Quantum Network Nodes Based on Diamond Qubits with an Efficient Nanophotonic Interface

Coherent Control of a Long-Lived Nuclear Memory Spin in a Germanium-Vacancy Multi-Qubit Node

The ability to process and store information on surrounding nuclear spins is a major requirement for group-IV color center-based repeater nodes. We demonstrate coherent control of a ^{13}C nuclear spin strongly coupled to a negatively charged germanium-vacancy center in diamond with coherence times beyond 2.5 s at mK temperatures, which is the longest reported for group-IV defects. Detailed analysis allows us to model the system's dynamics, extract the coupling parameters, and characterize noise. We estimate an achievable memory time of 18.1 s with heating limitations considered, paving the way to successful applications as a quantum repeater node.

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.

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.

Entanglement of nanophotonic quantum memory nodes in a telecom network

A key challenge in realizing practical quantum networks for long-distance quantum communication involves robust entanglement between quantum memory nodes connected by fibre optical infrastructure1-3. Here we demonstrate a two-node quantum network composed of multi-qubit registers based on silicon-vacancy (SiV) centres in nanophotonic diamond cavities integrated with a telecommunication fibre network. Remote entanglement is generated by the cavity-enhanced interactions between the electron spin qubits of the SiVs and optical photons. Serial, heralded spin-photon entangling gate operations with time-bin qubits are used for robust entanglement of separated nodes. Long-lived nuclear spin qubits are used to provide second-long entanglement storage and integrated error detection. By integrating efficient bidirectional quantum frequency conversion of photonic communication qubits to telecommunication frequencies (1,350 nm), we demonstrate the entanglement of two nuclear spin memories through 40 km spools of low-loss fibre and a 35-km long fibre loop deployed in the Boston area urban environment, representing an enabling step towards practical quantum repeaters and large-scale quantum networks.

Fast optoelectronic charge state conversion of silicon vacancies in diamond

Group IV vacancy color centers in diamond are promising spin-photon interfaces with strong potential for applications in photonic quantum technologies. Reliable methods for controlling and stabilizing their charge state are urgently needed for scaling to multiqubit devices. Here, we manipulate the charge state of silicon vacancy (SiV) ensembles by combining luminescence and photocurrent spectroscopy. We controllably convert the charge state between the optically active SiV- and dark SiV2- with megahertz rates and >90% contrast by judiciously choosing the local potential applied to in-plane surface electrodes and the laser excitation wavelength. We observe intense SiV- photoluminescence under hole capture, measure the intrinsic conversion time from the dark SiV2- to the bright SiV- to be 36.4(67) ms, and demonstrate how it can be enhanced by a factor of 105 via optical pumping. Moreover, we obtain previously unknown information on the defects that contribute to photoconductivity, indicating the presence of substitutional nitrogen and divacancies.

Transform-Limited Photon Emission from a Lead-Vacancy Center in Diamond above 10 K

Transform-limited photon emission from quantum emitters is essential for high-fidelity entanglement generation. In this Letter, we report the coherent optical property of a single negatively charged lead-vacancy (PbV) center in diamond. Photoluminescence excitation measurements reveal stable fluorescence with a linewidth of 39 MHz at 6 K, close to the transform limit estimated from the lifetime measurement. We observe 4 orders of magnitude different linewidths of the two zero-phonon lines, and find that the phonon-induced relaxation in the ground state contributes to this huge difference in the linewidth. Because of the suppressed phonon absorption in the PbV center, we observe nearly transform-limited photon emission up to 16 K, demonstrating its high temperature robustness compared to other color centers in diamond.

Hyperfine Spectroscopy and Fast, All-Optical Arbitrary State Initialization and Readout of a Single, Ten-Level ^{73}Ge Vacancy Nuclear Spin Qudit in Diamond

A high-spin nucleus coupled to a color center can act as a long-lived memory qudit in a spin-photon interface. The germanium vacancy (GeV) in diamond has attracted recent attention due to its excellent spectral properties and provides access to the ten-dimensional Hilbert space of the I=9/2 ^{73}Ge nucleus. Here, we observe the ^{73}GeV  hyperfine structure, perform nuclear spin readout, and optically initialize the ^{73}Ge spin into any eigenstate on a μs timescale and with a fidelity of up to ∼84%. Our results establish ^{73}GeV as an optically addressable high-spin quantum platform for a high-efficiency spin-photon interface as well as for foundational quantum physics and metrology.

Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates

The decoherence-free subspace (DFS) serves as a protective shield against certain types of environmental noise, allowing the system to remain coherent for extended periods of time. In this paper, we propose two protocols, i.e., one converts two-logic-qubit Knill-Laflamme-Milburn (KLM) state to two-logic-qubit Bell states, and the other converts three-logic-qubit KLM state to three-logic-qubit Greenberger-Horne-Zeilinger states, through cavity-assisted interaction in DFS. Especially, our innovative protocols achieve their objectives in a heralded way, thus enhancing experimental accessibility. Moreover, single photon detectors are incorporated into the setup, which can predict potential failures and ensure seamless interaction between the nitrogen-vacancy center and photons. Rigorous analyses and evaluations of two schemes demonstrate their abilities to achieve near-unit fidelities in principle and exceptional efficiencies. Further, our protocols offer progressive solutions to the challenges posed by decoherence, providing a pathway towards practical quantum technologies.

Germanium Vacancy in Diamond Quantum Memory Exceeding 20 ms

Negatively charged group-IV defects in diamond show great potential as quantum network nodes due to their efficient spin-photon interface. However, reaching sufficiently long coherence times remains a challenge. In this work, we demonstrate coherent control of germanium vacancy center (GeV) at millikelvin temperatures and extend its coherence time by several orders of magnitude to more than 20 ms. We model the magnetic and amplitude noise as an Ornstein-Uhlenbeck process, reproducing the experimental results well. The utilized method paves the way to optimized coherence times of group-IV defects in various experimental conditions and their successful applications in quantum technologies.

Shallow Silicon Vacancy Centers with Lifetime-Limited Optical Linewidths in Diamond Nanostructures

The negatively charged silicon vacancy center (SiV-) in diamond is a promising, yet underexplored candidate for single-spin quantum sensing at sub-kelvin temperatures and tesla-range magnetic fields. A key ingredient for such applications is the ability to perform all-optical, coherent addressing of the electronic spin of near-surface SiV- centers. We present a robust and scalable approach for creating individual, ∼50 nm deep SiV- with lifetime-limited optical linewidths in diamond nanopillars through an easy-to-realize and persistent optical charge-stabilization scheme. The latter is based on single, prolonged 445 nm laser illumination that enables continuous photoluminescence excitation spectroscopy without the need for any further charge stabilization or repumping. Our results constitute a key step toward the use of near-surface, optically coherent SiV- for sensing under extreme conditions, and offer a powerful approach for stabilizing the charge-environment of diamond color centers for quantum technology applications.

Resource-efficient fault-tolerant one-way quantum repeater with code concatenation

One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.

Selective and Scalable Control of Spin Quantum Memories in a Photonic Circuit

A central goal in many quantum information processing applications is a network of quantum memories that can be entangled with each other while being individually controlled and measured with high fidelity. This goal has motivated the development of programmable photonic integrated circuits (PICs) with integrated spin quantum memories using diamond color center spin-photon interfaces. However, this approach introduces a challenge into the microwave control of individual spins within closely packed registers. Here, we present a quantum memory-integrated photonics platform capable of (i) the integration of multiple diamond color center spins into a cryogenically compatible, high-speed programmable PIC platform, (ii) selective manipulation of individual spin qubits addressed via tunable magnetic field gradients, and (iii) simultaneous control of qubits using numerically optimized microwave pulse shaping. The combination of localized optical control, enabled by the PIC platform, together with selective spin manipulation opens the path to scalable quantum networks on intrachip and interchip platforms.

