Tip-based structures offer a pathway to strong-field, optical-driven field emission, holding the potential for generating high-brightness ultrashort electron sources. While direct optical-field-driven electron emission and acceleration within the single optical subcycle provides a straightforward solution for ultrafast electron generation, achieving precise control over the emission process to generate high-quality electron beams suitable for practical applications remains challenging. Here, we present THz-driven subcycle electron field emission in a ridged waveguide cavity, achieving the first practical high-energy femtosecond field-emission source. This ridged cavity is engineered to spatially and temporally confine the electric field, effectively minimizing dispersion and suppressing field leakage. Through carrier-envelope phase control of the THz field, we achieve subcycle field emission, generating, for the first time, isolated electron bunches with a 940-fs (FWHM) duration. Using dual $24\mathrm{\mu }\mathrm{J}$ ($2\times 24\mathrm{\mu }\mathrm{J}$) of THz energy, we achieve a peak field strength of approximately $23\mathrm{GV}/\mathrm{m}$, accelerating electrons to a record energy of 46 keV with a charge of 2 pC per bunch, thereby enabling single-shot imaging. The high-field strength suppresses emittance blowup due to space-charge effects, ensuring excellent beam quality. The generated electron pulse exhibits high stability. As an initial application, we investigate transient electric-field dynamics in real time and space using time-resolved schlieren radiography with this field-emission electron source. These proof-of-principle results signify a critical advancement in developing compact, high-performance electron sources for user-oriented applications.

We use symmetry analysis and density functional theory to show that changes in magnetic order at a surface with respect to magnetic order in the bulk can be generically determined by considering local magnetoelectric responses of the crystal. Specifically, analysis of the local atomic-site magnetoelectric responses, or, equivalently, the corresponding atomic-site magnetic multipoles, can be used to predict all surface magnetic modifications arising purely from symmetry lowering via termination of the bulk magnetic order. This analysis applies even in materials with no bulk magnetoelectric response or net surface magnetization. We then demonstrate our arguments for two example antiferromagnets, topological semimetal CuMnAs and rocksalt NiO. We find that the (010) and $(1\overline{1}0)$ surfaces of CuMnAs and NiO, respectively, exhibit a series of antiferroically, as well as roughness-sensitive, ferroically ordered, modifications of the surface magnetic dipole moments, via canting or changes in sublattice magnitude, consistent with the bulk ordering of the magnetic multipoles. Our findings demonstrate a universal bulk-boundary correspondence allowing the general prediction of minimal possible surface and interface magnetic modifications, even in materials with no net magnetoelectric response. Furthermore, it paves the way for more accurate interpretations of a wide variety of surface-sensitive measurements.

Current progress in artificial intelligence is centered around so-called large language models that consist of neural networks processing long sequences of high-dimensional vectors called tokens. Statistical physics provides powerful tools to study the functioning of learning with neural networks and has played a recognized role in the development of modern machine learning. The statistical physics approach relies on simplified and analytically tractable models of data. However, simple tractable models for long sequences of high-dimensional tokens are largely underexplored. Inspired by the crucial role models such as the single-layer teacher-student perceptron (also known as generalized linear regression) played in the theory of fully connected neural networks, in this paper, we introduce and study the bilinear sequence regression (BSR) as one of the most basic models for sequences of tokens. We note that modern architectures naturally subsume the BSR model due to the skip connections. Building on recent methodological progress, we compute the Bayes-optimal generalization error for the model in the limit of long sequences of high-dimensional tokens and provide a message-passing algorithm that matches this performance. We quantify the improvement that optimal learning brings with respect to vectorizing the sequence of tokens and learning via simple linear regression. We also unveil surprising properties of the gradient descent algorithms in the BSR model.

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary for emergent anyons and fermions by using the geometric entanglement measure (GEM), which quantifies the maximal overlap between a given state and any short-range-entangled states. For systems with emergent anyons, based on the braiding statistics, we show that the GEM scales linearly in the system size regardless of microscopic details. The phenomenon of emergent anyons can also be understood within the framework of quantum error correction (QEC). Specifically, we show that the GEM of any 2D stabilizer codes must be at least quadratic in the code distance. Our proof is based on a generic prescription for constructing string operators, establishing a rigorous and direct connection between emergent anyons and QEC. For systems with emergent fermions, despite that the ground state subspaces could be exponentially huge and their coding properties could be rather poor, we show that the GEM also scales linearly in the system size. Our analysis establishes an intriguing link between quantum anomaly and entanglement: A quantum state respecting anomalous 1-form symmetries must be long-range entangled and have large GEM. Our results also extend to mixed states, such as the $ZX$-dephased toric code, providing a provably nontrivial class of intrinsically mixed-state phases.

