The growing demands of remote detection and an increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles two traditional machine learning problems, the least-square fitting and softmax regression problems, in the scenario where the dataset is distributed across two parties. Our quantum algorithm finds the model parameters with a communication complexity of $O({\log }_2(N)/\epsilon )$, where $N$ is the number of data points and $\epsilon$ is the bound on parameter errors. Compared to classical and other quantum methods that achieve the same goal, our methods provide a communication advantage in the scaling with data volume. The core of our methods, the quantum bipartite correlator algorithm that estimates the correlation or the Hamming distance of two bit strings distributed across two parties, may be further applied to other information processing tasks.

Recently, a proper genuine multipartite entanglement measure has been found for three-qubit pure states [see Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)], but capturing useful entanglement measures for mixed states has remained an open challenge. So far, it requires not only a full tomography in experiments, but also huge calculational labor. A leading proposal was made by Gühne, Reimpell, and Werner [Phys. Rev. Lett. 98, 110502 (2007)], who used expectation values of entanglement witnesses to describe a lower bound estimation of entanglement. We provide here an extension that also gives genuine upper bounds of entanglement. This advance requires only the expectation value of any Hermitian operator. Moreover, we identify a class of operators ${\mathcal{A}}_1$ that not only give good estimates, but also require a remarkably small number of experimental measurements. In this Letter, we define our approach and illustrate it by estimating entanglement measures for a number of pure and mixed states prepared in our recent experiments.

We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in $2+1$ and $3+1$ dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to interesting renormalization group flows and for sufficiently large representations to complete or partial screening by charged fields. This result is universal: in large enough representations, Wilson lines are screened by the charged matter fields. We observe that the onset of the screening instability is associated with fixed-point mergers. We study this phenomenon in a variety of applications. In some cases, the screening of the Wilson lines takes place by dimensional transmutation and the generation of an exponentially large scale. We identify the space of infrared conformal Wilson lines in weakly coupled gauge theories in $3+1$ dimensions and determine the screening cloud due to bosons or fermions. We also study QED in $2+1$ dimensions in the large $N_f$ limit and identify the nontrivial conformal Wilson lines. We briefly discuss ‘t Hooft lines in $3+1$-dimensional gauge theories and find that they are screened in weakly coupled gauge theories with simply connected gauge groups. In non-Abelian gauge theories with $S$ duality, this together with our analysis of the Wilson lines gives a compelling picture for the screening of the line operators as a function of the coupling.

Parton saturation is one of the most intriguing phenomena in the high energy nuclear physics research frontier, especially in the upcoming era of the Electron-Ion Collider (EIC). The lepton-jet correlation in deep inelastic scattering provides us with a new gateway to the parton saturation at the EIC. In particular, we demonstrate that azimuthal angle anisotropies of the lepton-jet correlation are sensitive to the strength of the saturation momentum in the EIC kinematic region. In contrast to the predictions based on the collinear framework calculation, significant nuclear modification of the anisotropies is observed when we compare the saturation physics results in $e+p$ and $e+\mathrm{Au}$ scatterings. By measuring these harmonic coefficients at the EIC, one can conduct quantitative analyses in different collisional systems and unveil compelling evidence for saturation effects.

Using the data sample of $980{\mathrm{fb}}^{-1}$ collected with the Belle detector operating at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider, we present the results of an investigation of the $\mathrm{\Lambda }{\pi }^{+}$ and $\mathrm{\Lambda }{\pi }^{-}$ invariant mass distributions looking for substructure in the decay ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}{\pi }^{+}{\pi }^{-}$. We find a significant signal in each mass distribution. When interpreted as resonances, we find for the $\mathrm{\Lambda }{\pi }^{+}$ ($\mathrm{\Lambda }{\pi }^{-}$) combination a mass of $1434.3\pm 0.6(\mathrm{stat})\pm 0.9(\mathrm{syst})\mathrm{MeV}/c^2$ [$1438.5\pm 0.9(\mathrm{stat})\pm 2.5(\mathrm{syst})\mathrm{MeV}/c^2$], an intrinsic width of $11.5\pm 2.8(\mathrm{stat})\pm 5.3(\mathrm{syst})\mathrm{MeV}/c^2$ [$33.0\pm 7.5(\mathrm{stat})\pm 23.6(\mathrm{syst})\mathrm{MeV}/c^2$] with a significance of $7.5\sigma$ ($6.2\sigma$). As these two signals are very close to the $\overline{K}N$ threshold, we also investigate the possibility of a $\overline{K}N$ cusp, and find that we cannot discriminate between these two interpretations due to the limited size of the data sample.

