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Understanding the controls on temporal variation in plant leaf δ 2 H and δ 18 O values is important for understanding carbon–water dynamics of the biosphere and interpreting a wide range of proxies for past environments. Explaining the enrichment mechanisms under field conditions is challenging. To clarify the leaf water isotopic enrichment process at the ecosystem scale, four models with a range of complexities that were previously conducted at the leaf scale have been tested to simulate canopy foliage water in a multispecies grassland ecosystem. Although the exact importance of considering non-steady-state or/and isotopic diffusion in bulk leaf isotopic simulations has been reported in previous studies, our findings suggested that the steady-state assumption (SSA) is practically acceptable as a first-order approximation. The SSA two-pool model was the best option for reproducing seasonality of the bulk-leaf-water isotopic ratio for a grassland ecosystem. Relative humidity at canopy layer as the most controlling factor for canopy foliage water stable isotope composition because of its high sensitivity and variation. The results highlighted that canopy foliage water was a well-behaved property that was predictable for a multispecies grassland ecosystem at hourly or daily time-scales.

The isolation of qubits from noise sources, such as surrounding nuclear spins and spin–electric susceptibility1–4, has enabled extensions of quantum coherence times in recent pivotal advances towards the concrete implementation of spin-based quantum computation. In fact, the possibility of achieving enhanced quantum coherence has been substantially doubted for nanostructures due to the characteristic high degree of background charge fluctuations5–7. Still, a sizeable spin–electric coupling will be needed in realistic multiple-qubit systems to address single-spin and spin–spin manipulations8–10. Here, we realize a single-electron spin qubit with an isotopically enriched phase coherence time (20 μs)11,12 and fast electrical control speed (up to 30 MHz) mediated by extrinsic spin–electric coupling. Using rapid spin rotations, we reveal that the free-evolution dephasing is caused by charge noise—rather than conventional magnetic noise—as highlighted by a 1/f spectrum extended over seven decades of frequency. The qubit exhibits superior performance with single-qubit gate fidelities exceeding 99.9% on average, offering a promising route to large-scale spin-qubit systems with fault-tolerant controllability.

Universal quantum computation will require qubit technology based on a scalable platform 1 , together with quantum error correction protocols that place strict limits on the maximum infidelities for one- and two-qubit gate operations 2 , 3 . Although various qubit systems have shown high fidelities at the one-qubit level 4 – 10 , the only solid-state qubits manufactured using standard lithographic techniques that have demonstrated two-qubit fidelities near the fault-tolerance threshold 6 have been in superconductor systems. Silicon-based quantum dot qubits are also amenable to large-scale fabrication and can achieve high single-qubit gate fidelities (exceeding 99.9 per cent) using isotopically enriched silicon 11 , 12 . Two-qubit gates have now been demonstrated in a number of systems 13 – 15 , but as yet an accurate assessment of their fidelities using Clifford-based randomized benchmarking, which uses sequences of randomly chosen gates to measure the error, has not been achieved. Here, for qubits encoded on the electron spin states of gate-defined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80 to 89 per cent, and two-qubit randomized benchmarking with an average Clifford gate fidelity of 94.7 per cent and an average controlled-rotation fidelity of 98 per cent. These fidelities are found to be limited by the relatively long gate times used here compared with the decoherence times of the qubits. Silicon qubit designs employing fast gate operations with high Rabi frequencies 16 , 17 , together with advanced pulsing techniques 18 , should therefore enable much higher fidelities in the near future. Two-qubit logic gates in a silicon-based system are shown (using randomized benchmarking) to have high gate fidelities of operation and are used to generate Bell states, a step towards solid-state quantum computation.

