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Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor1. Optical atomic clocks2, the current state of the art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology3–6. Augmenting tweezer-based clocks featuring microscopic control and detection7–10with the high-fidelity entangling gates developed for atom-array information processing11,12offers a promising route towards making use of highly entangled quantum states for improved optical clocks. Here we develop and use a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger–Horne–Zeilinger (GHZ) type with up to nine optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit (SQL) using GHZ states of up to four qubits. However, because of their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared with unentangled atoms13. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval14–17. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision.

Polar molecules confined in an optical lattice are a versatile platform to explore spin-motion dynamics based on strong, long-range dipolar interactions1,2. The precise tunability3of Ising and spin-exchange interactions with both microwave and d.c. electric fields makes the molecular system particularly suitable for engineering complex many-body dynamics4–6. Here we used Floquet engineering7to realize new quantum many-body systems of polar molecules. Using a spin encoded in the two lowest rotational states of ultracold 40K87Rb molecules, we mutually validated XXZ spin models tuned by a Floquet microwave pulse sequence against those tuned by a d.c. electric field through observations of Ramsey contrast dynamics. This validation sets the stage for the realization of Hamiltonians inaccessible with static fields. In particular, we observed two-axis twisting8mean-field dynamics, generated by a Floquet-engineered XYZ model using itinerant molecules in two-dimensional layers. In the future, Floquet-engineered Hamiltonians could generate entangled states for molecule-based precision measurement9or could take advantage of the rich molecular structure for quantum simulation of multi-level systems10,11.

Titanium:sapphire (Ti:sapphire) lasers have been essential for advancing fundamental research and technological applications, including the development of the optical frequency comb1, two-photon microscopy2and experimental quantum optics3,4. Ti:sapphire lasers are unmatched in bandwidth and tuning range, yet their use is restricted because of their large size, cost and need for high optical pump powers5. Here we demonstrate a monocrystalline titanium:sapphire-on-insulator (Ti:SaOI) photonics platform that enables dramatic miniaturization, cost reduction and scalability of Ti:sapphire technology. First, through the fabrication of low-loss whispering-gallery-mode resonators, we realize a Ti:sapphire laser operating with an ultralow, sub-milliwatt lasing threshold. Then, through orders-of-magnitude improvement in mode confinement in Ti:SaOI waveguides, we realize an integrated solid-state (that is, non-semiconductor) optical amplifier operating below 1 μm. We demonstrate unprecedented distortion-free amplification of picosecond pulses to peak powers reaching 1.0 kW. Finally, we demonstrate a tunable integrated Ti:sapphire laser, which can be pumped with low-cost, miniature, off-the-shelf green laser diodes. This opens the doors to new modalities of Ti:sapphire lasers, such as massively scalable Ti:sapphire laser-array systems for several applications. As a proof-of-concept demonstration, we use a Ti:SaOI laser array as the sole optical control for a cavity quantum electrodynamics experiment with artificial atoms in silicon carbide6. This work is a key step towards the democratization of Ti:sapphire technology through a three-orders-of-magnitude reduction in cost and footprint and introduces solid-state broadband amplification of sub-micron wavelength light.

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.

Nanophotonic structures have shown promising routes to controlling and enhancing nonlinear optical processes at the nanoscale. However, most nonlinear nanostructures require a handling substrate, reducing their application scope. Due to the underwhelming heat dissipation, it has been a challenge to evaluate the nonlinear optical properties of free-standing nanostructures. Here, we overcome this challenge by performing shot-controlled fifth harmonic generation (FHG) measurements on a SiC meta-membrane – a free-standing transmission metasurface with pronounced optical resonances in the mid-infrared (λres≈ 4,000 nm). Back focal plane imaging of the FHG diffraction orders and rigorous finite-difference time-domain simulations reveal at least two orders of magnitude enhancement of the FHG from the meta-membrane, compared to the unstructured SiC film of the same thickness. Single-shot measurements of the meta-membrane with varying resonance positions reveal an unusual spectral behavior that we explain with Kerr-driven intensity-dependent resonance dynamics. This work paves the way for novel substrate-less nanophotonic architectures.