Using $4.7{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data at center-of-mass energies from 4.661 to 4.951 GeV collected by the BESIII detector at the BEPCII collider, we observe the $X(3872)$ production process $e^{+}{e}^{-}\to \omega X(3872)$ for the first time. The significance is $7.8\sigma$, including both the statistical and systematic uncertainties. The $e^{+}{e}^{-}\to \omega X(3872)$ Born cross section and the corresponding upper limit at 90% confidence level at each energy point are reported. The line shape of the cross section indicates that the $\omega X(3872)$ signals may be from the decays of some nontrivial structures.

Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an $N$-particle density matrix, known as $N$-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher-order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the ${\mathrm{H}}_8$ ring.

We report a combined experimental and theoretical study on the effect of autoionizing resonances in time-resolved photoelectron spectroscopy. The coherent excitation of ${\mathrm{N}}_2$ by $\sim 14.15\mathrm{eV}$ extreme-ultraviolet photons prepares a superposition of three dominant adjacent vibrational levels ($v^{\prime }=14–16$) in the valence $b^{\prime }$ ${}^1{\mathrm{\Sigma }}_u^{+}$ state, which are probed by the absorption of two or three near-infrared photons (800 nm). The superposition manifests itself as coherent oscillations in the measured photoelectron spectra. A quantum-mechanical simulation confirms that two autoionizing Rydberg states converging to the excited $A$ ${{}^2\mathrm{\Pi }}_u$ and $B$ ${}^2{\mathrm{\Sigma }}_u^{+}$ ${\mathrm{N}}_2^{+}$ cores are accessed by the resonant absorption of near-infrared photons. We show that these resonances apply different filters to the observation of the vibrational wave packet, which results in different phases and amplitudes of the oscillating photoelectron signal depending on the nature of the autoionizing resonance. This work clarifies the importance of resonances in time-resolved photoelectron spectroscopy and particularly reveals the phase of vibrational quantum beats as a powerful observable for characterizing the properties of such resonances.

We measure the momentum density in a Bose-Einstein condensate (BEC) with dilute spin impurities after an expansion in the presence of interactions. We observe tails decaying as $1/k^4$ at large momentum $k$ in the condensate and in the impurity cloud. These algebraic tails originate from the impurity-BEC interaction, but their amplitudes greatly exceed those expected from two-body contact interactions at equilibrium in the trap. Furthermore, in the absence of impurities, such algebraic tails are not found in the BEC density measured after the interaction-driven expansion. These results highlight the key role played by impurities when present, a possibility that had not been considered in our previous work [Chang et al., Phys. Rev. Lett. 117, 235303 (2016)]. Our measurements suggest that these unexpected algebraic tails originate from the nontrivial dynamics of the expansion in the presence of impurity-bath interactions.

We demonstrate an alignment-based ${}^{87}\mathrm{Rb}$ magnetometer that is immune to nonlinear Zeeman (NLZ) splitting, addressing an important problem in alkali-metal atomic magnetometry. In our scheme, there is a single magnetic resonance peak and well-separated hyperfine transition frequencies, making the magnetometer insensitive or even immune to NLZ-related heading errors. It is shown that the magnetometer can be implemented for practical measurements in geomagnetic environments, and the photon-shot-noise-limited sensitivity reaches $9\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at $5\mathrm{\mu }\mathrm{T}$ and remains at tens of $\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at $50\mathrm{\mu }\mathrm{T}$ at room temperature.