Quantum computers are expected to outperform conventional computers in several important applications, from molecular simulation to search algorithms, once they can be scaled up to large numbers—typically millions—of quantum bits (qubits) 1 – 3 . For most solid-state qubit technologies—for example, those using superconducting circuits or semiconductor spins—scaling poses a considerable challenge because every additional qubit increases the heat generated, whereas the cooling power of dilution refrigerators is severely limited at their operating temperature (less than 100 millikelvin) 4 – 6 . Here we demonstrate the operation of a scalable silicon quantum processor unit cell comprising two qubits confined to quantum dots at about 1.5 kelvin. We achieve this by isolating the quantum dots from the electron reservoir, and then initializing and reading the qubits solely via tunnelling of electrons between the two quantum dots 7 – 9 . We coherently control the qubits using electrically driven spin resonance 10 , 11 in isotopically enriched silicon 12 28 Si, attaining single-qubit gate fidelities of 98.6 per cent and a coherence time of 2 microseconds during ‘hot’ operation, comparable to those of spin qubits in natural silicon at millikelvin temperatures 13 – 16 . Furthermore, we show that the unit cell can be operated at magnetic fields as low as 0.1 tesla, corresponding to a qubit control frequency of 3.5 gigahertz, where the qubit energy is well below the thermal energy. The unit cell constitutes the core building block of a full-scale silicon quantum computer and satisfies layout constraints required by error-correction architectures 8 , 17 . Our work indicates that a spin-based quantum computer could be operated at increased temperatures in a simple pumped 4 He system (which provides cooling power orders of magnitude higher than that of dilution refrigerators), thus potentially enabling the integration of classical control electronics with the qubit array 18 , 19 . A scalable silicon quantum processor unit cell made of two qubits confined to quantum dots operates at about 1.5 K, achieving 98.6% single-qubit gate fidelities and a 2 μs coherence time.

A high-fidelity two-qubit CNOT logic gate is presented, which is realized by combining single- and two-qubit operations with controlled phase operations in a quantum dot system using the exchange interaction. A silicon CNOT logic gate Whilst many different types of quantum bit or qubit have been realized, there are compelling reasons to focus on the development of silicon-based qubits that can be easily integrated with the CMOS (complementary metal-oxide-semiconductor) semiconductor technology used in today's transistors and microchips. High-fidelity silicon qubits have been demonstrated, but until now they have not performed quantum logic operations. Menno Veldhorst et al . report a high-fidelity two-qubit controlled NOT (or CNOT) logic gate using spins in enriched silicon. This device is a step towards a scalable, solid-state platform for quantum computation. Quantum computation requires qubits that can be coupled in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates 1 , 2 . Many physical realizations of qubits exist, including single photons 3 , trapped ions 4 , superconducting circuits 5 , single defects or atoms in diamond 6 , 7 and silicon 8 , and semiconductor quantum dots 9 , with single-qubit fidelities that exceed the stringent thresholds required for fault-tolerant quantum computing 10 . Despite this, high-fidelity two-qubit gates in the solid state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits 5 , owing to the difficulties of coupling qubits and dephasing in semiconductor systems 11 , 12 , 13 . Here we present a two-qubit logic gate, which uses single spins in isotopically enriched silicon 14 and is realized by performing single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the Loss–DiVincenzo proposal 2 . We realize CNOT gates via controlled-phase operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is used in the two-qubit controlled-phase gate. By independently reading out both qubits, we measure clear anticorrelations in the two-spin probabilities of the CNOT gate.

Single-electron spin qubits employ magnetic fields on the order of 1 Tesla or above to enable quantum state readout via spin-dependent-tunnelling. This requires demanding microwave engineering for coherent spin resonance control, which limits the prospects for large scale multi-qubit systems. Alternatively, singlet-triplet readout enables high-fidelity spin-state measurements in much lower magnetic fields, without the need for reservoirs. Here, we demonstrate low-field operation of metal-oxide-silicon quantum dot qubits by combining coherent single-spin control with high-fidelity, single-shot, Pauli-spin-blockade-based ST readout. We discover that the qubits decohere faster at low magnetic fields with T 2 Rabi = 18.6  μs and T 2 * = 1.4  μs at 150 mT. Their coherence is limited by spin flips of residual 29 Si nuclei in the isotopically enriched 28 Si host material, which occur more frequently at lower fields. Our finding indicates that new trade-offs will be required to ensure the frequency stabilization of spin qubits, and highlights the importance of isotopic enrichment of device substrates for the realization of a scalable silicon-based quantum processor. One of the main sources of decoherence in silicon electron spin qubits is their interaction with nearby fluctuating nuclear spins. Zhao et al. present a device made from enriched silicon to reduce the nuclear spin density and find its performance is still limited by fluctuations of residual spins.

