One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment

An operating system for executing applications on quantum network nodes

The goal of future quantum networks is to enable new internet applications that are impossible to achieve using only classical communication1-3. Up to now, demonstrations of quantum network applications4-6 and functionalities7-12 on quantum processors have been performed in ad hoc software that was specific to the experimental setup, programmed to perform one single task (the application experiment) directly into low-level control devices using expertise in experimental physics. Here we report on the design and implementation of an architecture capable of executing quantum network applications on quantum processors in platform-independent high-level software. We demonstrate the capability of the architecture to execute applications in high-level software by implementing it as a quantum network operating system-QNodeOS-and executing test programs, including a delegated computation from a client to a server13 on two quantum network nodes based on nitrogen-vacancy (NV) centres in diamond14,15. We show how our architecture allows us to maximize the use of quantum network hardware by multitasking different applications. Our architecture can be used to execute programs on any quantum processor platform corresponding to our system model, which we illustrate by demonstrating an extra driver for QNodeOS for a trapped-ion quantum network node based on a single 40Ca+ atom16. Our architecture lays the groundwork for computer science research in quantum network programming and paves the way for the development of software that can bring quantum network technology to society.

Optical single-shot readout of spin qubits in silicon

Small registers of spin qubits in silicon can exhibit hour-long coherence times and exceeded error-correction thresholds. However, their connection to larger quantum processors is an outstanding challenge. To this end, spin qubits with optical interfaces offer key advantages: they can minimize the heat load and give access to modular quantum computing architectures that eliminate cross-talk and offer a large connectivity. Here, we implement such an efficient spin-photon interface based on erbium dopants in a nanophotonic resonator. We demonstrate optical single-shot readout of a spin in silicon whose coherence exceeds the Purcell-enhanced optical lifetime, paving the way for entangling remote spins via photon interference. As erbium dopants can emit coherent photons in the minimal-loss band of optical fibers, and tens of such qubits can be spectrally multiplexed in each resonator, the demonstrated hardware platform offers unique promise for distributed quantum information processing based on scalable, integrated silicon devices.

Cavity-assisted resonance fluorescence from a nitrogen-vacancy center in diamond

The nitrogen-vacancy center in diamond is an attractive resource for the generation of remote entangled states owing to its optically addressable and long-lived electronic spin. However, its low native fraction of coherent photon emission, ~3%, undermines the achievable spin-photon entanglement rates. Here, we couple a nitrogen-vacancy center with a narrow extrinsically-broadened linewidth (159 MHz), hosted in a micron-thin membrane, to an open microcavity. The resulting Purcell factor of ~1.8 increases the zero-phonon line fraction to over 44%. Operation in the Purcell regime, together with an efficient collection of the zero-phonon-line photons, allows resonance fluorescence to be detected for the first time without any temporal filtering. We achieve a >10 signal-to-laser background ratio. This selective enhancement of the center's zero-phonon transitions could increase spin-spin entanglement success probabilities beyond an order of magnitude compared to state-of-the-art implementations, and enable powerful quantum optics techniques such as wave-packet shaping or all-optical spin manipulation.

Metropolitan-scale heralded entanglement of solid-state qubits

A key challenge toward future quantum internet technology is connecting quantum processors at metropolitan scale. Here, we report on heralded entanglement between two independently operated quantum network nodes separated by 10 kilometers. The two nodes hosting diamond spin qubits are linked with a midpoint station via 25 kilometers of deployed optical fiber. We minimize the effects of fiber photon loss by quantum frequency conversion of the qubit-native photons to the telecom L-band and by embedding the link in an extensible phase-stabilized architecture enabling the use of the loss-resilient single-click entangling protocol. By capitalizing on the full heralding capabilities of the network link in combination with real-time feedback logic on the long-lived qubits, we demonstrate the delivery of a predefined entangled state on the nodes irrespective of the heralding detection pattern. Addressing key scaling challenges and being compatible with different qubit systems, our architecture establishes a generic platform for exploring metropolitan-scale quantum networks.

Direct-bonded diamond membranes for heterogeneous quantum and electronic technologies

Diamond has superlative material properties for a broad range of quantum and electronic technologies. However, heteroepitaxial growth of single crystal diamond remains limited, impeding integration and evolution of diamond-based technologies. Here, we directly bond single-crystal diamond membranes to a wide variety of materials including silicon, fused silica, sapphire, thermal oxide, and lithium niobate. Our bonding process combines customized membrane synthesis, transfer, and dry surface functionalization, allowing for minimal contamination while providing pathways for near unity yield and scalability. We generate bonded crystalline membranes with thickness as low as 10 nm, sub-nm interfacial regions, and nanometer-scale thickness variability over 200 by 200 μm2 areas. We measure spin coherence times T2 for nitrogen vacancy centers in 150 nm-thick bonded membranes of up to 623 ± 21 μs, suitable for advanced quantum applications. We demonstrate multiple methods for integrating high quality factor nanophotonic cavities with the diamond heterostructures, highlighting the platform versatility in quantum photonic applications. Furthermore, we show that our ultra-thin diamond membranes are compatible with total internal reflection fluorescence (TIRF) microscopy, which enables interfacing coherent diamond quantum sensors with living cells while rejecting unwanted background luminescence. The processes demonstrated herein provide a full toolkit to synthesize heterogeneous diamond-based hybrid systems for quantum and electronic technologies.

