Entanglement and control of single nuclear spins in isotopically engineered silicon carbide

Robust Nuclear Spin Polarization via Ground-State Level Anticrossing of Boron Vacancy Defects in Hexagonal Boron Nitride

Nuclear spin polarization plays a crucial role in quantum information processing and quantum sensing. In this work, we demonstrate a robust and efficient method for nuclear spin polarization with boron vacancy (V_{B}^{-}) defects in hexagonal boron nitride (h-BN) using ground-state level anticrossing (GSLAC). We show that GSLAC-assisted nuclear polarization can be achieved with significantly lower laser power than excited-state level anticrossing, making the process experimentally more viable. Furthermore, we have demonstrated direct optical readout of nuclear spins for V_{B}^{-} in h-BN. Our findings suggest that GSLAC is a promising technique for the precise control and manipulation of nuclear spins in V_{B}^{-} defects in h-BN.

Exploring High-Spin Color Centers in Wide Band Gap Semiconductors SiC: A Comprehensive Magnetic Resonance Investigation (EPR and ENDOR Analysis)

High-spin defects (color centers) in wide-gap semiconductors are considered as a basis for the implementation of quantum technologies due to the unique combination of their spin, optical, charge, and coherent properties. A silicon carbide (SiC) crystal can act as a matrix for a wide variety of optically active vacancy-type defects, which manifest themselves as single-photon sources or spin qubits. Among the defects, the nitrogen-vacancy centers (NV) are of particular importance. This paper is devoted to the application of the photoinduced electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) techniques at a high-frequency range (94 GHz) to obtain unique information about the nature and properties of NV defects in SiC crystal of the hexagonal 4H and 6H polytypes. Selective excitation by microwave and radio frequency pulses makes it possible to determine the microscopic structure of the color center, the zero-field splitting constant (D = 1.2-1.3 GHz), the phase coherence time (T2), and the values of hyperfine (≈1.1 MHz) and quadrupole (Cq ≈ 2.45 MHz) interactions and to define the isotropic (a = -1.2 MHz) and anisotropic (b = 10-20 kHz) contributions of the electron-nuclear interaction. The obtained data are essential for the implementation of the NV defects in SiC as quantum registers, enabling the optical initialization of the electron spin to establish spin-photon interfaces. Moreover, the combination of optical, microwave, and radio frequency resonant effects on spin centers within a SiC crystal shows the potential for employing pulse EPR and ENDOR sequences to implement protocols for quantum computing algorithms and gates.

Relativistic Douglas-Kroll-Hess calculations of hyperfine interactions within first-principles multireference methods

A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods, including spin-orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin-orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).

Enhancement of silicon vacancy fluorescence intensity in silicon carbide using a dielectric cavity

Over the past decades, spin qubits in silicon carbide (SiC) have emerged as promising platforms for a wide range of quantum technologies. The fluorescence intensity holds significant importance in the performance of quantum photonics, quantum information process, and sensitivity of quantum sensing. In this work, a dual-layer Au/SiO2 dielectric cavity is employed to enhance the fluorescence intensity of a shallow silicon vacancy ensemble in 4H-SiC. Experimental results demonstrate an effective fourfold augmentation in fluorescence counts at saturating laser power, corroborating our theoretical predictions. Based on this, we further investigate the influence of dielectric cavities on the contrast and linewidth of optically detected magnetic resonance (ODMR). There is a 1.6-fold improvement in magnetic field sensitivity. In spin echo experiments, coherence times remain constant regardless of the thickness of dielectric cavities. These experiments pave the way for broader applications of dielectric cavities in SiC-based quantum technologies.

Single-Shot Readout of a Nuclear Spin in Silicon Carbide

Solid-state qubits with a photonic interface is very promising for quantum networks. Color centers in silicon carbide have shown excellent optical and spin coherence, even when integrated with membranes and nanostructures. Additionally, nuclear spins coupled with electron spins can serve as long-lived quantum memories. Pioneering work previously has realized the initialization of a single nuclear spin and demonstrated its entanglement with an electron spin. In this Letter, we report the first realization of single-shot readout for a nuclear spin in SiC. We obtain a deterministic nuclear spin initialization and readout fidelity of 94.95% with a measurement duration of 1 ms. With a dual-step readout scheme, we obtain a readout fidelity as high as 99.03% within 0.28 ms by sacrificing the success efficiency. Our Letter complements the experimental toolbox of harnessing both electron and nuclear spins in SiC for future quantum networks.