Conventional optical components are limited to size scales much larger than the wavelength of light, as changes to the amplitude, phase and polarization of the electromagnetic fields are accrued gradually along an optical path. However, advances in nanophotonics have produced ultrathin, so-called 'flat' optical components that beget abrupt changes in these properties over distances significantly shorter than the free-space wavelength. Although high optical losses still plague many approaches, phonon polariton (PhP) materials have demonstrated long lifetimes for sub-diffractional modes in comparison to plasmon-polariton-based nanophotonics. We experimentally observe a threefold improvement in polariton lifetime through isotopic enrichment of hexagonal boron nitride (hBN). Commensurate increases in the polariton propagation length are demonstrated via direct imaging of polaritonic standing waves by means of infrared nano-optics. Our results provide the foundation for a materials-growth-directed approach aimed at realizing the loss control necessary for the development of PhP-based nanophotonic devices.

The continuous increase of the greenhouse gas nitrous oxide (N2O) in the atmosphere due to increasing anthropogenic nitrogen input in agriculture has become a global concern. In recent years, identification of the microbial assemblages responsible for soil N2O production has substantially advanced with the development of molecular technologies and the discoveries of novel functional guilds and new types of metabolism. However, few practical tools are available to effectively reduce in situ soil N2O flux. Combating the negative impacts of increasing N2O fluxes poses considerable challenges and will be ineffective without successfully incorporating microbially regulated N2O processes into ecosystem modeling and mitigation strategies. Here, we synthesize the latest knowledge of (i) the key microbial pathways regulating N2O production and consumption processes in terrestrial ecosystems and the critical environmental factors influencing their occurrence, and (ii) the relative contributions of major biological pathways to soil N2O emissions by analyzing available natural isotopic signatures of N2O and by using stable isotope enrichment and inhibition techniques. We argue that it is urgently necessary to incorporate microbial traits into biogeochemical ecosystem modeling in order to increase the estimation reliability of N2O emissions. We further propose a molecular methodology oriented framework from gene to ecosystem scales for more robust prediction and mitigation of future N2O emissions. This review summarizes the major microbial pathways of soil N2O production, and key environmental factors modulating their relative contributions, and further proposes to use a combination of state-of-the-art approaches for better source partitioning and incorporation of microbial datasets to achieve better predictive ecosystem models.

One-atom-thick crystals are impermeable to atoms and molecules, but hydrogen ions (thermal protons) penetrate through them. We show that monolayers of graphene and boron nitride can be used to separate hydrogen ion isotopes. Using electrical measurements and mass spectrometry, we found that deuterons permeate through these crystals much slower than protons, resulting in a separation factor of ≈10 at room temperature. The isotope effect is attributed to a difference of ≈60 milli–electron volts between zero-point energies of incident protons and deuterons, which translates into the equivalent difference in the activation barriers posed by two-dimensional crystals. In addition to providing insight into the proton transport mechanism, the demonstrated approach offers a competitive and scalable way for hydrogen isotope enrichment.

Copper(I)-catalyzed azide-alkyne cycloaddition has become a commonly employed method for the synthesis of complex molecular architectures under challenging conditions. Despite the widespread use of copper-catalyzed cycloaddition reactions, the mechanism of these processes has remained difficult to establish due to the involvement of multiple equilibria between several reactive intermediates. Real-time monitoring of a representative cycloaddition process via heat-flow reaction calorimetry revealed that monomeric copper acetylide complexes are not reactive toward organic azides unless an exogenous copper catalyst is added. Furthermore, crossover experiments with an isotopically enriched exogenous copper source illustrated the stepwise nature of the carbon-nitrogen bond-forming events and the equivalence of the two copper atoms within the cycloaddition steps.