Phonon engineering of atomic-scale defects in superconducting quantum circuits

Noise within solid-state systems at low temperatures can typically be traced back to material defects. In amorphous materials, these defects are broadly described by the tunneling two-level systems (TLSs) model. TLS have recently taken on further relevance in quantum computing because they dominate the coherence limit of superconducting quantum circuits. Efforts to mitigate TLS impacts have thus far focused on circuit design, material selection, and surface treatments. Our work takes an approach that directly modifies TLS properties. This is achieved by creating an acoustic bandgap that suppresses all microwave-frequency phonons around the operating frequency of a transmon qubit. For embedded TLS strongly coupled to the transmon qubit, we measure a pronounced increase in relaxation time by two orders of magnitude, with the longest T1 time exceeding 5 milliseconds. Our work opens avenues for studying the physics of highly coherent TLS and methods for mitigating noise within solid-state quantum devices.

Stable organic radical qubits and their applications in quantum information science

The past century has witnessed the flourishing of organic radical chemistry. Stable organic radicals are highly valuable for quantum technologies thanks to their inherent room temperature quantum coherence, atomic-level designability, and fine tunability. In this comprehensive review, we highlight the potential of stable organic radicals as high-temperature qubits and explore their applications in quantum information science, which remain largely underexplored. Firstly, we summarize known spin dynamic properties of stable organic radicals and examine factors that influence their electron spin relaxation and decoherence times. This examination reveals their design principles and optimal operating conditions. We further discuss their integration in solid-state materials and surface structures, and present their state-of-the-art applications in quantum computing, quantum memory, and quantum sensing. Finally, we analyze the primary challenges associated with stable organic radical qubits and provide tentative insights to future research directions.

Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport

Solid-state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multiqubit systems are currently difficult to achieve. We describe a method for programmable control of multiqubit spin systems, in which individual nitrogen-vacancy (NV) centers in diamond nanopillars are coupled to magnetically functionalized silicon nitride mechanical resonators in a scanning probe configuration. Qubits can be entangled via interactions with nanomechanical resonators while programmable connectivity is realized via mechanical transport of qubits in nanopillars. To demonstrate the feasibility of this approach, we characterize both the mechanical properties and the magnetic field gradients around the micromagnet placed on the nanobeam resonator. We demonstrate coherent manipulation of a spin qubit in the proximity of a transported micromagnet by utilizing nuclear spin memory and use the NV center to detect the time-varying magnetic field from the oscillating micromagnet, extracting a spin-mechanical coupling of 7.7(9) Hz. With realistic improvements, the high-cooperativity regime can be reached, offering a new avenue toward scalable quantum information processing with spin qubits.

Dipolar Order Induced Electron Spin Hyperpolarization

The structure of coupled electron spin systems is of fundamental interest to many applications, including dynamic nuclear polarization (DNP), enhanced nuclear magnetic resonance (NMR), the generation of electron spin qubits for quantum information science (QIS), and quantitative studies of paramagnetic systems by electron paramagnetic resonance (EPR). However, the characterization of electron spin coupling networks is nontrivial, especially at high magnetic fields. This study focuses on a system containing high concentrations of trityl radicals that give rise to a DNP enhancement profile of 1H NMR characteristic of the presence of electron spin clusters. When this system is subject to selective microwave saturation through pump-probe ELectron DOuble Resonance (ELDOR) experiments, electron spin hyperpolarization is observed. We show that the generation of an out-of-equilibrium longitudinal dipolar order is responsible for the transient hyperpolarization of electron spins. Notably, the coupled electron spin system needs to form an AX-like system (where the difference in the Zeeman interactions of two spins is larger than their coupling interaction) such that selective microwave irradiation can generate signatures of electron spin hyperpolarization. We show that the extent of dipolar order, as manifested in the extent of electron spin hyperpolarization generated, can be altered by tuning the pump or probe pulse length, or the interpulse delay in ELDOR experiments that change the efficiency to generate or readout longitudinal dipolar order. Pump-probe ELDOR with selective saturation is an effective means for characterizing coupled electron spins forming AX-type spin systems that are foundational for DNP and quantum sensing.