Recent experimental advances in creating dissipative couplings provide a new route for engineering exotic lattice systems and exploring topological dissipation. Using the spatial lattice of atomic spin waves in a vacuum vapor cell, where purely dissipative couplings arise from diffusion of atoms, we experimentally realize a dissipative version of the Su-Schrieffer-Heeger (SSH) model. We construct the dissipation spectrum of the topological or trivial lattices via electromagnetically induced-transparency spectroscopy. The topological dissipation spectrum is found to exhibit edge modes within a dissipative gap. We validate chiral symmetry of the dissipative SSH couplings and also probe topological features of the generalized dissipative SSH model. This work paves the way for realizing non-Hermitian topological quantum optics via dissipative couplings.

Bound states of solitons (“molecules”) occur in various settings, playing an important role in the operation of fiber lasers, optical emulation, encoding, and communications. Soliton interactions are generally related to breathing dynamics in nonlinear dissipative systems, and maintain potential applications in spectroscopy. In the present work, dichromatic breather molecules (DBMs) are created in a synchronized mode-locked fiber laser. Real-time delay-shifting interference spectra are measured to display the temporal evolution of the DBMs, that cannot be observed by means of the usual real-time spectroscopy. As a result, robust out-of-phase vibrations are found as a typical intrinsic mode of DBMs. The same bound states are produced numerically in the framework of a model combining equations for the population inversion in the mode-locked laser and cross-phase-modulation–coupled complex Ginzburg-Landau equations for amplitudes of the optical fields in the fiber segments of the laser cavity. The results demonstrate that the $Q$-switching instability induces the onset of breathing oscillations. The findings offer new possibilities for the design of various regimes of the operation of ultrafast lasers.

Solitons in microresonators have spurred intriguing nonlinear optical physics and photonic applications. Here, by combining Kerr and Brillouin nonlinearities in an over-modal microcavity, we demonstrate spatial multiplexing of soliton microcombs under a single external laser pumping operation. This demonstration offers an ideal scheme to realize highly coherent dual-comb sources in a compact, low-cost and energy-efficient manner, with uniquely low beating noise. Moreover, by selecting the dual-comb modes, the repetition rate difference of a dual-comb pair could be flexibly switched, ranging from 8.5 to 212 MHz. Beyond dual-comb, the high-density mode geometry allows the cascaded Brillouin lasers, driving the co-generation of up to 5 space-multiplexing frequency combs in distinct mode families. This Letter offers a novel physics paradigm for comb interferometry and provides a widely appropriate tool for versatile applications such as comb metrology, spectroscopy, and ranging.

Fluid elements deform in turbulence by stretching and folding. In this Letter, by projecting the material deformation tensor onto the largest stretching direction, we depict the dynamics of folding through the evolution of the material curvature. Results from direct numerical simulation (DNS) show that the curvature growth exhibits two regimes: first, a linear stage dominated by folding fluid elements through a persistent velocity Hessian that then transition to an exponential-growth stage driven by the stretching of already strongly bent fluid elements. This transition leads to strong curvature intermittency at later stages, which can be explained by a proposed curvature-evolution model. The link between velocity Hessian to folding provides a new way to understand the crucial steps in energy cascade and mixing in turbulence beyond the classical linear description of stretching dynamics.

Strong laser-driven magnetic fields are crucial for high-energy-density physics and laboratory astrophysics research, but generation of axial multikilotesla fields remains a challenge. The difficulty comes from the inability of a conventional linearly polarized laser beam to induce the required azimuthal current or, equivalently, angular momentum (AM). We show that several laser beams can overcome this difficulty. Our three-dimensional kinetic simulations demonstrate that a twist in their pointing directions enables them to carry orbital AM and transfer it to the plasma, thus generating a hot electron population carrying AM needed to sustain the magnetic field. The resulting multikilotesla field occupies a volume that is tens of thousands of cubic microns and it persists on a picosecond timescale. The mechanism can be realized for a wide range of laser intensities and pulse durations. Our scheme is well suited for implementation using multikilojoule petawatt-class lasers, because, by design, they have multiple beamlets and because the scheme requires only linear polarization.