A Solid-State Source of Single and Entangled Photons at Diamond SiV-Center Transitions Operating at 80K

Large-scale quantum networks require the implementation of long-lived quantum memories as stationary nodes interacting with qubits of light. Epitaxially grown quantum dots hold great potential for the on-demand generation of single and entangled photons with high purity and indistinguishability. Coupling these emitters to memories with long coherence times enables the development of hybrid nanophotonic devices that incorporate the advantages of both systems. Here we report the first GaAs/AlGaAs quantum dots grown by the droplet etching and nanohole infilling method, emitting single photons with a narrow wavelength distribution (736.2 ± 1.7 nm) close to the zero-phonon line of silicon-vacancy centers. Polarization entangled photons are generated via the biexciton-exciton cascade with a fidelity of (0.73 ± 0.09). High single photon purity is maintained from 4 K (g⁽²⁾(0) = 0.07 ± 0.02) up to 80 K (g⁽²⁾(0) = 0.11 ± 0.01), therefore making this hybrid system technologically attractive for real-world quantum photonic applications.

Manipulating the Charge State of Spin Defects in Hexagonal Boron Nitride

Negatively charged boron vacancies (V_B^-) in hexagonal boron nitride (hBN) have recently gained interest as spin defects for quantum information processing and quantum sensing by a layered material. However, the boron vacancy can exist in a number of charge states in the hBN lattice, but only the -1 state has spin-dependent photoluminescence and acts as a spin-photon interface. Here, we investigate the charge state switching of V_B defects under laser and electron beam excitation. We demonstrate deterministic, reversible switching between the -1 and 0 states (V_B^- ⇌ V_B⁰ + e^-), occurring at rates controlled by excess electrons or holes injected into hBN by a layered heterostructure device. Our work provides a means to monitor and manipulate the V_B charge state, and to stabilize the -1 state which is a prerequisite for spin manipulation and optical readout of the defect.

Neutral Silicon Vacancy Centers in Undoped Diamond via Surface Control

Neutral silicon vacancy centers (SiV^{0}) in diamond are promising candidates for quantum applications; however, stabilizing SiV^{0} requires high-purity, boron-doped diamond, which is not a readily available material. Here, we demonstrate an alternative approach via chemical control of the diamond surface. We use low-damage chemical processing and annealing in a hydrogen environment to realize reversible and highly stable charge state tuning in undoped diamond. The resulting SiV^{0} centers display optically detected magnetic resonance and bulklike optical properties. Controlling the charge state tuning via surface termination offers a route for scalable technologies based on SiV^{0} centers, as well as charge state engineering of other defects.

A Telecom O-Band Emitter in Diamond

Color centers in diamond are promising platforms for quantum technologies. Most color centers in diamond discovered thus far emit in the visible or near-infrared wavelength range, which are incompatible with long-distance fiber communication and unfavorable for imaging in biological tissues. Here, we report the experimental observation of a new color center that emits in the telecom O-band, which we observe in silicon-doped bulk single crystal diamonds and microdiamonds. Combining absorption and photoluminescence measurements, we identify a zero-phonon line at 1221 nm and phonon replicas separated by 42 meV. Using transient absorption spectroscopy, we measure an excited state lifetime of around 270 ps and observe a long-lived baseline that may arise from intersystem crossing to another spin manifold.

Single-Spin Readout and Quantum Sensing Using Optomechanically Induced Transparency

Solid-state spin defects are promising quantum sensors for a large variety of sensing targets. Some of these defects couple appreciably to strain in the host material. We propose to use this strain coupling for mechanically mediated dispersive single-shot spin readout by an optomechanically induced transparency measurement. Surprisingly, the estimated measurement times for negatively charged silicon-vacancy defects in diamond are an order of magnitude shorter than those for single-shot optical fluorescence readout. Our scheme can also be used for general parameter-estimation metrology and offers a higher sensitivity than conventional schemes using continuous position detection.

