making characterization and suppression of their influence crucial for further improvement. Here we report that the control fidelity of Si/SiGe spin qubits can be limited by the microwave-induced frequency shift of electric dipole spin resonance and it can be improved by optimization of control pulses. As we increase the control microwave amplitude, we observe a shift of the qubit resonance frequency, in addition to the increasing Rabi frequency. We reveal that this limits control fidelity with a conventional amplitude-modulated microwave pulse below 99.8%. In order to achieve a gate fidelity >99.9%, we introduce a quadrature control method, and validate this approach experimentally by randomized benchmarking. Our finding facilitates realization of an ultra-high-fidelity qubit with electron spins in quantum dots.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{2}^{\,\text{Rabi}\,}=18.6$$\end{document}T2Rabi=18.6 μs and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{2}^{* }=1.4$$\end{document}T2*=1.4 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., One of the main sources of decoherence in silicon electron spin qubits is their interaction with nearby fluctuating nuclear spins. Zhao et al. present a device made from enriched silicon to reduce the nuclear spin density and find its performance is still limited by fluctuations of residual spins.

Recent advances towards spin-based quantum computation have been primarily fuelled by elaborate isolation from noise sources, such as surrounding nuclear spins and spin-electric susceptibility, to extend spin coherence. In the meanwhile, addressable single-spin and spin-spin manipulations in multiple-qubit systems will necessitate sizable spin-electric coupling. Given background charge fluctuation in nanostructures, however, its compatibility with enhanced coherence should be crucially questioned. Here we realise a single-electron spin qubit with isotopically-enriched phase coherence time (20 microseconds) and fast electrical control speed (up to 30 MHz) mediated by extrinsic spin-electric coupling. Using rapid spin rotations, we reveal that the free-evolution dephasing is caused by charge (instead of conventional magnetic) noise featured by a 1/f spectrum over seven decades of frequency. The qubit nevertheless exhibits superior performance with single-qubit gate fidelities exceeding 99.9% on average. Our work strongly suggests that designing artificial spin-electric coupling with account taken of charge noise is a promising route to large-scale spin-qubit systems having fault-tolerant controllability.

The connection between ferromagnetic (FM) fluctuations and superconductivity has been well established in FM superconductors UCoGe and URhGe. However, this connection has not been clarified in UGe2...

Single nuclear spins in the solid state are a potential future platform for quantum computing

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers

We analyze the electron spin relaxation rate $1/T_1$ of individual ion-implanted $^{31}$P donors, in a large set of metal-oxide-semiconductor (MOS) silicon nanoscale devices, with the aim of identifying spin relaxation mechanisms peculiar to the environment of the spins. The measurements are conducted at low temperatures ($T\approx 100$~mK), as a function of external magnetic field $B_0$ and donor electrochemical potential $��_{\rm D}$. We observe a magnetic field dependence of the form $1/T_1\propto B_0^5$ for $B_0\gtrsim 3\,$ T, corresponding to the phonon-induced relaxation typical of donors in the bulk. However, the relaxation rate varies by up to two orders of magnitude between different devices. We attribute these differences to variations in lattice strain at the location of the donor. For $B_0\lesssim 3\,$T, the relaxation rate changes to $1/T_1\propto B_0$ for two devices. This is consistent with relaxation induced by evanescent-wave Johnson noise created by the metal structures fabricated above the donors. At such low fields, where $T_1>1\,$s, we also observe and quantify the spurious increase of $1/T_1$ when the electrochemical potential of the spin excited state $|\uparrow\rangle$ comes in proximity to empty states in the charge reservoir, leading to spin-dependent tunneling that resets the spin to $|\downarrow\rangle$. These results give precious insights into the microscopic phenomena that affect spin relaxation in MOS nanoscale devices, and provide strategies for engineering spin qubits with improved spin lifetimes., 14 pages, 8 figures. Version 2 has extensive text revisions, typo corrections, and two extra authors