Experimental Generation of Spin-Photon Entanglement in Silicon Carbide

A solid-state approach for quantum networks is advantageous, as it allows the integration of nanophotonics to enhance the photon emission and the utilization of weakly coupled nuclear spins for long-lived storage. Silicon carbide, specifically point defects within it, shows great promise in this regard due to the easy of availability and well-established nanofabrication techniques. Despite of remarkable progresses made, achieving spin-photon entanglement remains a crucial aspect to be realized. In this Letter, we experimentally generate entanglement between a silicon vacancy defect in silicon carbide and a scattered single photon in the zero-phonon line. The spin state is measured by detecting photons scattered in the phonon sideband. The photonic qubit is encoded in the time-bin degree of freedom and measured using an unbalanced Mach-Zehnder interferometer. Photonic correlations not only reveal the quality of the entanglement but also verify the deterministic nature of the entanglement creation process. By harnessing two pairs of such spin-photon entanglement, it becomes straightforward to entangle remote quantum nodes at long distance.

Mapping a 50-spin-qubit network through correlated sensing

Spins associated to optically accessible solid-state defects have emerged as a versatile platform for exploring quantum simulation, quantum sensing and quantum communication. Pioneering experiments have shown the sensing, imaging, and control of multiple nuclear spins surrounding a single electron spin defect. However, the accessible size of these spin networks has been constrained by the spectral resolution of current methods. Here, we map a network of 50 coupled spins through high-resolution correlated sensing schemes, using a single nitrogen-vacancy center in diamond. We develop concatenated double-resonance sequences that identify spin-chains through the network. These chains reveal the characteristic spin frequencies and their interconnections with high spectral resolution, and can be fused together to map out the network. Our results provide new opportunities for quantum simulations by increasing the number of available spin qubits. Additionally, our methods might find applications in nano-scale imaging of complex spin systems external to the host crystal.

Ligand field design enables quantum manipulation of spins in Ni2+ complexes

Creating the next generation of quantum systems requires control and tunability, which are key features of molecules. To design these systems, one must consider the ground-state and excited-state manifolds. One class of systems with promise for quantum sensing applications, which require water solubility, are d8 Ni2+ ions in octahedral symmetry. Yet, most Ni2+ complexes feature large zero-field splitting, precluding manipulation by commercial microwave sources due to the relatively large spin-orbit coupling constant of Ni2+ (630 cm-1). Since low lying excited states also influence axial zero-field splitting, D, a combination of strong field ligands and rigidly held octahedral symmetry can ameliorate these challenges. Towards these ends, we performed a theoretical and computational analysis of the electronic and magnetic structure of a molecular qubit, focusing on the impact of ligand field strength on D. Based on those results, we synthesized 1, [Ni(ttcn)2](BF4)2 (ttcn = 1,4,7-trithiacyclononane), which we computationally predict will have a small D (Dcalc = +1.15 cm-1). High-field high-frequency electron paramagnetic resonance (EPR) data yield spin Hamiltonian parameters: gx = 2.1018(15), gx = 2.1079(15), gx = 2.0964(14), D = +0.555(8) cm-1 and E = +0.072(5) cm-1, which confirm the expected weak zero-field splitting. Dilution of 1 in the diamagnetic Zn analogue, [Ni0.01Zn0.99(ttcn)2](BF4)2 (1') led to a slight increase in D to ∼0.9 cm-1. The design criteria in minimizing D in 1via combined computational and experimental methods demonstrates a path forward for EPR and optical addressability of a general class of S = 1 spins.

