Mapping a 50-spin-qubit network through correlated sensing

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

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

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

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

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

[Figure: see text].

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

Single electron spins coupled to multiple nuclear spins provide promising multi-qubit registers for quantum sensing and quantum networks. The obtainable level of control is determined by how well the electron spin can be selectively coupled to, and decoupled from, the surrounding nuclear spins. Here we realize a coherence time exceeding a second for a single nitrogen-vacancy electron spin through decoupling sequences tailored to its microscopic nuclear-spin environment. First, we use the electron spin to probe the environment, which is accurately described by seven individual and six pairs of coupled carbon-13 spins. We develop initialization, control and readout of the carbon-13 pairs in order to directly reveal their atomic structure. We then exploit this knowledge to store quantum states in the electron spin for over a second by carefully avoiding unwanted interactions. These results provide a proof-of-principle for quantum sensing of complex multi-spin systems and an opportunity for multi-qubit quantum registers with long coherence times.

Neutral Silicon-Vacancy Center in Diamond: Spin Polarization and Lifetimes

We demonstrate optical spin polarization of the neutrally charged silicon-vacancy defect in diamond (SiV^{0}), an S=1 defect which emits with a zero-phonon line at 946 nm. The spin polarization is found to be most efficient under resonant excitation, but nonzero at below-resonant energies. We measure an ensemble spin coherence time T_{2}>100  μs at low-temperature, and a spin relaxation limit of T_{1}>25  s. Optical spin-state initialization around 946 nm allows independent initialization of SiV^{0} and NV^{-} within the same optically addressed volume, and SiV^{0} emits within the telecoms down-conversion band to 1550 nm: when combined with its high Debye-Waller factor, our initial results suggest that SiV^{0} is a promising candidate for a long-range quantum communication technology.

Entanglement distillation between solid-state quantum network nodes

The impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable imperfections necessitate a means to improve remote entanglement by local quantum operations. We realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. The heralded generation of two copies of a remote entangled state is demonstrated through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. The key combination of generating, storing, and processing entangled states should enable the exploration of multiparticle entanglement on an extended quantum network.

Experimental creation of quantum Zeno subspaces by repeated multi-spin projections in diamond

Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates quantum Zeno subspaces and simultaneously suppresses the dephasing caused by a quasi-static environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide experimental insight into the interplay between frequent multi-spin measurements and slowly varying noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.

Repeated observations of quantum states inhibit coherent evolution through the Zeno effect, providing opportunities for controlling multi-qubit systems. Here the authors demonstrate that projecting joint observables of three spins in diamond creates quantum Zeno subspaces that suppress dephasing.

Optimized quantum sensing with a single electron spin using real-time adaptive measurements

Quantum sensors based on single solid-state spins promise a unique combination of sensitivity and spatial resolution. The key challenge in sensing is to achieve minimum estimation uncertainty within a given time and with high dynamic range. Adaptive strategies have been proposed to achieve optimal performance, but their implementation in solid-state systems has been hindered by the demanding experimental requirements. Here, we realize adaptive d.c. sensing by combining single-shot readout of an electron spin in diamond with fast feedback. By adapting the spin readout basis in real time based on previous outcomes, we demonstrate a sensitivity in Ramsey interferometry surpassing the standard measurement limit. Furthermore, we find by simulations and experiments that adaptive protocols offer a distinctive advantage over the best known non-adaptive protocols when overhead and limited estimation time are taken into account. Using an optimized adaptive protocol we achieve a magnetic field sensitivity of 6.1 ± 1.7 nT Hz(-1/2) over a wide range of 1.78 mT. These results open up a new class of experiments for solid-state sensors in which real-time knowledge of the measurement history is exploited to obtain optimal performance.

Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers

We report direct measurement of population dynamics in the excited state manifold of a nitrogen-vacancy (NV) center in diamond. We quantify the phonon-induced mixing rate and demonstrate that it can be completely suppressed at low temperatures. Further, we measure the intersystem crossing (ISC) rate for different excited states and develop a theoretical model that unifies the phonon-induced mixing and ISC mechanisms. We find that our model is in excellent agreement with experiment and that it can be used to predict unknown elements of the NV center's electronic structure. We discuss the model's implications for enhancing the NV center's performance as a room-temperature sensor.

Quantum information. Unconditional quantum teleportation between distant solid-state quantum bits

Realizing robust quantum information transfer between long-lived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photon-mediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bell-state measurement combined with real-time feed-forward, quantum teleportation is achieved upon each attempt with an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and network-based quantum computing.

Coherent optical transitions in implanted nitrogen vacancy centers

We report the observation of stable optical transitions in nitrogen-vacancy (NV) centers created by ion implantation. Using a combination of high temperature annealing and subsequent surface treatment, we reproducibly create NV centers with zero-phonon lines (ZPL) exhibiting spectral diffusion that is close to the lifetime-limited optical line width. The residual spectral diffusion is further reduced by using resonant optical pumping to maintain the NV(-) charge state. This approach allows for placement of NV centers with excellent optical coherence in a well-defined device layer, which is a crucial step in the development of diamond-based devices for quantum optics, nanophotonics, and quantum information science.