A fundamental problem of out-of-equilibrium physics is the speed at which the order parameter grows upon crossing a phase transition. Here, we investigate the ordering dynamics in a Fermi gas undergoing a density-wave phase transition induced by quenching infinite-range, cavity-mediated interactions. We observe, in real time, the exponential rise of the order parameter and track its growth over several orders of magnitude. Remarkably, the growth rate can exceed the Fermi energy by an order of magnitude, consistent with predictions from a linearized instability analysis. This case contrasts with the ordering process driven by short-range interactions. We then generalize our results to linear interaction ramps, where deviations from the adiabatic behavior are captured by a simple dynamical ansatz. Our study offers a paradigmatic example of the interplay between strong short- and long-range interactions in quantum nonequilibrium dynamics.

We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in Calderbank-Shor-Steane stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice surgery and some of its recent generalizations are shown to be special cases of homological measurement. Using this framework, we develop a specific protocol called edge expanded homological measurement for fault-tolerant measurement of arbitrary logical Pauli operators of general quantum low density parity-check codes, requiring a number of ancillary qubits growing only linearly with the weight of the logical operator measured, and guarantee that the distance of the code is preserved. We further benchmark our protocol numerically in a photonic architecture based on Gottesman-Kitaev-Preskill qubits, showing that the logical error rates of various codes are on par with other methods requiring more ancilla qubits.

Twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: quantum Hall physics and Hubbard physics. On one hand, TBG hosts flat topological Landau-level-like bands which exhibit the quantum anomalous Hall effects under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show signs of extensive entropy usually attributed to local moments. The combination of these features leads to a question: Can decoupled moments emerge in an isolated topological band, despite the lack of exponentially localized Wannier orbitals? In this work, we answer the question affirmatively by proposing a minimal model for the flat topological bands in TBG that combines topology and charge concentration at the AA sites, leading to analytic wave functions that closely approximate those of the Bistritzer-MacDonald model with realistic parameters. Importantly, charge concentration also leads to Berry curvature concentration at $\mathrm{\Gamma }$, giving rise to a small parameter $s$ that makes the model analytically tractable. We show that, rather surprisingly, the model hosts nearly decoupled flavor moments without invoking any extra degrees of freedom. These moments are nonlocal due to topology-enforced power-law tails, yet have parametrically small overlap. We develop a systematic diagrammatic expansion in which the self-energy can be computed exactly to leading order in $s^2$ in the fluctuating moment regime and predict momentum-resolved spectral functions for future experiments to verify. Our key discovery is a charge-neutrality state we refer to as the “Mott semimetal” characterized by high flavor entropy and a Mott gap that exists throughout most of the Brillouin zone but closes at the $\mathrm{\Gamma }$ point. At $\mathrm{\Gamma }$, the spectral function contains a single Dirac cone per spin per valley and responds to perturbations in an exotic manner that is distinct from any other theoretical picture of TBG. Away from neutrality, the Mott semimetal gaps out in a spectrally imbalanced manner, with one Mott band having zero quasiparticle residue at the $\mathrm{\Gamma }$ point. The model accurately reproduces results from finite-temperature thermodynamic measurements, leads to new experimental predictions, and resolves the problem of the emergence of Hubbard physics in isolated topological bands.

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in ${}^{239}\mathrm{Pu}$ nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called differential, look at one nuclear physics observable at a time. They are contrasted to application-driven, integral, data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to ${}^{239}\mathrm{Pu}$ fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate ${}^{63}\mathrm{Cu}$ and ${}^{239}\mathrm{Pu}$ total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with ${\mathrm{Al}}_2{\mathrm{O}}_3$ and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry.

Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorized structure with a rank growing proportionally to its dimension remains a challenge, except when it is rotationally invariant. In this case, the information-theoretic limits and an efficient Bayes-optimal denoising algorithm, called the rotational invariant estimator, are known. Beyond this setting, few results can be found. The reason is that the model is not a usual spin system because of the growing rank dimension, nor a matrix model (as appearing in high-energy physics) due to the lack of rotation symmetry, but rather a hybrid between the two. In this paper, we make progress toward the understanding of Bayesian matrix denoising when the hidden signal is a factored matrix $\mathbf{X}{\mathbf{X}}^{⊺}$ that is not rotationally invariant. Monte Carlo simulations suggest the existence of a denoising-factorization transition separating a phase where denoising using the rotational-invariant estimator remains Bayes-optimal due to universality properties of the same nature as in random matrix theory, from one where universality breaks down and better denoising is possible, though algorithmically hard. We also argue that it is only beyond the transition that factorization, i.e., estimating $\mathbf{X}$ itself, becomes possible up to irresolvable ambiguities. On the theoretical side, we combine mean-field techniques in an interpretable multiscale fashion in order to access the minimum mean-square error and mutual information. Interestingly, our alternative method yields equations reproducible by the replica approach of Sakata and Kabashima. Using numerical insights, we delimit the portion of phase diagram where we conjecture the mean-field theory to be exact and correct it using universality when it is not. Our complete Ansatz matches well the numerics in the whole phase diagram when considering finite-size effects.