Isotope engineering for spin defects in van der Waals materials

Spin defects in van der Waals materials offer a promising platform for advancing quantum technologies. Here, we propose and demonstrate a powerful technique based on isotope engineering of host materials to significantly enhance the coherence properties of embedded spin defects. Focusing on the recently-discovered negatively charged boron vacancy center ([Formula: see text]) in hexagonal boron nitride (hBN), we grow isotopically purified h10B15N crystals. Compared to [Formula: see text] in hBN with the natural distribution of isotopes, we observe substantially narrower and less crowded [Formula: see text] spin transitions as well as extended coherence time T2 and relaxation time T1. For quantum sensing, [Formula: see text] centers in our h10B15N samples exhibit a factor of 4 (2) enhancement in DC (AC) magnetic field sensitivity. For additional quantum resources, the individual addressability of the [Formula: see text] hyperfine levels enables the dynamical polarization and coherent control of the three nearest-neighbor 15N nuclear spins. Our results demonstrate the power of isotope engineering for enhancing the properties of quantum spin defects in hBN, and can be readily extended to improving spin qubits in a broad family of van der Waals materials.

First-Principles Investigation of Near-Surface Divacancies in Silicon Carbide

The realization of quantum sensors using spin defects in semiconductors requires a thorough understanding of the physical properties of the defects in the proximity of surfaces. We report a study of the divacancy (VSiVC) in 3C-SiC, a promising material for quantum applications, as a function of surface reconstruction and termination with -H, -OH, -F and oxygen groups. We show that a VSiVC close to hydrogen-terminated (2 × 1) surfaces is a robust spin-defect with a triplet ground state and no surface states in the band gap and with small variations of many of its physical properties relative to the bulk, including the zero-phonon line and zero-field splitting. However, the Debye-Waller factor decreases in the vicinity of the surface and our calculations indicate it may be improved by strain-engineering. Overall our results show that the VSiVC close to SiC surfaces is a promising spin defect for quantum applications, similar to its bulk counterpart.

Ultra-narrow inhomogeneous spectral distribution of telecom-wavelength vanadium centres in isotopically-enriched silicon carbide

Spin-active quantum emitters have emerged as a leading platform for quantum technologies. However, one of their major limitations is the large spread in optical emission frequencies, which typically extends over tens of GHz. Here, we investigate single V4+ vanadium centres in 4H-SiC, which feature telecom-wavelength emission and a coherent S = 1/2 spin state. We perform spectroscopy on single emitters and report the observation of spin-dependent optical transitions, a key requirement for spin-photon interfaces. By engineering the isotopic composition of the SiC matrix, we reduce the inhomogeneous spectral distribution of different emitters down to 100 MHz, significantly smaller than any other single quantum emitter. Additionally, we tailor the dopant concentration to stabilise the telecom-wavelength V4+ charge state, thereby extending its lifetime by at least two orders of magnitude. These results bolster the prospects for single V emitters in SiC as material nodes in scalable telecom quantum networks.

Enhancing Coherence Times of Chromophore-Radical Molecular Qubits and Qudits by Rational Design

An important criterion for quantum operations is long qubit coherence times. To elucidate the influence of molecular structure on the coherence times of molecular spin qubits and qudits, a series of molecules featuring perylenediimide (PDI) chromophores covalently linked to stable nitroxide radicals were synthesized and investigated by pulse electron paramagnetic resonance spectroscopy. Photoexcitation of PDI in these systems creates an excited quartet state (Q) followed by a spin-polarized doublet ground state (D0), which hold promise as spin qudits and qubits, respectively. By tailoring the molecular structure of these spin qudit/qubit candidates by selective deuteration and eliminating intramolecular motion, coherence times of Tm = 9.1 ± 0.3 and 4.2 ± 0.3 μs at 85 K for D0 and Q, respectively, are achieved. These coherence times represent a nearly 3-fold enhancement compared to those of the initial molecular design. This approach offers a rational structural design protocol for effectively extending coherence times in molecular spin qudits/qubits.

Van der Waals isotope heterostructures for engineering phonon polariton dispersions

Element isotopes are characterized by distinct atomic masses and nuclear spins, which can significantly influence material properties. Notably, however, isotopes in natural materials are homogenously distributed in space. Here, we propose a method to configure material properties by repositioning isotopes in engineered van der Waals (vdW) isotopic heterostructures. We showcase the properties of hexagonal boron nitride (hBN) isotopic heterostructures in engineering confined photon-lattice waves-hyperbolic phonon polaritons. By varying the composition, stacking order, and thicknesses of h10BN and h11BN building blocks, hyperbolic phonon polaritons can be engineered into a variety of energy-momentum dispersions. These confined and tailored polaritons are promising for various nanophotonic and thermal functionalities. Due to the universality and importance of isotopes, our vdW isotope heterostructuring method can be applied to engineer the properties of a broad range of materials.