Coherent electric field control of orbital state of a neutral nitrogen-vacancy center

The coherent control of the orbital state is crucial for realizing the extremely-low power manipulation of the color centers in diamonds. Herein, a neutrally-charged nitrogen-vacancy center, NV0, is proposed as an ideal system for orbital control using electric fields. The electric susceptibility in the ground state of NV0 is estimated, and found to be comparable to that in the excited state of NV-. Also, the coherent control of the orbital states of NV0 is demonstrated. The required power for orbital control is three orders of magnitude smaller than that for spin control, highlighting the potential for interfacing a superconducting qubit operated in a dilution refrigerator.

High-fidelity initialization and control of electron and nuclear spins in a four-qubit register

Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubitSWAP gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( F = 10 0 - 6 + 0 %) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to⇓ ⇓ ⇓ , we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time ofT 2 * = 12 μ s .

Automatic Detection of Nuclear Spins at Arbitrary Magnetic Fields via Signal-to-Image AI Model

Quantum sensors leverage matter's quantum properties to enable measurements with unprecedented spatial and spectral resolution. Among these sensors, those utilizing nitrogen-vacancy (NV) centers in diamond offer the distinct advantage of operating at room temperature. Nevertheless, signals received from NV centers are often complex, making interpretation challenging. This is especially relevant in low magnetic field scenarios, where standard approximations for modeling the system fail. Additionally, NV signals feature a prominent noise component. In this Letter, we present a signal-to-image deep learning model capable of automatically inferring the number of nuclear spins surrounding a NV sensor and the hyperfine couplings between the sensor and the nuclear spins. Our model is trained to operate effectively across various magnetic field scenarios, requires no prior knowledge of the involved nuclei, and is designed to handle noisy signals, leading to fast characterization of nuclear environments in real experimental conditions. With detailed numerical simulations, we test the performance of our model in scenarios involving varying numbers of nuclei, achieving an average error of less than 2 kHz in the estimated hyperfine constants.

Multidimensional Spectroscopy of Nuclear Spin Clusters in Diamond

Optically active spin defects in solids offer promising platforms to investigate nuclear spin clusters with high sensitivity and atomic-site resolution. To leverage near-surface defects for molecular structure analysis in chemical and biological contexts using nuclear magnetic resonance (NMR), further advances in spectroscopic characterization of nuclear environments are essential. Here, we report Fourier spectroscopy techniques to improve localization and mapping of the test bed ^{13}C nuclear spin environment of individual, shallow nitrogen-vacancy centers at room temperature. We use multidimensional spectroscopy, well-known from classical NMR, in combination with weak measurements of single-nuclear-spin precession. We demonstrate two examples of multidimensional NMR: (i) improved nuclear spin localization by separate encoding of the two hyperfine components along spectral dimensions and (ii) spectral editing of nuclear-spin pairs, including measurement of internuclear coupling constants. Our work adds important tools for the spectroscopic analysis of molecular structures by single-spin probes.

Twisted van der Waals Quantum Materials: Fundamentals, Tunability, and Applications

Twisted van der Waals (vdW) quantum materials have emerged as a rapidly developing field of two-dimensional (2D) semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single photon emission, nonlinear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This paper offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes, lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

Fiber-taper collected emission from NV centers in high-Q/V diamond microdisks

Fiber-coupled microdisks are a promising platform for enhancing the spontaneous emission from color centers in diamond. The measured cavity-enhanced emission from the microdisk is governed by the effective volume (V) of each cavity mode, the cavity quality factor (Q), and the coupling between the microdisk and the fiber. Here we observe room temperature photoluminescence from an ensemble of nitrogen-vacancy centers into high Q/V microdisk modes, which when combined with coherent spectroscopy of the microdisk modes, allows us to elucidate the relative contributions of these factors. The broad emission spectrum acts as an internal light source facilitating mode identification over several cavity free spectral ranges. Analysis of the fiber taper collected microdisk emission reveals spectral filtering both by the cavity and the fiber taper, the latter of which we find preferentially couples to higher-order microdisk modes. Coherent mode spectroscopy is used to measure Q ∼ 1 × 105 - the highest reported values for diamond microcavities operating at visible wavelengths. With realistic optimization of the microdisk dimensions, we predict that Purcell factors of ∼50 are within reach.

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes

Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted through asymmetric channels. Currently, a significant body of literature has investigated the construction of asymmetric QEC codes. However, the asymmetry of most QEC codes identified in the literature is limited by the dual-containing condition within the Calderbank-Shor-Steane (CSS) framework. This limitation restricts the exploration of their full potential in terms of asymmetry. In order to enhance the asymmetry of asymmetric QEC codes, we utilize entanglement-assisted technology and exploit the algebraic structure of cyclotomic cosets of constacyclic codes to achieve this goal. In this paper, we generalize the decomposition method of the defining set for constacyclic codes and apply it to count the number of pre-shared entangled states in order to construct four new classes of asymmetric entanglement-assisted quantum maximal-distance separable (EAQMDS) codes that satisfy the asymmetric entanglement-assisted quantum Singleton bound. Compared with the codes existing in the literature, the lengths of the constructed EAQMDS codes and the number of pre-shared entangled states are more general, and the codes constructed in this paper have greater asymmetry.