Frequency Combs with Parity-Protected Cross-Correlations and Entanglement from Dynamically Modulated Qubit Arrays

We develop a general theoretical framework to dynamically engineer quantum correlations and entanglement in the frequency-comb emission from an array of superconducting qubits in a waveguide, rigorously accounting for the temporal modulation of the qubit resonance frequencies. We demonstrate that when the resonance frequencies of the two qubits are periodically modulated with a π phase shift, it is possible to realize simultaneous bunching and antibunching in cross-correlations as well as Bell states of the scattered photons from different sidebands. Our approach, based on the dynamical conversion between the quantum excitations with different parity symmetry, is quite universal. It can be used to control multiparticle correlations in generic dynamically modulated dissipative quantum systems.

Spin-defect qubits in two-dimensional transition metal dichalcogenides operating at telecom wavelengths

Solid state quantum defects are promising candidates for scalable quantum information systems which can be seamlessly integrated with the conventional semiconductor electronic devices within the 3D monolithically integrated hybrid classical-quantum devices. Diamond nitrogen-vacancy (NV) center defects are the representative examples, but the controlled positioning of an NV center within bulk diamond is an outstanding challenge. Furthermore, quantum defect properties may not be easily tuned for bulk crystalline quantum defects. In comparison, 2D semiconductors, such as transition metal dichalcogenides (TMDs), are promising solid platform to host a quantum defect with tunable properties and a possibility of position control. Here, we computationally discover a promising defect family for spin qubit realization in 2D TMDs. The defects consist of transition metal atoms substituted at chalcogen sites with desirable spin-triplet ground state, zero-field splitting in the tens of GHz, and strong zero-phonon coupling to optical transitions in the highly desirable telecom band.

An optical interface for quantum networks

A silicon atom embedded in diamond can be entangled with a photon

Robust multi-qubit quantum network node with integrated error detection

Long-distance quantum communication and networking require quantum memory nodes with efficient optical interfaces and long memory times. We report the realization of an integrated two-qubit network node based on silicon-vacancy centers (SiVs) in diamond nanophotonic cavities. Our qubit register consists of the SiV electron spin acting as a communication qubit and the strongly coupled silicon-29 nuclear spin acting as a memory qubit with a quantum memory time exceeding 2 seconds. By using a highly strained SiV, we realize electron-photon entangling gates at temperatures up to 1.5 kelvin and nucleus-photon entangling gates up to 4.3 kelvin. We also demonstrate efficient error detection in nuclear spin–photon gates by using the electron spin as a flag qubit, making this platform a promising candidate for scalable quantum repeaters.

Few-mode field quantization for multiple emitters

The control of the interaction between quantum emitters using nanophotonic structures holds great promise for quantum technology applications, while its theoretical description for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes form a high-dimensional continuum. We here introduce an approach that permits a quantized description of the full EM field through a small number of discrete modes. This extends the previous work in ref. (I. Medina, F. J. García-Vidal, A. I. Fernández-Domínguez, and J. Feist, "Few-mode field quantization of arbitrary electromagnetic spectral densities," Phys. Rev. Lett., vol. 126, p. 093601, 2021) to the case of an arbitrary number of emitters, without any restrictions on the emitter level structure or dipole operators. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. We illustrate the power of our approach for a system of three emitters placed within a hybrid metallodielectric photonic structure and show that excitation transfer is highly sensitive to the properties of the hybrid photonic-plasmonic modes.

Quantum Interference of Resonance Fluorescence from Germanium-Vacancy Color Centers in Diamond

Resonance fluorescence from a quantum emitter is an ideal source to extract indistinguishable photons. By using the cross-polarization to suppress the laser scattering, we observed resonance fluorescence from GeV color centers in diamond at cryogenic temperature. The Fourier-transform-limited line width emission with T₂/2T₁ ∼ 0.86 allows for two-photon interference based on single GeV color center. Under pulsed excitation, the separated photons exhibit a Hong-Ou-Mandel quantum interference above classical limit, whereas the continuous-wave excitation leads to a coalescence time window of 1.05 radiative lifetime. In addition, we demonstrated a single-shot readout of spin states with a fidelity of 74%. Our experiments lay down the foundation for building a quantum network with GeV color centers in diamond.