Characterizing Temperature and Strain Variations with Qubit Ensembles for Their Robust Coherence Protection

Solid-state spin defects, especially nuclear spins with potentially achievable long coherence times, are compelling candidates for quantum memories and sensors. However, their current performances are still limited by dephasing due to variations of their intrinsic quadrupole and hyperfine interactions. We propose an unbalanced echo to overcome this challenge by using a second spin to refocus variations of these interactions while preserving the quantum information stored in the nuclear spin free evolution. The unbalanced echo can be used to probe the temperature and strain distribution in materials. We develop first-principles methods to predict variations of these interactions and reveal their correlation over large temperature and strain ranges. Experiments performed in an ensemble of ∼10^{10} nuclear spins in diamond demonstrate a 20-fold dephasing time increase, limited by other noise sources. We further numerically show that our method can refocus even stronger noise variations than present in our experiments.

Experimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration

Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.

Layered materials as a platform for quantum technologies

Layered materials are taking centre stage in the ever-increasing research effort to develop material platforms for quantum technologies. We are at the dawn of the era of layered quantum materials. Their optical, electronic, magnetic, thermal and mechanical properties make them attractive for most aspects of this global pursuit. Layered materials have already shown potential as scalable components, including quantum light sources, photon detectors and nanoscale sensors, and have enabled research of new phases of matter within the broader field of quantum simulations. In this Review we discuss opportunities and challenges faced by layered materials within the landscape of material platforms for quantum technologies. In particular, we focus on applications that rely on light-matter interfaces.

Quantum sensing of radio-frequency signal with NV centers in SiC

Silicon carbide is an emerging platform for quantum technologies that provides wafer scale and low-cost industrial fabrication. The material also hosts high-quality defects with long coherence times that can be used for quantum computation and sensing applications. Using an ensemble of nitrogen-vacancy centers and an XY8-2 correlation spectroscopy approach, we demonstrate a room-temperature quantum sensing of an artificial AC field centered at ~900 kHz with a spectral resolution of 10 kHz. Implementing the synchronized readout technique, we further extend the frequency resolution of our sensor to 0.01 kHz. These results pave the first steps for silicon carbide quantum sensors toward low-cost nuclear magnetic resonance spectrometers with a wide range of practical applications in medical, chemical, and biological analysis.

1H multiple quantum NMR in alternating quasi-one-dimensional spin chains of hambergite

Multiple quantum (MQ) dynamics was investigated in quasi-one-dimensional ¹H zigzag spin chains in hambergite (Be₂BO₃OH) single crystals. Due to the non-linear arrangement of the spins, dipolar coupling strengths alternate along the chain. To solve the problem of MQ NMR experiments taking too much time due to extremely long ¹H spin-lattice relaxation times, the samples were exposed to gamma irradiation to produce the defects accelerating the relaxation. The influence of the radiation dose was investigated. The experimental dependencies of MQ coherence intensities on the MQ excitation time in alternating spin chains were obtained and compared with the theory for inhomogeneous spin chains with nearest neighbor interactions developed earlier. The correspondence of the observed MQ dynamics to the alternating spin chain was demonstrated.

Magnetic-field-dependent spin properties of divacancy defects in silicon carbide

In recent years, spin defects in silicon carbide have become promising platforms for quantum sensing, quantum information processing and quantum networks. It has been shown that their spin coherence times can be dramatically extended with an external axial magnetic field. However, little is known about the effect of magnetic-angle-dependent coherence time, which is an essential complement to defect spin properties. Here, we investigate the optically detected magnetic resonance (ODMR) spectra of divacancy spins in silicon carbide with a magnetic field orientation. The ODMR contrast decreases as the off-axis magnetic field strength increases. We then study the coherence times of divacancy spins in two different samples with magnetic field angles, and both of the coherence times decrease with the angle. The experiments pave the way for all-optical magnetic field sensing and quantum information processing.