Colour-causing defects and their related optoelectronic transitions in single crystal CVD diamond

Defects causing colour in nitrogen-doped chemical vapour-deposited (CVD) diamond can adversely affect the exceptional optical, electronic and spintronic properties of the material. Several techniques were used to study these defects, namely optical absorption spectroscopy, thermoluminescence (TL) and electron paramagnetic resonance (EPR). From our studies, the defects causing colour in nitrogen-doped CVD diamond are clearly not the same as those causing similar colour in natural diamonds. The brown colour arises due to a featureless absorption profile that decreases in intensity with increasing wavelength, and a broad feature at 360 nm (3.49 eV) that scales in intensity with it. Another prominent absorption band, centred at 520 nm (2.39 eV), is ascribed to the neutral nitrogen-vacancy-hydrogen defect. The defects responsible for the brown colour possess acceptor states that are 1.5 eV from the valence band (VB) edge. The brown colour is removed by heat treatment at 1600 ° C, whereupon new defects possessing shallow (<1 eV) trap states are generated.

Integrated high-quality factor optical resonators in diamond

The realization of an integrated diamond photonic platform, based on a thin single crystal diamond film on top of a silicon dioxide/silicon substrate, is reported. Using this approach, we demonstrate high-quality factor single crystal diamond race-track resonators, operating at near-infrared wavelengths (1550 nm). The devices are integrated with low-loss diamond waveguides terminated with polymer pads (spot size converters) to facilitate in- (out-) coupling of light from (to) an optical fiber. Optical characterization of these resonators reveal quality factors as high as ~250,000 and overall insertion losses as low as 1 dB/facet. Scattering induced mode splitting as well as signatures of nonlinear effects such as optical bistability are observed at an input pump power of ~100 mW in the waveguides.

Coupling of NV centers to photonic crystal nanobeams in diamond

The realization of efficient optical interfaces for solid-state atom-like systems is an important problem in quantum science with potential applications in quantum communications and quantum information processing. We describe and demonstrate a technique for coupling single nitrogen vacancy (NV) centers to suspended diamond photonic crystal cavities with quality factors up to 6000. Specifically, we present an enhancement of the NV center's zero-phonon line fluorescence by a factor of ~ 7 in low-temperature measurements.

Quantum interference of single photons from remote nitrogen-vacancy centers in diamond

We demonstrate quantum interference between indistinguishable photons emitted by two nitrogen-vacancy centers in distinct diamond samples separated by two meters. Macroscopic solid immersion lenses are used to enhance photon collection efficiency. Quantum interference is verified by measuring a value of the second-order cross-correlation function g((2))(0)=0.35±0.04<0.5. In addition, optical transition frequencies of two separated nitrogen-vacancy centers are tuned into resonance with each other by applying external electric fields. An extension of the present approach to generate entanglement of remote solid-state qubits is discussed.

High-dynamic-range magnetometry with a single nuclear spin in diamond

Sensors based on the nitrogen-vacancy defect in diamond are being developed to measure weak magnetic and electric fields at the nanoscale. However, such sensors rely on measurements of a shift in the Lamor frequency of the defect, so an accumulation of quantum phase causes the measurement signal to exhibit a periodic modulation. This means that the measurement time is either restricted to half of one oscillation period, which limits accuracy, or that the magnetic field range must be known in advance. Moreover, the precision increases only slowly (as T(-0.5)) with measurement time T (ref. 3). Here, we implement a quantum phase estimation algorithm on a single nuclear spin in diamond to combine both high sensitivity and high dynamic range. By achieving a scaling of the precision with time to T(-0.85), we improve the sensitivity by a factor of 7.4 for an accessible field range of 16 mT, or, alternatively, we improve the dynamic range by a factor of 130 for a sensitivity of 2.5 µT Hz(-1/2). Quantum phase estimation algorithms have also recently been implemented using a single electron spin in a nitrogen-vacancy centre. These methods are applicable to a variety of field detection schemes, and do not require quantum entanglement.

Diamond-metal contacts: interface barriers and real-time characterization

A review of diamond-metal contacts is presented with reference to reported values of interfacial potential (Schottky) barriers and their dependence on macroscopic and microscopic properties of the diamond surface, the interface and the metal. No simple model can account for the overall spread of p-diamond barriers, although there are, for certain metals, correlations with metal electronegativity, interface chemistry and diamond surface preparation. Detailed studies are presented for a selected contact (Al-p-diamond) using real-time monitoring during metal growth from sub-nanometre to bulk films and subsequent in situ heating to 1000 °C. This contact, prepared in a clean vacuum environment on characterized single-crystal substrates, provides a case study for a combined in situ electrical and spectroscopic investigation using IV measurements for macroscopic diodes and real-time photoelectron spectroscopy for nanoscale metal films. Band bending during growth leads to a rectifying contact with a measured IV barrier height of 1.05 V and an ideality factor of 1.4. A transition from layered to clustered growth of the metal film is revealed in the real-time measurements and this is confirmed by AFM. For the annealed contact, a direct correlation is revealed by real-time photoemission between the onset of interfacial carbide formation and the change from a rectifying to an ohmic contact at 482 °C.