Efficient Source of Shaped Single Photons Based on an Integrated Diamond Nanophotonic System

An efficient, scalable source of shaped single photons that can be directly integrated with optical fiber networks and quantum memories is at the heart of many protocols in quantum information science. We demonstrate a deterministic source of arbitrarily temporally shaped single-photon pulses with high efficiency [detection efficiency=14.9%] and purity [g^{(2)}(0)=0.0168] and streams of up to 11 consecutively detected single photons using a silicon-vacancy center in a highly directional fiber-integrated diamond nanophotonic cavity. Combined with previously demonstrated spin-photon entangling gates, this system enables on-demand generation of streams of correlated photons such as cluster states and could be used as a resource for robust transmission and processing of quantum information.

One decade of quantum optimal control in the chopped random basis

The chopped random basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications such as quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints-while maintaining an access to the usually trap-free control landscape-and to switch from open-loop to closed-loop optimization (including with remote access-or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

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.

Qubit teleportation between non-neighbouring nodes in a quantum network

Future quantum internet applications will derive their power from the ability to share quantum information across the network^1,2. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections³. Although many experimental demonstrations have been performed on different quantum network platforms^4-10, moving beyond directly connected nodes has, so far, been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation between remote, non-neighbouring nodes in a quantum network. The network uses three optically connected nodes based on solid-state spin qubits. The teleporter is prepared by establishing remote entanglement on the two links, followed by entanglement swapping on the middle node and storage in a memory qubit. We demonstrate that, once successful preparation of the teleporter is heralded, arbitrary qubit states can be teleported with fidelity above the classical bound, even with unit efficiency. These results are enabled by key innovations in the qubit readout procedure, active memory qubit protection during entanglement generation and tailored heralding that reduces remote entanglement infidelities. Our work demonstrates a prime building block for future quantum networks and opens the door to exploring teleportation-based multi-node protocols and applications^2,11-13.

Development of hard masks for reactive ion beam angled etching of diamond

Diamond offers good optical properties and hosts bright color centers with long spin coherence times. Recent advances in angled-etching of diamond, specifically with reactive ion beam angled etching (RIBAE), have led to successful demonstration of quantum photonic devices operating at visible wavelengths. However, larger devices operating at telecommunication wavelengths have been difficult to fabricate due to the increased mask erosion, arising from the increased size of devices requiring longer etch times. We evaluated different mask materials for RIBAE of diamond photonic crystal nanobeams and waveguides, and how their thickness, selectivity, aspect ratio and sidewall smoothness affected the resultant etch profiles and optical performance. We found that a thick hydrogen silesquioxane (HSQ) layer on a thin alumina adhesion layer provided the best etch profile and optical performance. The techniques explored in this work can also be adapted to other bulk materials that are not available heteroepitaxially or as thin films-on-insulator.

Density functionals with asymptotic-potential corrections are required for the simulation of spectroscopic properties of materials

Five effects of correction of the asymptotic potential error in density functionals are identified that significantly improve calculated properties of molecular excited states involving charge-transfer character. Newly developed materials-science computational methods are used to demonstrate how these effects manifest in materials spectroscopy. Connection is made considering chlorophyll-a as a paradigm for molecular spectroscopy, 22 iconic materials as paradigms for 3D materials spectroscopy, and the VN - defect in hexagonal boron nitride as an example of the spectroscopy of defects in 2D materials pertaining to nanophotonics. Defects can equally be thought of as being "molecular" and "materials" in nature and hence bridge the relms of molecular and materials spectroscopies. It is concluded that the density functional HSE06, currently considered as the standard for accurate calculations of materials spectroscopy, should be replaced, in most instances, by the computationally similar but asymptotically corrected CAM-B3LYP functional, with some specific functionals for materials-use only providing further improvements.

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.