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.

Antiferromagnetic materials (AFMs) have been gaining lots of attention due to their great potential in spintronics devices and the recently discovered novel spin structure in the momentum space, i.e., $C$-paired spin-valley or spin-momentum locking (CSML), where spins and valleys or momenta are locked to each other due to the crystal symmetry guaranteeing zero magnetization. Here, we systematically study CSMLs and propose a general theory and algorithm using little cogroup and coset representatives, which reveals that 12 elementary kinds of CSMLs, determined by the geometric relation of spins and valleys and the essential symmetry guaranteeing zero magnetization, are sufficient to fully represent all possible CSMLs. By combining the proposed algorithm and high-throughput first-principles calculations, we predict 38 magnetic point groups and identify 142 experimentally verified AFMs that can realize CSML. Besides predicting new materials, our theory can naturally reveal underlying mechanisms of CSMLs’ responses to external fields. As an example, two qualitatively different types of piezomagnetism via occupation imbalance or spin tilting are predicted in ${\mathrm{RbV}}_2{\mathrm{Te}}_2\mathrm{O}$. The algorithm and conclusions can be directly extended to the locking between valley or momentum and any other pseudovector degree of freedom, e.g., Berry curvature, as exemplified in ${\mathrm{RbV}}_2{\mathrm{Te}}_2\mathrm{O}$ and the new proposed piezo-Hall effect, where a strain can induce a nonzero anomalous Hall conductance. In addition, the proposed concept and methodology can be straightforwardly applied to other symmetry groups, such as spin group.

Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight $w$. For sufficiently small values of $w$ and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of $w$ values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

High-speed, nonvolatile tunability is critical for advancing reconfigurable photonic devices used in neuromorphic information processing, sensing, and communication. Despite significant progress in developing phase-change and ferroelectric materials, achieving highly efficient, reversible, rapid switching of optical properties has remained a challenge. Recently, sliding ferroelectricity has been discovered in 2D semiconductors, which also host strong excitonic effects. Here, we demonstrate that these materials enable nanosecond ferroelectric switching in the complex refractive index, substantially modulating their linear optical responses. The maximum index modulation reaches about 4, resulting in a relative reflectance change exceeding 85%. Both on and off switching occur within 2.5 ns, with switching energy at femtojoule levels. The switching mechanism is driven by tuning the excitonic peak splitting of a rhombohedral molybdenum disulfide bilayer in an engineered Coulomb screening environment. This new switching mechanism establishes a new direction for developing high-speed, nonvolatile optical memories and highly efficient, compact reconfigurable photonic devices. Additionally, the demonstrated imaging technique offers a rapid method to characterize domains and domain walls in 2D semiconductors with rhombohedral stacking.

Atomic defects underpin the properties of van der Waals materials, and their understanding is essential for advancing quantum and energy technologies. Scanning transmission electron microscopy is a powerful tool for defect identification in atomically thin materials, and extending it to multilayer and beam-sensitive materials would accelerate their exploration. Here, we establish a comprehensive defect library in a bilayer of the magnetic quasi-1D semiconductor CrSBr by combining atomic-resolution imaging, deep learning, and ab initio calculations. We apply a custom-developed machine learning work flow to detect, classify, and average point vacancy defects. This classification enables us to uncover several distinct Cr interstitial defect complexes, combined Cr and Br vacancy defect complexes, and lines of vacancy defects that extend over many unit cells. We show that their occurrence is in agreement with our computed structures and binding energy densities, reflecting the intriguing layer interlocked crystal structure of CrSBr. Our ab initio calculations show that the interstitial defect complexes give rise to highly localized electronic states. These states are of particular interest due to the reduced electronic dimensionality and magnetic properties of CrSBr and are, furthermore, predicted to be optically active. Our results broaden the scope of defect studies in challenging materials and reveal new defect types in bilayer CrSBr that can be extrapolated to the bulk and to over 20 materials belonging to the same FeOCl structural family.