Multicone Diamond Waveguides for Nanoscale Quantum Sensing

The long-lived electronic spin of the nitrogen-vacancy (NV) center in diamonds is a promising quantum sensor for detecting nanoscopic magnetic and electric fields in various environments. However, the poor signal-to-noise ratio (SNR) of prevalent optical spin-readout techniques presents a critical challenge in improving measurement sensitivity. Here, we address this limitation by coupling individual NVs to optimized diamond nanopillars, thereby enhancing the collection efficiency of fluorescence. Guided by near-field optical simulations, we predict improved performance for tall (≥5 μm) pillars with tapered sidewalls. This is subsequently verified by fabricating and characterizing a representative set of structures using a newly developed nanofabrication process. We observe increased SNR for optimized devices, owing to improved emission collimation and directionality. Promisingly, these devices are compatible with low-numerical-aperture collection optics and a reduced tip radius, reducing experimental overhead and facilitating improved spatial resolution for scanning applications.

Extending the coherence of spin defects in hBN enables advanced qubit control and quantum sensing

Negatively-charged boron vacancy centers ([Formula: see text]) in hexagonal Boron Nitride (hBN) are attracting increasing interest since they represent optically-addressable qubits in a van der Waals material. In particular, these spin defects have shown promise as sensors for temperature, pressure, and static magnetic fields. However, their short spin coherence time limits their scope for quantum technology. Here, we apply dynamical decoupling techniques to suppress magnetic noise and extend the spin coherence time by two orders of magnitude, approaching the fundamental T1 relaxation limit. Based on this improvement, we demonstrate advanced spin control and a set of quantum sensing protocols to detect radiofrequency signals with sub-Hz resolution. The corresponding sensitivity is benchmarked against that of state-of-the-art NV-diamond quantum sensors. This work lays the foundation for nanoscale sensing using spin defects in an exfoliable material and opens a promising path to quantum sensors and quantum networks integrated into ultra-thin structures.

Temperature-Dependent Spin-Lattice Relaxation of the Nitrogen-Vacancy Spin Triplet in Diamond

Spin-lattice relaxation within the nitrogen-vacancy (NV) center's electronic ground-state spin triplet limits its coherence times, and thereby impacts its performance in quantum applications. We report measurements of the relaxation rates on the NV center's |m_{s}=0⟩↔|m_{s}=±1⟩ and |m_{s}=-1⟩↔|m_{s}=+1⟩ transitions as a function of temperature from 9 to 474 K in high-purity samples. We show that the temperature dependencies of the rates are reproduced by an ab initio theory of Raman scattering due to second-order spin-phonon interactions, and we discuss the applicability of the theory to other spin systems. Using a novel analytical model based on these results, we suggest that the high-temperature behavior of NV spin-lattice relaxation is dominated by interactions with two groups of quasilocalized phonons centered at 68.2(17) and 167(12) meV.

Enhanced Tripartite Interactions in Spin-Magnon-Mechanical Hybrid Systems

Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single nitrogen-vacancy (NV) center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons, and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive) to modulate the mechanical motion (such as the center-of-mass motion of a NV spin in diamond trapped in an electrical trap or a levitated micromagnet in a magnetic trap), we can obtain a tunable and strong spin-magnon-phonon coupling at the single quantum level, with up to 2 orders of magnitude enhancement for the tripartite coupling strength. This enables, for example, tripartite entanglement among solid-state spins, magnons, and mechanical motions in quantum spin-magnonics-mechanics with realistic experimental parameters. This protocol can be readily implemented with the well-developed techniques in ion traps or magnetic traps and could pave the way for general applications in quantum simulations and information processing based on directly and strongly coupled tripartite systems.

99.92%-Fidelity cnot Gates in Solids by Noise Filtering

Inevitable interactions with the reservoir largely degrade the performance of entangling gates, which hinders practical quantum computation from coming into existence. Here, we experimentally demonstrate a 99.920(7)%-fidelity controlled-not gate by suppressing the complicated noise in a solid-state spin system at room temperature. We found that the fidelity limited at 99% in previous works results from considering only static classical noise, and, thus, in this work, a complete noise model is constructed by also considering the time dependence and the quantum nature of the spin bath. All noises in the model are dynamically corrected by an exquisitely designed shaped pulse, giving the resulting error below 10^{-4}. The residual gate error is mainly originated from the longitudinal relaxation and the waveform distortion that can both be further reduced technically. Our noise-resistant method is universal and will benefit other solid-state spin systems.