Dynamic control of Purcell enhanced emission of erbium ions in nanoparticles

The interaction of single quantum emitters with an optical cavity enables the realization of efficient spin-photon interfaces, an essential resource for quantum networks. The dynamical control of the spontaneous emission rate of quantum emitters in cavities has important implications in quantum technologies, e.g., for shaping the emitted photons’ waveform or for driving coherently the optical transition while preventing photon emission. Here we demonstrate the dynamical control of the Purcell enhanced emission of a small ensemble of erbium ions doped into a nanoparticle. By embedding the nanoparticles into a fully tunable high finesse fiber based optical microcavity, we demonstrate a median Purcell factor of 15 for the ensemble of ions. We also show that we can dynamically control the Purcell enhanced emission by tuning the cavity on and out of resonance, by controlling its length with sub-nanometer precision on a time scale more than two orders of magnitude faster than the natural lifetime of the erbium ions. This capability opens prospects for the realization of efficient nanoscale quantum interfaces between solid-state spins and single telecom photons with controllable waveform, for non-destructive detection of photonic qubits, and for the realization of quantum gates between rare-earth ion qubits coupled to an optical cavity.

Control of quantum emitters is needed in order to enable many applications. Here, the authors demonstrate enhancement and dynamical control of the Purcell emission from erbium ions doped in a nanoparticle within a fiber-based microcavity.

Unconventional Quantum Sound-Matter Interactions in Spin-Optomechanical-Crystal Hybrid Systems

We predict a set of unusual quantum acoustic phenomena resulting from sound-matter interactions in a fully tunable solid-state platform in which an array of solid-state spins in diamond are coupled to quantized acoustic waves in a one-dimensional optomechanical crystal. We find that, by using a spatially varying laser drive that introduces a position-dependent phase in the optomechanical interaction, the mechanical band structure can be tuned in situ, consequently leading to unconventional quantum sound-matter interactions. We show that quasichiral sound-matter interactions can occur, with tunable ranges from bidirectional to quasiunidirectional, when the spins are resonant with the bands. When the solid-state spin frequency lies within the acoustic band gap, we demonstrate the emergence of an exotic polariton bound state that can mediate long-range tunable, odd-neighbor, and complex spin-spin interactions. This work expands the present exploration of quantum phononics and can have wide applications in quantum simulations and quantum information processing.

Accurate prediction of the properties of materials using the CAM-B3LYP density functional

Density functionals with asymptotic corrections to the long-range potential provide entry-level methods for calculations on molecules that can sustain charge transfer, but similar applications in materials science are rare. We describe an implementation of the CAM-B3LYP range-separated functional within the Vienna Ab-initio Simulation Package (VASP) framework, together with its analytical functional derivatives. Results obtained for eight representative materials: aluminum, diamond, graphene, silicon, NaCl, MgO, 2D h-BN, and 3D h-BN, indicate that CAM-B3LYP predictions embody mean-absolute deviations (MAD) compared to HSE06 that are reduced by a factor of six for lattice parameters, four for quasiparticle band gaps, three for the lowest optical excitation energies, and six for exciton binding energies. Further, CAM-B3LYP appears competitive compared to ab initio G₀ W₀ and Bethe-Salpeter equation approaches. The CAM-B3LYP implementation in VASP was verified by comparison of optimized geometries and reaction energies for isolated molecules taken from the ACCDB database, evaluated in large periodic unit cells, to analogous results obtained using Gaussian basis sets. Using standard GW pseudopotentials and energy cutoffs for the plane-wave calculations and the aug-cc-pV5Z basis set for the atomic-basis ones, the MAD in energy for 1738 chemical reactions was 0.34 kcal mol^-1 , while for 480 unique bond lengths this was 0.0036 Å; these values reduced to 0.28 kcal mol^-1 (largest error 0.94 kcal mol^-1 ) and 0.0009 Å by increasing the plane-wave cutoff energy to 850 eV.