Older people living with frailty are frequent users of emergency care and have multiple and complex problems. Typical evidence-based guidelines and protocols provide guidance for the management of single and simple acute issues. Meanwhile, person-centred care orientates interventions around the perspectives of the individual. Using a case vignette, we illustrate the potential pitfalls of applying exclusively either evidence-based or person-centred care in isolation, as this may trigger inappropriate clinical processes or place undue onus on patients and families. We instead advocate for delivering a combined evidence-based, person-centred approach to healthcare which considers the person’s situation and values, apparent problem and available options.

Suppressing errors is the central challenge for useful quantum computing1, requiring quantum error correction (QEC)2–6for large-scale processing. However, the overhead in the realization of error-corrected ‘logical’ qubits, in which information is encoded across many physical qubits for redundancy2–4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays7, our system combines high two-qubit gate fidelities8, arbitrary connectivity7,9, as well as fully programmable single-qubit rotations and mid-circuit readout10–15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code6distance from d= 3 to d= 7, preparation of colour-code qubits with break-even fidelities5, fault-tolerant creation of logical Greenberger–Horne–Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks16,17, we realize computationally complex sampling circuits18with up to 48 logical qubits entangled with hypercube connectivity19with 228 logical two-qubit gates and 48 logical CCZ gates20. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, potentially enabling low-overhead fault-tolerant quantum computing. However, implementing qLDPC codes involves nonlocal operations that require long-range connectivity between qubits. This makes their physical realization challenging in comparison to geometrically local codes, such as the surface code. Here we propose a hardware-efficient scheme for fault-tolerant quantum computation with high-rate qLDPC codes that is compatible with the recently demonstrated capabilities of reconfigurable atom arrays. Our approach utilizes the product structure inherent in many qLDPC codes to implement the nonlocal syndrome extraction circuit through atom rearrangement, resulting in an effectively constant overhead. We prove the fault tolerance of these protocols, and our simulations show that the qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits. We further find that quantum algorithms involving thousands of logical qubits can be performed using less than 105physical qubits. Our work suggests that low-overhead quantum computing with qLDPC codes is within reach using current experimental technologies.

The present study considers the role of adjectives and adverbs in stylometric analysis and authorship attribution. Adjectives and adverbs allow both for variations in placement and order (adverbs) and variations in type (adjectives). This preliminary study examines a collection of 25 English-language blogs taken from the Schler Blog corpus, and the Project Gutenberg corpus with specific emphasis on 3 works. Within the blog corpora, the first and last 100 lines were extracted for the purpose of analysis. Project Gutenberg corpora were used in full. All texts were processed and part-of-speech tagged using the Python NLTK package. All adverbs were classified as sentence-initial, preverbal, interverbal, postverbal, sentence-final, or none-of-the-above. The adjectives were classified into types according to the universal English type hierarchy (Cambridge Dictionary Online, 2021; Annear, 1964) manually by one of the authors. Ambiguous adjectives were classified according to their context. For the adverbs, the initial samples were paired and used as training data to attribute the final samples. This resulted in 600 trials under each of five experimental conditions. We were able to attribute authorship with an average accuracy of 9.7% greater than chance across all five conditions. Confirmatory experiments are ongoing with a larger sample of English-language blogs. This strongly suggests that adverbial placement is a useful and novel idiolectal variable for authorship attribution (Juola et al., 2021). For the adjective, differences were found in the type of adjective used by each author. Percent use of each type varied based upon individual preference and subject-matter (e.g. Moby Dick had a large number of adjectives related to size and color). While adverbial order and placement are highly variable, adjectives are subject to rigid restrictions that are not violated across texts and authors. Stylometric differences in adjective use generally involve the type and category of adjectives preferred by the author. Future investigation will focus, likewise, on whether adverbial variation is similarly analyzable by type and category of adverb.

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7and digital simulations15.