Diamond surface engineering for molecular sensing with nitrogen-vacancy centers

Quantum sensing using optically addressable atomic-scale defects, such as the nitrogen-vacancy (NV) center in diamond, provides new opportunities for sensitive and highly localized characterization of chemical functionality. Notably, near-surface defects facilitate detection of the minute magnetic fields generated by nuclear or electron spins outside of the diamond crystal, such as those in chemisorbed and physisorbed molecules. However, the promise of NV centers is hindered by a severe degradation of critical sensor properties, namely charge stability and spin coherence, near surfaces (< ca. 10 nm deep). Moreover, applications in the chemical sciences require methods for covalent bonding of target molecules to diamond with robust control over density, orientation, and binding configuration. This forward-looking Review provides a survey of the rapidly converging fields of diamond surface science and NV-center physics, highlighting their combined potential for quantum sensing of molecules. We outline the diamond surface properties that are advantageous for NV-sensing applications, and discuss strategies to mitigate deleterious effects while simultaneously providing avenues for chemical attachment. Finally, we present an outlook on emerging applications in which the unprecedented sensitivity and spatial resolution of NV-based sensing could provide unique insight into chemically functionalized surfaces at the single-molecule level.

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 networks1,2. Recent experiments have demonstrated high-quality control over multi-qubit systems3-8, elementary quantum algorithms8-11 and non-fault-tolerant error correction12-14. Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations15-18. Overcoming imperfections in this way remains an important outstanding challenge for quantum science15,19-27. 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 qubits28-30. 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.

Optical Entanglement of Distinguishable Quantum Emitters

Solid-state quantum emitters are promising candidates for the realization of quantum networks, owing to their long-lived spin memories, high-fidelity local operations, and optical connectivity for long-range entanglement. However, due to differences in local environment, solid-state emitters typically feature a range of distinct transition frequencies, which makes it challenging to create optically mediated entanglement between arbitrary emitter pairs. We propose and demonstrate an efficient method for entangling emitters with optical transitions separated by many linewidths. In our approach, electro-optic modulators enable a single photon to herald a parity measurement on a pair of spin qubits. We experimentally demonstrate the protocol using two silicon-vacancy centers in a diamond nanophotonic cavity, with optical transitions separated by 7.4 GHz. Working with distinguishable emitters allows for individual qubit addressing and readout, enabling parallel control and entanglement of both colocated and spatially separated emitters, a key step toward scaling up quantum information processing systems.

Parallel detection and spatial mapping of large nuclear spin clusters

Nuclear magnetic resonance imaging (MRI) at the atomic scale offers exciting prospects for determining the structure and function of individual molecules and proteins. Quantum defects in diamond have recently emerged as a promising platform towards reaching this goal, and allowed for the detection and localization of single nuclear spins under ambient conditions. Here, we present an efficient strategy for extending imaging to large nuclear spin clusters, fulfilling an important requirement towards a single-molecule MRI technique. Our method combines the concepts of weak quantum measurements, phase encoding and simulated annealing to detect three-dimensional positions from many nuclei in parallel. Detection is spatially selective, allowing us to probe nuclei at a chosen target radius while avoiding interference from strongly-coupled proximal nuclei. We demonstrate our strategy by imaging clusters containing more than 20 carbon-13 nuclear spins within a radius of 2.4 nm from single, near-surface nitrogen-vacancy centers at room temperature. The radius extrapolates to 5-6 nm for ¹H. Beside taking an important step in nanoscale MRI, our experiment also provides an efficient tool for the characterization of large nuclear spin registers in the context of quantum simulators and quantum network nodes.

Addressing Single Nuclear Spins Quantum Memories by a Central Electron Spin

Nuclei surrounding single electron spins are valuable resources for quantum technology. For application in this area, one is often interested in weakly coupled nuclei with coupling strength on the order of a few 10-100 kHz. In this paper, we compare methods to address single nuclear spins with this type of hyperfine coupling to a single electron spin. To achieve the required spectral resolution, we specifically focus on two methods, namely dynamical decoupling and correlation spectroscopy. We demonstrate spectroscopy of two single nuclear spins and present a method to derive components of their hyperfine coupling tensor from those measurements.

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.

Optical charge injection and coherent control of a quantum-dot spin-qubit emitting at telecom wavelengths

Solid-state quantum emitters with manipulable spin-qubits are promising platforms for quantum communication applications. Although such light-matter interfaces could be realized in many systems only a few allow for light emission in the telecom bands necessary for long-distance quantum networks. Here, we propose and implement an optically active solid-state spin-qubit based on a hole confined in a single InAs/GaAs quantum dot grown on an InGaAs metamorphic buffer layer emitting photons in the C-band. We lift the hole spin-degeneracy using an external magnetic field and demonstrate hole injection, initialization, read-out and complete coherent control using picosecond optical pulses. These results showcase a solid-state spin-qubit platform compatible with preexisting optical fiber networks.

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.