Chemical vapour deposition synthetic diamond: materials, technology and applications

Substantial developments have been achieved in the synthesis of chemical vapour deposition (CVD) diamond in recent years, providing engineers and designers with access to a large range of new diamond materials. CVD diamond has a number of outstanding material properties that can enable exceptional performance in applications as diverse as medical diagnostics, water treatment, radiation detection, high power electronics, consumer audio, magnetometry and novel lasers. Often the material is synthesized in planar form; however, non-planar geometries are also possible and enable a number of key applications. This paper reviews the material properties and characteristics of single crystal and polycrystalline CVD diamond, and how these can be utilized, focusing particularly on optics, electronics and electrochemistry. It also summarizes how CVD diamond can be tailored for specific applications, on the basis of the ability to synthesize a consistent and engineered high performance product.

High crystalline quality single crystal chemical vapour deposition diamond

Homoepitaxial chemical vapour deposition (CVD) on high pressure, high temperature (HPHT) synthetic diamond substrates allows the production of diamond material with controlled point defect content. In order to minimize the extended defect content, however, it is necessary to minimize the number of substrate extended defects that reach the initial growth surface and the nucleation of dislocations at the interface between the CVD layer and its substrate. X-ray topography has indicated that when type IIa HPHT synthetic substrates are used, the density of dislocations nucleating at the interface can be less than 400  cm(-2). X-ray topography, photoluminescence imaging and birefringence microscopy of HPHT grown synthetic type IIa diamond clearly show that the extended defect content is growth sector dependent. ⟨111⟩ sectors contain the highest concentration of both stacking faults and dislocations but ⟨100⟩ sectors are relatively free of both. It has been shown that HPHT treatment of such material can significantly reduce the area of stacking faults and cause dislocations to move. This knowledge, coupled with an understanding of how growth sectors develop during HPHT synthesis, has been used to guide selection and processing of substrates suitable for CVD synthesis of material with high crystalline perfection and controlled point defect content.

Charge transfer effects, thermo and photochromism in single crystal CVD synthetic diamond

We report on the effects of thermal treatment and ultraviolet irradiation on the point defect concentrations and optical absorption profiles of single crystal CVD synthetic diamond. All thermal treatments were below 850 K, which is lower than the growth temperature and unlikely to result in any structural change. UV-visible absorption spectroscopy measurements showed that upon thermal treatment (823 K), various broad absorption features diminished: an absorption band at 270 nm (used to deduce neutral single substitutional nitrogen (N(S)(0)) concentrations) and also two broad features centred at approximately 360 and 520 nm. Point defect centre concentrations as a function of temperature were also deduced using electron paramagnetic resonance (EPR) spectroscopy. Above ∼500 K, we observed a decrease in the concentration of N(S)(0) centres and a concomitant increase in the negatively charged nitrogen-vacancy-hydrogen (NVH) complex (NVH(-)) concentration. Both transitions exhibited an activation energy between 0.6 and 1.2 eV, which is lower than that for the N(S)(0) donor (∼1.7 eV). Finally, it was found that illuminating samples with intense short-wave ultraviolet light recovered the N(S)(0) concentration and also the 270, 360 and 520 nm absorption features. From these results, we postulate a valence band mediated charge transfer process between NVH and single nitrogen centres with an acceptor trap depth for NVH of 0.6-1.2 eV. Because the loss of N(S)(0) concentration is greater than the increase in NVH(-) concentration we also suggest the presence of another unknown acceptor existing at a similar energy to NVH. The extent to which the colour in CVD synthetic diamond is dependent on prior history is discussed.

Hydrogen incorporation in diamond: the vacancy-hydrogen complex

We report the identification of the vacancy-hydrogen complex in single crystal diamond synthesized by chemical vapor deposition. The S=1 defect is observed by electron paramagnetic resonance in the negative charge state. The hydrogen atom is bonded to one of the carbon atoms neighboring the vacancy. Unlike the analogous defect in silicon, no symmetry lowering reconstruction occurs between the three remaining carbon dangling orbitals. The very small measured hydrogen hyperfine interaction is explained by dipolar coupling between the hydrogen and the unpaired electron probability density delocalized on the three equivalent carbon neighbors.

Hydrogen incorporation in diamond: the nitrogen-vacancy-hydrogen complex

We report the identification of the nitrogen-vacancy-hydrogen complex in a freestanding nitrogen-doped isotopically engineered single crystal diamond synthesized by chemical vapor deposition. The hydrogen atom is located in the vacancy of a nearest-neighbor nitrogen-vacancy defect and appears to be bonded to the nitrogen atom maintaining the trigonal symmetry of the center. The defect is observed by electron paramagnetic resonance in the negative charge state in samples containing a suitable electron donor (e.g., substitutional nitrogen N(0)(S)).