The self-consistent problem of electromagnetic (EM) field excitation by a rectilinear electron beam moving along either uniform grating Smith–Purcell radiation (SPR) or bi-periodic grating (leaky wave radiation of spoof surface plasmon polariton) and the influence of the excited EM field on the electron beam has been considered. It is shown that a deceleration of electrons (energy transfer from electrons to EM wave) in both the Smith–Purcell radiation and the leaky wave radiation of the spoof surface plasmon polariton regimes may occur for essentially increased slow wave circuit length in comparison with conventional backward wave oscillator (BWO) and orotrons. This allows either to enhance the output power or to reduce the beam current density of the THz oscillator. The simulations show the output power of 18 W with the corresponding efficiency of 1.5% at 0.64 THz in the case of the circuit length of 28 mm while the current density is 180 A/cm2. Such operation is based on the hybrid bulk-surface mode (HBSM) excitation in the THz oscillator cavity with bi-periodic grating and the top reflector for leaky waves. This is promising for the increase of the output efficiency higher than 1% and providing the Watt level of output power in the THz oscillator based on hybrid bulk-surface modes.

The controlled reaction between [Pt2(DVTMS)3], where DVTMS represents 1,3-divinyl-1,1,3,3-tetramethyldisiloxane, and dialkylbiaryl phosphines (Buchwald ligands) 2-(di-tert-butylphosphino)biphenyl (JohnPhos, 1), 2-(dicyclohexylphosphino)biphenyl (CyJohnPhos, 2), 2-di-tert-butylphosphino-2′,4′,6′-triisopropylbiphenyl (tBuXPhos, 3), 2-dicyclohexylphosphino-2′,4′,6′-triisopropylbiphenyl (XPhos, 4), 2-dicyclohexylphosphino-2′,6′-dimethoxybiphenyl (SPhos, 5), 2-dicyclohexylphosphino-2′-(N,N-dimethylamino)biphenyl (DavePhos, 6), and 2-dicyclohexylphosphino-2′,4′,6′-trimethoxybiphenyl (MeOSPhos, 7) generates an efficient platinum catalyst of type [Pt(DVTMS)(L)] (1a–7a), where L represents the Buchwald ligand, applied for hydrosilylation of phenylacetylene by diphenylsilane. The X-ray crystal structure analysis of the obtained Pt catalysts showed the presence of specific Pt-aryl interactions with the phenyl group of the dialkylbiarylphosphine ligand in complex 1a, while the same effect was not observed for the related 2′,4′,6′-triisopropyl substituted aromatic ring in 3a. The evaluation of the steric parameters from X-ray diffraction analysis (XRD) showed the increase of the steric hindrances around the platinum atom improves the selectivity and the yield of the β(E)-product.

Strongly correlated systems can exhibit unexpected phenomena when brought in a state far from equilibrium. An example is many-body localization, which prevents generic interacting systems from reaching thermal equilibrium even at long times1,2. The stability of the many-body localized phase has been predicted to be hindered by the presence of small thermal inclusions that act as a bath, leading to the delocalization of the entire system through an avalanche propagation mechanism3–8. Here we study the dynamics of a thermal inclusion of variable size when it is coupled to a many-body localized system. We find evidence for accelerated transport of thermal inclusion into the localized region. We monitor how the avalanche spreads through the localized system and thermalizes it site by site by measuring the site-resolved entropy over time. Furthermore, we isolate the strongly correlated bath-induced dynamics with multipoint correlations between the bath and the system. Our results have implications on the robustness of many-body localized systems and their critical behaviour.

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The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits8and a toric code state on a torus with sixteen data and eight ancillary qubits9. Finally, we use this architecture to realize a hybrid analogue–digital evolution2and use it for measuring entanglement entropy in quantum simulations10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.

Abstract—: The article summarizes the results of research into analysis and modeling of interregional value chains (IRVCs). The necessity of developing state policy aimed at IRVC development is substantiated. The existing analytical and modeling tools for improving the quality of management of these processes are systematized and tested. The primary directions and instruments of IRVC regulation are presented.

Soliton microcombs—phase-locked microcavity frequency combs—have become the foundation of several classical technologies in integrated photonics, including spectroscopy, LiDAR and optical computing. Despite the predicted multimode entanglement across the comb, experimental study of the quantum optics of the soliton microcomb has been elusive. In this work we use second-order photon correlations to study the underlying quantum processes of soliton microcombs in an integrated silicon carbide microresonator. We show that a stable temporal lattice of solitons can isolate a multimode below-threshold Gaussian state from any admixture of coherent light, and predict that all-to-all entanglement can be realized for the state. Our work opens a pathway toward a soliton-based multimode quantum resource.