Twenty-three-millisecond electron spin coherence of erbium ions in a natural-abundance crystal

Erbium ions embedded in crystals have unique properties for quantum information processing, because of their optical transition at 1.5 μm and of the large magnetic moment of their effective spin-1/2 electronic ground state. Most applications of erbium require, however, long electron spin coherence times, and this has so far been missing. Here, by selecting a host matrix with a low nuclear-spin density (CaWO4) and by quenching the spectral diffusion due to residual paramagnetic impurities at millikelvin temperatures, we obtain a 23-ms coherence time on the Er3+ electron spin transition. This is the longest Hahn echo electron spin coherence time measured in a material with a natural abundance of nuclear spins and on a magnetically sensitive transition. Our results establish Er3+:CaWO4 as a potential platform for quantum networks.

Many-body-localized discrete time crystal with a programmable spin-based quantum simulator

[Figure: see text].

High-capacity and high-power collective charging with spin chargers

Quantum battery works as a micro- or nanodevice to store and redistribute energy at the quantum level. Here we propose a spin-charger protocol, in which the battery cells are charged by a finite number of spins through a general Heisenberg XY interaction. Under the isotropic interaction, the spin-charger protocol is endowed with a higher capacity in terms of the maximum stored energy than the conventional protocols, where the battery is charged by a continuous-variable system, e.g., a cavity mode. By tuning the charger size, a tradeoff between the maximum stored energy and the average charging power is found in comparison to the cavity-charger protocol in the Tavis-Cummings model. Quantum advantage of our protocol is manifested by the scaling behavior of the optimal average power with respect to the battery size, in comparing the collective charging scheme to its parallel counterpart. We also discuss the detrimental effect on the charging performance from the anisotropic interaction between the battery and the charger, the nonideal initial states for both of them, and the crosstalk among the charger spins. A strong charger-charger interaction can be used to decouple the battery and the charger. Our findings about the advantages of the spin-charger protocol over the conventional cavity-charger protocols, including the high capacity of energy storage and the superior power law in the collective charging, provide an insight to exploit an efficient quantum battery based on the spin-spin-environment model.

Room-temperature control and electrical readout of individual nitrogen-vacancy nuclear spins

Nuclear spins in semiconductors are leading candidates for future quantum technologies, including quantum computation, communication, and sensing. Nuclear spins in diamond are particularly attractive due to their long coherence time. With the nitrogen-vacancy (NV) centre, such nuclear qubits benefit from an auxiliary electronic qubit, which, at cryogenic temperatures, enables probabilistic entanglement mediated optically by photonic links. Here, we demonstrate a concept of a microelectronic quantum device at ambient conditions using diamond as wide bandgap semiconductor. The basic quantum processor unit – a single ¹⁴N nuclear spin coupled to the NV electron – is read photoelectrically and thus operates in a manner compatible with nanoscale electronics. The underlying theory provides the key ingredients for photoelectric quantum gate operations and readout of nuclear qubit registers. This demonstration is, therefore, a step towards diamond quantum devices with a readout area limited by inter-electrode distance rather than by the diffraction limit. Such scalability could enable the development of electronic quantum processors based on the dipolar interaction of spin-qubits placed at nanoscopic proximity.

Nuclear spins in diamond are promising for applications in quantum technologies due to their long coherence times. Here, the authors demonstrate a scalable electrical readout of individual intrinsic ¹⁴N nuclear spins in diamond, mediated by hyperfine coupling to electron spin of the NV center, as a step towards room-temperature nanoscale diamond quantum devices.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Entanglement of dark electron-nuclear spin defects in diamond

A promising approach for multi-qubit quantum registers is to use optically addressable spins to control multiple dark electron-spin defects in the environment. While recent experiments have observed signatures of coherent interactions with such dark spins, it is an open challenge to realize the individual control required for quantum information processing. Here, we demonstrate the heralded initialisation, control and entanglement of individual dark spins associated to multiple P1 centers, which are part of a spin bath surrounding a nitrogen-vacancy center in diamond. We realize projective measurements to prepare the multiple degrees of freedom of P1 centers-their Jahn-Teller axis, nuclear spin and charge state-and exploit these to selectively access multiple P1s in the bath. We develop control and single-shot readout of the nuclear and electron spin, and use this to demonstrate an entangled state of two P1 centers. These results provide a proof-of-principle towards using dark electron-nuclear spin defects as qubits for quantum sensing, computation and networks.

Low Field Nano-NMR via Three-Level System Control

Conventional control strategies for nitrogen-vacancy centers in quantum sensing are based on a two-level model of their triplet ground state. However, this approach fails in regimes of weak bias magnetic fields or strong microwave pulses, as we demonstrate. To overcome this limitation, we propose a novel control sequence that exploits all three levels by addressing a hidden Raman configuration with microwave pulses tuned to the zero-field transition. We report excellent performance in typical dynamical decoupling sequences, opening up the possibility for nano-NMR operation in low field environments.

Heterodyne sensing of microwaves with a quantum sensor

Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system’s resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.

