Magnetic skyrmions are spatially localized whirls of spin moments in two dimensions, featuring a nontrivial topological charge and a well-defined topological charge density. We demonstrate that the quantum dynamics of magnetic skyrmions is governed by a dipole conservation law associated with the topological charge, akin to that in fracton theories of excitations with constrained mobility. The dipole conservation law enables a natural definition of the collective coordinate to specify the skyrmion’s position, which ultimately leads to a greatly simplified equation of motion in the form of the Thiele equation. In this formulation, the skyrmion mass, whose existence is often debated, actually vanishes. As a result, an isolated skyrmion is intrinsically pinned to be immobile and cannot move at a constant velocity. In a spin-wave theory, we show that such dynamics corresponds to a precise cancellation between a highly nontrivial motion of the quasiclassical skyrmion spin texture and a cloud of quantum fluctuations in the form of spin waves. Given this quenched kinetic energy of quantum skyrmions, we identify close analogies to the bosonic quantum Hall problem. In particular, the topological charge density is shown to obey the Girvin-MacDonald-Platzman algebra that describes neutral modes of the lowest Landau level in the fractional quantum Hall problem. Consequently, the conservation of the topological dipole suggests that magnetic skyrmion materials offer a promising platform for exploring fractonic phenomena with close analogies to fractional quantum Hall states.

Coherent terahertz (THz) emission is emerging as a powerful new tool to probe symmetry breakings in quantum materials. This method relies on second order optical nonlinearities and is complementary to second harmonic generation spectroscopy. Here, we report coherent THz emission from Josephson plasmons in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$, and find that the amplitude of the emitted field increases dramatically close to the superconducting transition temperature, $T_C$. We show theoretically how emission is enhanced by critical superconducting fluctuations, a nonlinear analog of critical opalescence. This observation is expected to be of general importance for the study of many thermal and quantum phase transitions.

The quantum spin liquid is a state manifesting extraordinary many-body entanglement, and the material ${\mathrm{NaYbSe}}_2$ is thought to be one of the most promising candidates for its realization. Through low-temperature heat capacity and thermal conductivity measurements, we identify an apparent contradiction familiar to many quantum spin liquid candidates: While entropy is stored by apparently gapless excitations, the itinerant carriers of entropy are gapped. By studying the compositional series ${\mathrm{NaYb}}_x{\mathrm{Lu}}_{1-x}{\mathrm{Se}}_2$ across a percolation transition of the magnetic lattice, we suggest that this contradiction can be resolved by the presence of entanglement scales of random sizes. Moreover, as we truncate the scale of entanglement by magnetic dilution, we show that the itinerant magnetic entropy carrier in ${\mathrm{NaYbSe}}_2$ does not arise from a uniform globally entangled spin ground state but rather materializes through the stochastic propagation of boundaries between locally entangled spin objects.

Origami principles are used to create strong, lightweight structures with complex mechanical response. However, identifying the fundamental physical principles that determine a sheet’s behavior remains a challenge. We introduce a new analytic theory to account for the low-energy, spatially varying deformations of parallelogram-face origami, a broad class that includes widely studied sheets. We identify topological classes—previously predicted in quantum systems—with sharply distinct mechanical properties, offering a mechanism for control over origami’s effective stiffness and the smoothness of its mechanical response to external loads. The key control parameter is the Poisson’s ratio; when it is negative, as in the Miura ori, sheets have conventional, smooth mechanical response amenable to continuum-based approaches. In contrast, positive Poisson’s ratio, as in the eggbox ori, generates a topological transition to lines of doubly degenerate zero modes that lead to dramatically softer structures with uneven, complex patterns of spatial response. These patterns interact in complicated ways with origami boundary conditions and source terms, leading to rich physical phenomena in experimentally accessible systems. Indeed, these rich topological phenomena demonstrate that the complex response of some origami sheets is both intrinsic and topological in origin and cannot be captured via continuum-based approaches. Doubly degenerate modes, such as the topological ones identified here, are related to non-Abelian physics and coherent computing paradigms. By exploring such consequences and extending the theory to the broader class of origami with nonparallelogram faces, this work sheds light on intriguing new areas of physics.