Optical Spin Polarization of a Narrow-Linewidth Electron-Spin Qubit in a Chromophore/Stable-Radical System

Photoexcited organic chromophores appended to stable radicals can serve as qubit and/or qudit candidates for quantum information applications. 1,6,7,12-Tetra-(4-tert-butylphenoxy)-perylene-3,4 : 9,10-bis(dicarboximide) (tpPDI) linked to a partially deuterated α,γ-bisdiphenylene-β-phenylallyl radical (BDPA-d₁₆ ) was synthesized and characterized by time-resolved optical and electron paramagnetic resonance (EPR) spectroscopies. Photoexcitation of tpPDI-BDPA-d₁₆ results in ultrafast radical-enhanced intersystem crossing to produce a quartet state (Q) followed by formation of a spin-polarized doublet ground state (D₀ ). Pulse-EPR experiments confirmed the spin multiplicity of Q and yielded coherence times of T_m =2.1±0.1 μs and 2.8±0.2 μs for Q and D₀ , respectively. BDPA-d₁₆ eliminates the dominant ¹ H hyperfine couplings, resulting in a single narrow line for both the Q and D₀ states, which enhances the spectral resolution needed for good qubit addressability.

Predicting Phonon-Induced Spin Decoherence from First Principles: Colossal Spin Renormalization in Condensed Matter

Developing a microscopic understanding of spin decoherence is essential to advancing quantum technologies. Electron spin decoherence due to atomic vibrations (phonons) plays a special role as it sets an intrinsic limit to the performance of spin-based quantum devices. Two main sources of phonon-induced spin decoherence-the Elliott-Yafet and Dyakonov-Perel mechanisms-have distinct physical origins and theoretical treatments. Here, we show calculations that unify their modeling and enable accurate predictions of spin relaxation and precession in semiconductors. We compute the phonon-dressed vertex of the spin-spin correlation function with a treatment analogous to the calculation of the anomalous electron magnetic moment in QED. We find that the vertex correction provides a giant renormalization of the electron spin dynamics in solids, greater by many orders of magnitude than the corresponding correction from photons in vacuum. Our Letter demonstrates a general approach for quantitative analysis of spin decoherence in materials, advancing the quest for spin-based quantum technologies.

Fault-tolerant operation of a logical qubit in a diamond quantum processor

Solid-state spin qubits is a promising platform for quantum computation and quantum networks^1,2. Recent experiments have demonstrated high-quality control over multi-qubit systems^3–8, elementary quantum algorithms^8–11 and non-fault-tolerant error correction^12–14. Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations^15–18. Overcoming imperfections in this way remains an important outstanding challenge for quantum science^15,19–27. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the five-qubit code with a recently discovered flag protocol that enables fault tolerance using a total of seven qubits^28–30. We encode the logical qubit using a new protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. Although future improvements in fidelity and the number of qubits will be required to suppress logical error rates below the physical error rates, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards quantum information processing based on solid-state spins.

By using a five-qubit error-correcting code with a recently discovered flag protocol, a logical qubit that is operated fault-tolerantly is realized based on solid-state spin qubits in diamond.

Generalized scaling of spin qubit coherence in over 12,000 host materials

Atomic defects in solid-state materials are promising candidates as quantum bits, or qubits. New materials are actively being investigated as hosts for new defect qubits; however, there are no unifying guidelines that can quantitatively predict qubit performance in a new material. One of the most critical property of qubits is their quantum coherence. While cluster correlation expansion (CCE) techniques are useful to simulate the coherence of electron spins in defects, they are computationally expensive to investigate broad classes of stable materials. Using CCE simulations, we reveal a general scaling relation between the electron spin coherence time and the properties of qubit host materials that enables rapid and quantitative exploration of new materials hosting spin defects.

Spin defect centers with long quantum coherence times (T₂) are key solid-state platforms for a variety of quantum applications. Cluster correlation expansion (CCE) techniques have emerged as a powerful tool to simulate the T₂ of defect electron spins in these solid-state systems with good accuracy. Here, based on CCE, we uncover an algebraic expression for T₂ generalized for host compounds with dilute nuclear spin baths under a magnetic field that enables a quantitative and comprehensive materials exploration with a near instantaneous estimate of the coherence time. We investigated more than 12,000 host compounds at natural isotopic abundance and found that silicon carbide (SiC), a prominent widegap semiconductor for quantum applications, possesses the longest coherence times among widegap nonchalcogenides. In addition, more than 700 chalcogenides are shown to possess a longer T₂ than SiC. We suggest potential host compounds with promisingly long T₂ up to 47 ms and pave the way to explore unprecedented functional materials for quantum applications.