High-resolution microwave detection with NV centers in diamond is currently applicable to signals with frequencies below 10 MHz, thus limiting their range of applications. Here, the authors demonstrate detection of GHz signals with sub-Hz spectral resolution, not limited by the quantum sensor lifetime.

Fabrication and Characterization of Single-Crystal Diamond Membranes for Quantum Photonics with Tunable Microcavities

The development of quantum technologies is one of the big challenges in modern research. A crucial component for many applications is an efficient, coherent spin-photon interface, and coupling single-color centers in thin diamond membranes to a microcavity is a promising approach. To structure such micrometer thin single-crystal diamond (SCD) membranes with a good quality, it is important to minimize defects originating from polishing or etching procedures. Here, we report on the fabrication of SCD membranes, with various diameters, exhibiting a low surface roughness down to 0.4 nm on a small area scale, by etching through a diamond bulk mask with angled holes. A significant reduction in pits induced by micromasking and polishing damages was accomplished by the application of alternating Ar/Cl₂ + O₂ dry etching steps. By a variation of etching parameters regarding the Ar/Cl₂ step, an enhanced planarization of the surface was obtained, in particular, for surfaces with a higher initial surface roughness of several nanometers. Furthermore, we present the successful bonding of an SCD membrane via van der Waals forces on a cavity mirror and perform finesse measurements which yielded values between 500 and 5000, depending on the position and hence on the membrane thickness. Our results are promising for, e.g., an efficient spin-photon interface.

Algorithmic decomposition for efficient multiple nuclear spin detection in diamond

Efficiently detecting and characterizing individual spins in solid-state hosts is an essential step to expand the fields of quantum sensing and quantum information processing. While selective detection and control of a few ¹³C nuclear spins in diamond have been demonstrated using the electron spin of nitrogen-vacancy (NV) centers, a reliable, efficient, and automatic characterization method is desired. Here, we develop an automated algorithmic method for decomposing spectral data to identify and characterize multiple nuclear spins in diamond. We demonstrate efficient nuclear spin identification and accurate reproduction of hyperfine interaction components for both virtual and experimental nuclear spectroscopy data. We conduct a systematic analysis of this methodology and discuss the range of hyperfine interaction components of each nuclear spin that the method can efficiently detect. The result demonstrates a systematic approach that automatically detects nuclear spins with the aid of computational methods, facilitating the future scalability of devices.

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.

Ultralong Spin-Coherence Times for Rubidium Atoms in Solid Parahydrogen via Dynamical Decoupling

Coherence time is an essential parameter for quantum sensing, quantum information, and quantum computation. In this work, we demonstrate electron spin coherence times as long as 0.1 s for an ensemble of rubidium atoms trapped in a solid parahydrogen matrix. We explore the underlying physics limiting the coherence time. The properties of these matrix isolated atoms are very promising for future applications, including quantum sensing of nuclear spins. If combined with efficient single-atom readout, this would enable NMR and magnetic resonance imaging of single molecules cotrapped with alkali-metal atom quantum sensors within a parahydrogen matrix.

Motional Dynamical Decoupling for Interferometry with Macroscopic Particles

We extend the concept of dynamical decoupling from spin to mechanical degrees of freedom of macroscopic objects, for application in interferometry. In this manner, the superposition of matter waves can be made resilient to many important sources of noise when these are driven along suitable paths in space. As a concrete implementation, we present the case of levitated (or free falling) nanodiamonds hosting a color center in a magnetic field gradient. We point out that these interferometers are inherently affected by diamagnetic forces, which restrict the separation of the superposed states to distances that scale with the inverse of the magnetic field gradient. Periodic forcing of the mechanical degree of freedom is shown to overcome this limitation, achieving a linear-in-time growth of the separation distance independent of the magnetic field gradient, while simultaneously protecting the coherence of the superposition from environmental perturbations.

Spin-controlled generation of indistinguishable and distinguishable photons from silicon vacancy centres in silicon carbide

Quantum systems combining indistinguishable photon generation and spin-based quantum information processing are essential for remote quantum applications and networking. However, identification of suitable systems in scalable platforms remains a challenge. Here, we investigate the silicon vacancy centre in silicon carbide and demonstrate controlled emission of indistinguishable and distinguishable photons via coherent spin manipulation. Using strong off-resonant excitation and collecting zero-phonon line photons, we show a two-photon interference contrast close to 90% in Hong-Ou-Mandel type experiments. Further, we exploit the system’s intimate spin-photon relation to spin-control the colour and indistinguishability of consecutively emitted photons. Our results provide a deep insight into the system’s spin-phonon-photon physics and underline the potential of the industrially compatible silicon carbide platform for measurement-based entanglement distribution and photonic cluster state generation. Additional coupling to quantum registers based on individual nuclear spins would further allow for high-level network-relevant quantum information processing, such as error correction and entanglement purification.

Defects in silicon carbide can act as single photon sources that also have the benefit of a host material that is already used in electronic devices. Here the authors demonstrate that they can control the distinguishability of the emitted photons by changing the defect spin state.