Despite ground-breaking observations of supersolidity in spin-orbit-coupled Bose-Einstein condensates, until now the dynamics of the emerging spatially periodic density modulations has been vastly unexplored. Here, we demonstrate the nonrigidity of the density stripes in such a supersolid condensate and explore their dynamic behavior subject to spin perturbations. We show both analytically in infinite systems and numerically in the presence of a harmonic trap how spin waves affect the supersolid’s density profile in the form of crystal waves, inducing oscillations of the periodicity as well as the orientation of the fringes. Both these features are well within reach of present-day experiments. Our results show that this system is a paradigmatic supersolid, featuring superfluidity in conjunction with a fully dynamic crystalline structure.

Recent years have seen the discovery of systems featuring fragile topological states. These states of matter lack certain protection attributes typically associated with topology and are therefore characterized by weaker signatures that make them elusive to observe. Moreover, they are typically confined to special symmetry classes and, in general, rarely studied in the context of phononic media. In this Letter, we theoretically predict the emergence of fragile topological bands in the spectrum of a twisted kagome elastic lattice with threefold rotational symmetry, in the so-called self-dual configuration. A necessary requirement is that the lattice is a structural metamaterial, in which the role of the hinges is played by elastic finite-thickness ligaments. The interplay between the edge modes appearing in the band gaps bounding the fragile topological states is also responsible for the emergence of corner modes at selected corners of a finite hexagonal domain, which qualifies the lattice as a second-order topological insulator. We demonstrate our findings through a series of experiments via 3D scanning laser doppler vibrometry conducted on a physical prototype. The selected configuration stands out for its remarkable geometric simplicity and ease of physical implementation in the panorama of dynamical systems exhibiting fragile topology.

Scattering processes in quantum materials emerge as resonances in electronic transport, including confined modes, Andreev states, and Yu-Shiba-Rusinov states. However, in most instances, these resonances are driven by a single scattering mechanism. Here, we show the appearance of resonances due to the combination of two simultaneous scattering mechanisms, one from superconductivity and the other from graphene $p\text{−}n$ junctions. These resonances stem from Andreev reflection and Klein tunneling that occur at two different interfaces of a hole-doped region of graphene formed at the boundary with superconducting graphene due to proximity effects from ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_1{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. The resonances persist with gating from $p^{+}\text{−}p$ and $p\text{−}n$ configurations. The suppression of the oscillation amplitude above the bias energy which is comparable to the induced superconducting gap indicates the contribution from Andreev reflection. Our experimental measurements are supported by quantum transport calculations in such interfaces, leading to analogous resonances. Our results put forward a hybrid scattering mechanism in graphene–high-temperature superconductor heterojunctions of potential impact for graphene-based Josephson junctions.

$1T\text{−}{\mathrm{TaSe}}_2$ is widely believed to host a Mott metal-insulator transition in the charge density wave (CDW) phase according to the spectroscopic observation of a band gap that extends across all momentum space. Previous investigations inferred that the occurrence of the Mott phase is limited to the surface only of bulk specimens, but recent analysis on thin samples revealed that the Mott-like behavior, observed in the monolayer, is rapidly suppressed with increasing thickness. Here, we report combined time- and angle-resolved photoemission spectroscopy and theoretical investigations of the electronic structure of $1T\text{−}{\mathrm{TaSe}}_2$. Our experimental results confirm the existence of a state above $E_F$, previously ascribed to the upper Hubbard band, and an overall band gap of $\sim 0.7\mathrm{eV}$ at $\overline{\mathrm{\Gamma }}$. However, supported by density functional theory calculations, we demonstrate that the origin of this state and the gap rests on band structure modifications induced by the CDW phase alone, without the need for Mott correlation effects.