Nuclear spin-wave quantum register for a solid-state qubit

Solid-state nuclear spins surrounding individual, optically addressable qubits^1,2 are a crucial resource for quantum networks^3-6, computation^7-11 and simulation¹². Although hosts with sparse nuclear spin baths are typically chosen to mitigate qubit decoherence¹³, developing coherent quantum systems in nuclear-spin-rich hosts enables exploration of a much broader range of materials for quantum information applications. The collective modes of these dense nuclear spin ensembles provide a natural basis for quantum storage¹⁴; however, using them as a resource for single-spin qubits has thus far remained elusive. Here, by using a highly coherent, optically addressed ¹⁷¹Yb³⁺ qubit doped into a nuclear-spin-rich yttrium orthovanadate crystal¹⁵, we develop a robust quantum control protocol to manipulate the multi-level nuclear spin states of neighbouring ⁵¹V⁵⁺ lattice ions. Via a dynamically engineered spin-exchange interaction, we polarize this nuclear spin ensemble, generate collective spin excitations, and subsequently use them to implement a quantum memory. We additionally demonstrate preparation and measurement of maximally entangled ¹⁷¹Yb-⁵¹V Bell states. Unlike conventional, disordered nuclear-spin-based quantum memories^16-24, our platform is deterministic and reproducible, ensuring identical quantum registers for all ¹⁷¹Yb³⁺ qubits. Our approach provides a framework for utilizing the complex structure of dense nuclear spin baths, paving the way towards building large-scale quantum networks using single rare-earth ion qubits^15,25-28.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

Five-second coherence of a single spin with single-shot readout in silicon carbide

An outstanding hurdle for defect spin qubits in silicon carbide (SiC) is single-shot readout, a deterministic measurement of the quantum state. Here, we demonstrate single-shot readout of single defects in SiC via spin-to-charge conversion, whereby the defect's spin state is mapped onto a long-lived charge state. With this technique, we achieve over 80% readout fidelity without pre- or postselection, resulting in a high signal-to-noise ratio that enables us to measure long spin coherence times. Combined with pulsed dynamical decoupling sequences in an isotopically purified host material, we report single-spin T₂ > 5 seconds, over two orders of magnitude greater than previously reported in this system. The mapping of these coherent spin states onto single charges unlocks both single-shot readout for scalable quantum nodes and opportunities for electrical readout via integration with semiconductor devices.

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.

Fabrication and nanophotonic waveguide integration of silicon carbide colour centres with preserved spin-optical coherence

Optically addressable spin defects in silicon carbide (SiC) are an emerging platform for quantum information processing compatible with nanofabrication processes and device control used by the semiconductor industry. System scalability towards large-scale quantum networks demands integration into nanophotonic structures with efficient spin-photon interfaces. However, degradation of the spin-optical coherence after integration in nanophotonic structures has hindered the potential of most colour centre platforms. Here, we demonstrate the implantation of silicon vacancy centres (V_Si) in SiC without deterioration of their intrinsic spin-optical properties. In particular, we show nearly lifetime-limited photon emission and high spin-coherence times for single defects implanted in bulk as well as in nanophotonic waveguides created by reactive ion etching. Furthermore, we take advantage of the high spin-optical coherences of V_Si centres in waveguides to demonstrate controlled operations on nearby nuclear spin qubits, which is a crucial step towards fault-tolerant quantum information distribution based on cavity quantum electrodynamics.