Enhancing the Robustness of Dynamical Decoupling Sequences with Correlated Random Phases

We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to π pulse imperfections and spurious responses due to finite-width π pulses. This enhances the selectivity of quantum sensors such as those based on NV centers in diamond.

Sensing Individual Nuclear Spins with a Single Rare-Earth Electron Spin

Rare-earth related electron spins in crystalline hosts are unique material systems, as they can potentially provide a direct interface between telecom band photons and long-lived spin quantum bits. Specifically, their optically accessible electron spins in solids interacting with nuclear spins in their environment are valuable quantum memory resources. Detection of nearby individual nuclear spins, so far exclusively shown for few dilute nuclear spin bath host systems such as the nitrogen-vacancy center in diamond or the silicon vacancy in silicon carbide, remained an open challenge for rare earths in their host materials, which typically exhibit dense nuclear spin baths. Here, we present the electron spin spectroscopy of single Ce^{3+} ions in a yttrium orthosilicate host, featuring a coherence time of T_{2}=124  μs. This coherent interaction time is sufficiently long to isolate proximal ^{89}Y nuclear spins from the nuclear spin bath of ^{89}Y. Furthermore, it allows for the detection of a single nearby ^{29}Si nuclear spin, native to the host material with ∼5% abundance. This study opens the door to quantum memory applications in rare-earth ion related systems based on coupled environmental nuclear spins, potentially useful for quantum error correction schemes.

Single-Spin Magnetomechanics with Levitated Micromagnets

We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micromagnets are trapped using a type-II superconductor in proximity of spin qubits, enabling direct magnetic coupling between the two systems. Controlling the distance between the magnet and the superconductor during cooldown, we demonstrate three-dimensional trapping with quality factors around 1×10^{6} and kHz trapping frequencies. We further exploit the large magnetic moment to mass ratio of this mechanical oscillator to couple its motion to the spin degrees of freedom of an individual nitrogen vacancy center in diamond. Our approach provides a new path towards interfacing individual spin qubits with mechanical motion for testing quantum mechanics with mesoscopic objects, realization of quantum networks, and ultrasensitive metrology.

Control and single-shot readout of an ion embedded in a nanophotonic cavity

Distributing entanglement over long distances using optical networks is an intriguing macroscopic quantum phenomenon with applications in quantum systems for advanced computing and secure communication^1,2. Building quantum networks requires scalable quantum light-matter interfaces¹ based on atoms³, ions⁴ or other optically addressable qubits. Solid-state emitters⁵, such as quantum dots and defects in diamond or silicon carbide^6-10, have emerged as promising candidates for such interfaces. So far, it has not been possible to scale up these systems, motivating the development of alternative platforms. A central challenge is identifying emitters that exhibit coherent optical and spin transitions while coupled to photonic cavities that enhance the light-matter interaction and channel emission into optical fibres. Rare-earth ions in crystals are known to have highly coherent 4f-4f optical and spin transitions suited to quantum storage and transduction^11-15, but only recently have single rare-earth ions been isolated^16,17 and coupled to nanocavities^18,19. The crucial next steps towards using single rare-earth ions for quantum networks are realizing long spin coherence and single-shot readout in photonic resonators. Here we demonstrate spin initialization, coherent optical and spin manipulation, and high-fidelity single-shot optical readout of the hyperfine spin state of single ¹⁷¹Yb³⁺ ions coupled to a nanophotonic cavity fabricated in an yttrium orthovanadate host crystal. These ions have optical and spin transitions that are first-order insensitive to magnetic field fluctuations, enabling optical linewidths of less than one megahertz and spin coherence times exceeding thirty milliseconds for cavity-coupled ions, even at temperatures greater than one kelvin. The cavity-enhanced optical emission rate facilitates efficient spin initialization and single-shot readout with conditional fidelity greater than 95 per cent. These results showcase a solid-state platform based on single coherent rare-earth ions for the future quantum internet.

A silicon quantum-dot-coupled nuclear spin qubit

Single nuclear spins in the solid state are a potential future platform for quantum computing^1-3, because they possess long coherence times^4-6 and offer excellent controllability⁷. Measurements can be performed via localized electrons, such as those in single atom dopants^8,9 or crystal defects^10-12. However, establishing long-range interactions between multiple dopants or defects is challenging^13,14. Conversely, in lithographically defined quantum dots, tunable interdot electron tunnelling allows direct coupling of electron spin-based qubits in neighbouring dots^15-20. Moreover, the compatibility with semiconductor fabrication techniques²¹ may allow for scaling to large numbers of qubits in the future. 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 initialize, read out and control single ²⁹Si nuclear spins. This approach combines 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. Hence we envision long-range nuclear-nuclear entanglement via electron shuttling³. Our results establish nuclear spins in quantum dots as a powerful new resource for quantum processing.