A novel two-qubit entangling gate for trapped-ion quantum processors is proposed theoretically and demonstrated experimentally. During the gate, double-dressed quantum states are created by applying a phase-modulated continuous driving field. The speed of this quantum gate is an order of magnitude higher than that of previously demonstrated rf controlled two-qubit entangling gates in static magnetic field gradients. At the same time, the field driving the gate dynamically decouples the qubits from amplitude and frequency noise, increasing the qubits’ coherence time by 3 orders of magnitude. The gate requires only a single continuous rf field per qubit, making it well suited for scaling a quantum processor to large numbers of qubits. Implementing this entangling gate, we generate the Bell states $|{\mathrm{\Phi }}^{+}⟩$ and $|{\mathrm{\Psi }}^{+}⟩$ in less than or equal to $313\mathrm{\mu }\mathrm{s}$ with fidelities up to ${98}_{-3}^{+2}\%$ in a static magnetic gradient of only $19.09\mathrm{T}/\mathrm{m}$. At higher magnetic field gradients, the entangling gate speed can be further improved to match that of laser-based counterparts.

The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is challenging. We formulate an efficiently implementable multiscale entanglement renormalization ansatz model of AdS/CFT, providing a mapping between a ($1+1$)-dimensional critical spin system and a ($2+1$)-dimensional bulk theory. Using a combination of numerics and analytics, we show that the bulk theory arising from this optimized tensor network furnishes excitations with attractive interactions. Remarkably, these excitations have one- and two-particle energies matching the predictions for matter coupled to AdS gravity at long distances, thus displaying key features of AdS physics. We show that these potentials arise as a direct consequence of entanglement renormalization and discuss how this approach can be used to efficiently simulate bulk dynamics using realistic quantum devices.

We describe a quantum algorithm for the Planted Noisy $k\mathrm{XOR}$ Problem (also known as Sparse Learning Parity with Noise) that achieves a nearly quartic (fourth-power) speedup over the best known classical algorithm while using exponentially less space. Our work generalizes and simplifies prior work of Hastings [Quantum 4, 237 (2020)], by building on his quantum algorithm for the tensor principal component analysis (PCA) problem. We achieve our quantum speedup using a general framework based on the Kikuchi method (recovering the quartic speedup for Tensor PCA), and we anticipate it will yield similar speedups for further planted inference problems. These speedups rely on the fact that planted inference problems naturally instantiate the guided sparse Hamiltonian problem. Since the Planted Noisy $k\mathrm{XOR}$ Problem has been used as a component of certain cryptographic constructions, our work suggests that some of these are susceptible to superquadratic quantum attacks.

The spin-$1/2$ kagome Heisenberg antiferromagnets are believed to host exotic quantum entangled states. Recently, the reports of $1/9$ magnetization plateau and magnetic oscillations in a kagome antiferromagnet ${\mathrm{YCu}}_3{(\mathrm{OH})}_6{\mathrm{Br}}_2[{\text{Br}}_x{(\mathrm{OH})}_{1-x}]$ (YCOB) have made this material a promising candidate for experimentally realizing quantum spin liquid states. Here, we present measurements of the specific heat $C_p$ in YCOB in high magnetic fields (up to 41.5 T) down to 0.46 K, and the $1/9$ plateau feature has been confirmed. Moreover, the temperature dependence of $C_p/T$ in the vicinity of $1/9$ plateau region can be fitted by a linear in $T$ term which indicates the presence of a Dirac spectrum, together with a constant term, which indicates a finite density of states contributed by other spinon Fermi surfaces. Surprisingly, the constant term is highly anisotropic in the direction of the magnetic field. Additionally, we observe a double-peak feature near 30 T above the $1/9$ plateau which is another hallmark of fermionic excitations in the specific heat. This combination of gapless behavior and the double-peak structure strongly suggests that the $1/9$ plateau in YCOB is nontrivial and hosts fermionic quasiparticles.

The discovery of multiple superconducting phases in ${\mathrm{UTe}}_2$ boosted research on correlated-electron physics. This heavy-fermion paramagnet was rapidly identified as a reference compound to study the interplay between magnetism and unconventional superconductivity with multiple degrees of freedom. The proximity to a ferromagnetic quantum phase transition was initially proposed as a driving force to triplet-pairing superconductivity. However, we find here that long-range incommensurate antiferromagnetic order is established under pressure. The propagation vector ${\mathbf{k}}_{\mathbf{m}}=(0.07,0.33,1)$ of the antiferromagnetic phase is close to a wave vector where antiferromagnetic fluctuations have previously been observed at ambient pressure. These elements support that ${\mathrm{UTe}}_2$ is a nearly antiferromagnet at ambient pressure. Our work appeals for theories modeling the evolution of the magnetic interactions and electronic properties, driving a correlated paramagnetic regime at ambient pressure to a long-range antiferromagnetic order under pressure. A deeper understanding of itinerant-$f$-electron magnetism in ${\mathrm{UTe}}_2$ will be a key for describing its unconventional superconducting phases.