Tunable Cr4+ Molecular Color Centers

The inherent atomistic precision of synthetic chemistry enables bottom-up structural control over quantum bits, or qubits, for quantum technologies. Tuning paramagnetic molecular qubits that feature optical-spin initialization and readout is a crucial step toward designing bespoke qubits for applications in quantum sensing, networking, and computing. Here, we demonstrate that the electronic structure that enables optical-spin initialization and readout for S = 1, Cr(aryl)₄, where aryl = 2,4-dimethylphenyl (1), o-tolyl (2), and 2,3-dimethylphenyl (3), is readily translated into Cr(alkyl)₄ compounds, where alkyl = 2,2,2-triphenylethyl (4), (trimethylsilyl)methyl (5), and cyclohexyl (6). The small ground state zero field splitting values (<5 GHz) for 1-6 allowed for coherent spin manipulation at X-band microwave frequency, enabling temperature-, concentration-, and orientation-dependent investigations of the spin dynamics. Electronic absorption and emission spectroscopy confirmed the desired electronic structures for 4-6, which exhibit photoluminescence from 897 to 923 nm, while theoretical calculations elucidated the varied bonding interactions of the aryl and alkyl Cr⁴⁺ compounds. The combined experimental and theoretical comparison of Cr(aryl)₄ and Cr(alkyl)₄ systems illustrates the impact of the ligand field on both the ground state spin structure and excited state manifold, laying the groundwork for the design of structurally precise optically addressable molecular qubits.

Stability and molecular pathways to the formation of spin defects in silicon carbide

Spin defects in wide-bandgap semiconductors provide a promising platform to create qubits for quantum technologies. Their synthesis, however, presents considerable challenges, and the mechanisms responsible for their generation or annihilation are poorly understood. Here, we elucidate spin defect formation processes in a binary crystal for a key qubit candidate-the divacancy complex (VV) in silicon carbide (SiC). Using atomistic models, enhanced sampling simulations, and density functional theory calculations, we find that VV formation is a thermally activated process that competes with the conversion of silicon (VSi) to carbon monovacancies (VC), and that VV reorientation can occur without dissociation. We also find that increasing the concentration of VSi relative to VC favors the formation of divacancies. Moreover, we identify pathways to create spin defects consisting of antisite-double vacancy complexes and determine their electronic properties. The detailed view of the mechanisms that underpin the formation and dynamics of spin defects presented here may facilitate the realization of qubits in an industrially relevant material.

Room temperature coherent manipulation of single-spin qubits in silicon carbide with a high readout contrast

Spin defects in silicon carbide (SiC) with mature wafer-scale fabrication and micro/nano-processing technologies have recently drawn considerable attention. Although room-temperature single-spin manipulation of colour centres in SiC has been demonstrated, the typically detected contrast is less than 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\%$\end{document}, and the photon count rate is also low. Here, we present the coherent manipulation of single divacancy spins in 4H-SiC with a high readout contrast (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$-30\%$\end{document}) and a high photon count rate (150 kilo counts per second) under ambient conditions, which are competitive with the nitrogen-vacancy centres in diamond. Coupling between a single defect spin and a nearby nuclear spin is also observed. We further provide a theoretical explanation for the high readout contrast by analysing the defect levels and decay paths. Since the high readout contrast is of utmost importance in many applications of quantum technologies, this work might open a new territory for SiC-based quantum devices with many advanced properties of the host material.

Quantum Interfaces to the Nanoscale

Scalable quantum information systems would store, manipulate, and transmit quantum information locally and across a quantum network, but no single qubit technology is currently robust enough to perform all necessary tasks. Defect centers in solid-state materials have emerged as potential intermediaries between other physical manifestations of qubits, such as superconducting qubits and photonic qubits, to leverage their complementary advantages. It remains an open question, however, how to design and to control quantum interfaces to defect centers. Such interfaces would enable quantum information to be moved seamlessly between different physical systems. Understanding and constructing the required interfaces would, therefore, unlock the next big steps in quantum computing, sensing, and communications. In this Perspective, we highlight promising coupling mechanisms, including dipole-, phonon-, and magnon-mediated interactions, and discuss how contributions from nanotechnologists will be paramount in realizing quantum information processors in the near-term.

Universal coherence protection in a solid-state spin qubit

Decoherence limits the physical realization of qubits, and its mitigation is critical for the development of quantum science and technology. We construct a robust qubit embedded in a decoherence-protected subspace, obtained by applying microwave dressing to a clock transition of the ground-state electron spin of a silicon carbide divacancy defect. The qubit is universally protected from magnetic, electric, and temperature fluctuations, which account for nearly all relevant decoherence channels in the solid state. This culminates in an increase of the qubit's inhomogeneous dephasing time by more than four orders of magnitude (to >22 milliseconds), while its Hahn-echo coherence time approaches 64 milliseconds. Requiring few key platform-independent components, this result suggests that substantial coherence improvements can be achieved in a wide selection of quantum architectures.