Realization of a multinode quantum network of remote solid-state qubits

The distribution of entangled states across the nodes of a future quantum internet will unlock fundamentally new technologies. Here, we report on the realization of a three-node entanglement-based quantum network. We combine remote quantum nodes based on diamond communication qubits into a scalable phase-stabilized architecture, supplemented with a robust memory qubit and local quantum logic. In addition, we achieve real-time communication and feed-forward gate operations across the network. We demonstrate two quantum network protocols without postselection: the distribution of genuine multipartite entangled states across the three nodes and entanglement swapping through an intermediary node. Our work establishes a key platform for exploring, testing, and developing multinode quantum network protocols and a quantum network control stack.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Strain-Induced Modification of the Optical Characteristics of Quantum Emitters in Hexagonal Boron Nitride

Quantum emitters in hexagonal boron nitride (hBN) are promising building blocks for the realization of integrated quantum photonic systems. However, their spectral inhomogeneity currently limits their potential applications. Here, tensile strain is applied to quantum emitters embedded in few-layer hBN films and both red and blue spectral shifts are realized with tuning magnitudes up to 65 meV, a record for any 2D quantum source. Reversible tuning of the emission and related photophysical properties is demonstrated. Rotation of the optical dipole in response to strain is also observed, suggesting the presence of a second excited state. A theoretical model is derived to describe strain-based tuning in hBN, and the rotation of the optical dipole. The study demonstrates the immense potential for strain tuning of quantum emitters in layered materials to enable their employment in scalable quantum photonic networks.

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.

Experimental demonstration of memory-enhanced quantum communication

The ability to communicate quantum information over long distances is of central importance in quantum science and engineering¹. Although some applications of quantum communication such as secure quantum key distribution^2,3 are already being successfully deployed^4-7, their range is currently limited by photon losses and cannot be extended using straightforward measure-and-repeat strategies without compromising unconditional security⁸. Alternatively, quantum repeaters⁹, which utilize intermediate quantum memory nodes and error correction techniques, can extend the range of quantum channels. However, their implementation remains an outstanding challenge^10-16, requiring a combination of efficient and high-fidelity quantum memories, gate operations, and measurements. Here we use a single solid-state spin memory integrated in a nanophotonic diamond resonator^17-19 to implement asynchronous photonic Bell-state measurements, which are a key component of quantum repeaters. In a proof-of-principle experiment, we demonstrate high-fidelity operation that effectively enables quantum communication at a rate that surpasses the ideal loss-equivalent direct-transmission method while operating at megahertz clock speeds. These results represent a crucial step towards practical quantum repeaters and large-scale quantum networks^20,21.

Generation of Tin-Vacancy Centers in Diamond via Shallow Ion Implantation and Subsequent Diamond Overgrowth

Group IV color centers in diamond have garnered great interest for their potential as optically active solid-state spin qubits. The future utilization of such emitters requires the development of precise site-controlled emitter generation techniques that are compatible with high-quality nanophotonic devices. This task is more challenging for color centers with large group IV impurity atoms, which are otherwise promising because of their predicted long spin coherence times without a dilution refrigerator. For example, when applied to the negatively charged tin-vacancy (SnV^-) center, conventional site-controlled color center generation methods either damage the diamond surface or yield bulk spectra with unexplained features. Here we demonstrate a novel method to generate site-controlled SnV^- centers with clean bulk spectra. We shallowly implant Sn ions through a thin implantation mask and subsequently grow a layer of diamond via chemical vapor deposition. This method can be extended to other color centers and integrated with quantum nanophotonic device fabrication.

Integrated Photonic Platform for Rare-Earth Ions in Thin Film Lithium Niobate

Rare-earth ion ensembles doped in single crystals are a promising materials system with widespread applications in optical signal processing, lasing, and quantum information processing. Incorporating rare-earth ions into integrated photonic devices could enable compact lasers and modulators, as well as on-chip optical quantum memories for classical and quantum optical applications. To this end, a thin film single crystalline wafer structure that is compatible with planar fabrication of integrated photonic devices would be highly desirable. However, incorporating rare-earth ions into a thin film form-factor while preserving their optical properties has proven challenging. We demonstrate an integrated photonic platform for rare-earth ions doped in a single crystalline thin film lithium niobate on insulator. The thin film is composed of lithium niobate doped with Tm³⁺. The ions in the thin film exhibit optical lifetimes identical to those measured in bulk crystals. We show narrow spectral holes in a thin film waveguide that require up to 2 orders of magnitude lower power to generate than previously reported bulk waveguides. Our results pave the way for scalable on-chip lasers, optical signal processing devices, and integrated optical quantum memories.