Single nuclear spins in the solid state have long been envisaged as a platform for quantum computing, due to their long coherence times and excellent controllability. Measurements can be performed via localised electrons, for example those in single atom dopants or crystal defects. However, establishing long-range interactions between multiple dopants or defects is challenging. Conversely, in lithographically-defined quantum dots, tuneable interdot electron tunnelling allows direct coupling of electron spin-based qubits in neighbouring dots. Moreover, compatibility with semiconductor fabrication techniques provides a compelling route to scaling to large numbers of qubits. Unfortunately, hyperfine interactions are typically too weak to address single nuclei. Here we show that for electrons in silicon metal-oxide-semiconductor quantum dots the hyperfine interaction is sufficient to initialise, read-out and control single silicon-29 nuclear spins, yielding a combination of the long coherence times of nuclear spins with the flexibility and scalability of quantum dot systems. We demonstrate high-fidelity projective readout and control of the nuclear spin qubit, as well as entanglement between the nuclear and electron spins. Crucially, we find that both the nuclear spin and electron spin retain their coherence while moving the electron between quantum dots, paving the way to long range nuclear-nuclear entanglement via electron shuttling. Our results establish nuclear spins in quantum dots as a powerful new resource for quantum processing.

Once the periodic properties of elements were unveiled, chemical behaviour could be understood in terms of the valence of atoms. Ideally, this rationale would extend to quantum dots, and quantum computation could be performed by merely controlling the outer-shell electrons of dot-based qubits. Imperfections in semiconductor materials disrupt this analogy, so real devices seldom display a systematic many-electron arrangement. We demonstrate here an electrostatically confined quantum dot that reveals a well defined shell structure. We observe four shells (31 electrons) with multiplicities given by spin and valley degrees of freedom. Various fillings containing a single valence electron—namely 1, 5, 13 and 25 electrons—are found to be potential qubits. An integrated micromagnet allows us to perform electrically-driven spin resonance (EDSR), leading to faster Rabi rotations and higher fidelity single qubit gates at higher shell states. We investigate the impact of orbital excitations on single qubits as a function of the dot deformation and exploit it for faster qubit control., Quantum dots are often referred to as “artificial atoms” as they create zero-dimensional traps for electrons, with characteristic atom-like spectra. Leon et al. demonstrate that higher shell and orbital states of a multi-electron silicon quantum dot with better control fidelity than single electron dots.

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, e.g. in chemistry, medicine, materials science and mining. Nuclear spins also featured in early ideas and demonstrations of quantum information processing. Scaling up these ideas requires controlling individual nuclei, which can be detected when coupled to an electron. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods relied upon transducing electric signals into magnetic fields via the electron-nuclear hyperfine interaction, which severely affects the nuclear coherence. Here we demonstrate the coherent quantum control of a single antimony (spin-7/2) nucleus, using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea first proposed in 1961 but never realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction, in the presence of lattice strain, results in coherent nuclear spin transitions. The spin dephasing time, 0.1 seconds, surpasses by orders of magnitude those obtained via methods that require a coupled electron spin for electrical drive. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots could pave the way to scalable nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields., Comment: Main text and figures followed by methods, extended data, and supplementary information

We present isotopically engineered Si-28/SiGe heterostructures for development of silicon-based quantum computers using a standard silicon CMOS integration technology. Our Si-28 quantum-wells are well-strained and demonstrate high electron mobility and large valley-splitting. These properties provide promising platforms for realization of highly integrated spin qubits working together with silicon CMOS circuits.

We present a scalable strategy to manufacture quantum computer devices, by encoding quantum information in the combined electron-nuclear spin state of individual ion-implanted phosphorus dopant atoms in silicon. Our strategy allows a typical pitch between quantum bits of order 200 nm, and retains compatibility with the standard fabrication processes adopted in classical CMOS nanoelectronic devices. We theoretically predict fast and high-fidelity quantum logic operations, and present preliminary experimental progress towards the realization of a “flip-flop” qubit system.

The effect of fluorine (F) on diffusion of boron (B) in silicon (Si) is investigated by secondary ion mass spectrometry of Si, B, and F diffusion using pre-amorphized natSi/28Si isotope multilayers that are co-implanted with B and F. By the presence of F, diffusion of B is suppressed while that of Si is enhanced. A quantitative analysis of the experimental results based on our diffusion model shows that the suppression of B diffusion is due to (1) Si interstitial undersaturation caused by the time-dependent formation and dissolution of F-vacancy (FV) clusters and (2) direct interaction between B and FV clusters. The model developed in this study enables an accurate simulation of B and Si diffusion in the presence of F in Si.

Silicon isotope engineering invokes a new paradigm into material science for nanoscale device applications [1]. The development of planer CMOS devices confronts an immediate issue of its downscaling limit, requiring a basal changeover to three-dimensional (3D) vertical transistors as a possible solution. General gate-all-around transistors involve formation of reliable gate-oxide film surrounding Si nanopillar structures. For the precise 3D process simulator, silicon isotopes are used as a self-diffusive marker for experimental determination of its model parameters. Recent advancement of atom probe tomography enables nearly atomic-resolution mass spectroscopy for 3D limited areas, together with great sensitivity to different Si isotopic mass [2]. By extending this technique to isotopically programmed Si nanopillars, individual self-diffused Si isotopes were visualized at MBE-grown isotopic layer interface [3, 4]. Recently, our quantitative evaluation revealed that Si self-diffusivity in gate-oxidized nanopillars was the same as the one measured for standard planar oxidation despite of its high interface-to-volume ratio [4]. In addition, silicon isotope engineering provides a crucial solution to eliminate unwanted decoherence for silicon quantum computers (QCs). Strong compatibility with industrial CMOS technology is expected to satisfy a scalability criterion significant for realizing practical QCs. In order to support the Si-QC research, we adopted silicon isotope engineering to tailor high-quality CVD-grown 28Si epi-wafers [1], where state-of-the-art Si-MOS nanoelectronic devices were implemented to demonstrate two-qubits operations encoded by single donor electron and nuclear spins [5]. Following an original Kane’s proposal, selective control of the electron spins was successfully achieved by adding a local gate bias thanks to the Stark tuning [6], while the nuclear-spin resonance has been recently shown to be driven by local electric fields in the presence of lattice strain [7]. Additionally, the isotopically enriched wafers were, in parallel, employed to demonstrate single and two spin-qubit operations in 28Si-MOS quantum dots (QDs) that were defined by standard CMOS lithography [8]. A series of proof-of-concepts experiments has given a boost to several proposals of Si-QC architectures based on advanced manufacturing technology [9]. Meanwhile, an alternative approach following conventional III-V QDs was made to obtain buried-type QDs utilizing strained-Si/SiGe quantum-well (QW) heterostructures, which are placed away from gate-oxide interface traps that can work as sources for charge noise to disturb spin-qubit operation. In fact, we accomplished isotope enrichment of Si-QW layer to efficiently remove magnetic nuclear-spin noise. As a consequence, the electron-spin dephasing time was prolonged to T 2 * ~ 20 ms for 28Si/SiGe QDs, where local single-spin controllability was introduced by a magnetic-field gradient from an on-chip micro-magnet [10]. These 28Si-QD devices amenable to several technical improvements have recorded the highest single-spin gate fidelities of 99.93% for 28Si/SiGe QDs [10] and 99.96% for 28Si-MOS QDs [11], respectively. Concurrently, it was revealed that inherent charge noise and/or residual nuclear-spin noise induced spin-resonance frequency fluctuations during the benchmark test executions. For higher-fidelity operations, including spin-qubit readout and initialization, low-energy excited states responsible for Si valley degeneracy should be also well-lifted by rendering the QD confinement atomically sharp. In these contexts, we will present recent development of high-quality 28Si/SiGe QWs appropriate for the silicon quantum information research. This work has been in part supported by MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant Number JPMXS0118069228 and the Center for Spintronics Research Network, Keio University. The authors acknowledge fruitful collaborations with Yasuyoshi Nagai’s group, Seigo Tarucha’s group, Mark Eriksson’s group, Andrew Dzurak’s group and Andrea Morello’s group. [1] K. M. Itoh and H. Watanabe, MRS Communications 4, 143 (2014). [2] Y. Shimizu et al., J. Appl. Phys. 106, 076102 (2009). [3] T. Südkamp et al., J. Appl. Phys. 123, 161515 (2018). [4] R. Kiga et al., J. Appl. Phys. under review. [5] J.T. Mohonen et al., Nature Nanotechnol. 9, 986 (2014). [6] A. Laucht et al., Sci. Adv. 1, e1500022 (2015). [7] S. Asaad et al., arXiv:1906.01086. [8] M. Veldhorst et al., Nature Nanotechnol. 9, 981 (2014); M. Veldhorst et al., Nature 526, 410 (2015). [9] L.M.K. Vandersypen et al., npj Quantum Information 3, 34 (2017); M. Veldhorst et al., Nature Comm. 8, 1766 (2017); R. Li et al., Sci. Adv. 4, eaar3960 (2018). [10] J. Yoneda et al., Nature Nanotechnol. 13, 102 (2018). [11] C.H. Yang et al., Nature Electronics 2, 151 (2019).