While extensively studied in normal metals, semimetals, and semiconductors, the superconducting (SC) proximity effect remains elusive in the emerging field of flat-band systems. In this study, we probe proximity-induced superconductivity in Josephson junctions (JJs) formed between superconducting NbTiN electrodes and twisted bilayer graphene (TBG) weak links. Here, the TBG acts as a highly tunable topological flat-band system, which, due to its twist-angle-dependent bandwidth, allows us to probe the SC proximity effect at the crossover from the dispersive to the flat-band limit. Contrary to our original expectations, we find that the induced superconductivity remains strong even in the flat-band limit and gives rise to broad, dome-shaped SC regions, in the filling-dependent phase diagram. In addition, we find that, unlike in conventional JJs, the critical current $I_c$ strongly deviates from a scaling with the normal state conductance $G_N$. We attribute these findings to the onset of strong electron interactions, which can give rise to an excess critical current. By also studying the dependence of $I_c$ on the filling and twist angle across multiple samples, we further uncover the importance of quantum geometric terms as well as multiband pairing mechanisms in describing the induced superconductivity in the TBG flat bands as their bandwidth decreases. To the best of our knowledge, our results present the first detailed study of the SC proximity effect in the flat-band limit and shed new light on the mechanisms that drive the formation of SC domes in flat-band systems.

Gate operations composed in quantum circuits form the basis for digital quantum simulation and quantum processing. While two-qubit gates generally operate on nearest neighbors, many circuits require nonlocal connectivity and necessitate some form of quantum information transport. Yet, connecting distant nodes of a quantum processor still remains challenging, particularly for neutral atoms in optical lattices. Here, we create singlet pairs of two magnetic states of fermionic potassium-40 atoms in an optical lattice and use a bidirectional topological Thouless pump to transport, coherently split, and separate the pairs, as well as to demonstrate interaction between them via tuneable $(\mathrm{SWAP}{)}^{\alpha }$-gate operations. We achieve pumping with a single-shift fidelity of 99.78(3)% over 50 lattice sites and split the pairs within a decoherence-free subspace. Gates are implemented by superexchange interaction, allowing us to produce interwoven atomic singlets. For readout, we apply a magnetic field gradient, resulting in single- and multifrequency singlet-triplet oscillations. Our work shows avenues to create complex patterns of entanglement and new approaches to quantum processing, sensing, and atom interferometry.

Attosecond photoemission or photoionization delays are a unique probe of the structure and the electronic dynamics of matter. However, the spectral congestion of valence photoelectron spectra sets fundamental limits to the complexity of systems that can be studied, and the delocalization of valence electron wave functions blurs the spatial origin of the photoelectron wave packet. Using attosecond x-ray pulses from LCLS, we demonstrate the key advantages of measuring core-level delays: The photoelectron spectra remain atomlike, the measurements become element specific, and the observed scattering dynamics originate from a pointlike source when multicenter interference effects are negligible. We exploit these unique features to reveal the effects of changing functional groups (C-H vs N) and symmetry on attosecond scattering dynamics by measuring and calculating the photoionization delays between $\mathrm{N}\text{−}1s$ and $\mathrm{C}\text{−}1s$ core shells of a series of aromatic azabenzene molecules. Remarkably, the delays increase with the number of nitrogen atoms in the molecule and reveal multiple resonances. We identify two previously unknown mechanisms regulating the associated attosecond dynamics, namely the enhanced confinement of the trapped wave function with the replacement of C-H groups by N atoms and the decrease of the coupling strength among the photoemitted partial waves with increasing symmetry. This study demonstrates the unique opportunities opened by measurements of core-level photoionization delays for unraveling attosecond electron dynamics in complex matter.

Layered oxide materials, with their two-dimensional crystalline architectures and tunable interlayer interaction, serve as a fertile field for harnessing emergent quantum phenomena. Among these materials, metallic delafossites (e.g., ${\mathrm{PdCoO}}_2$) have emerged as a prominent system with extraordinary two-dimensional electronic properties, though their intrinsic lack of ferromagnetism has remained a fundamental constraint. Here, we report the creation of robust, bulk high-temperature ferromagnetism ($T_c>420\mathrm{K}$) in inherently nonmagnetic ${\mathrm{PdCoO}}_2$ through controlled hydrogenation while preserving the delafossite structure. This process induces layer-selective electron doping into ${\mathrm{CoO}}_2$ layers, stabilizing Ising-type ferromagnetism with pronounced perpendicular magnetic anisotropy while preserving the material’s exceptional metallicity. Remarkably, the system self-assembles into a superlattice of alternating metallic Pd and insulating ferromagnetic hydrogenated ${\mathrm{CoO}}_2$ layers, enabling an unconventional anomalous Hall effect mediated by interlayer spin-charge coupling. These findings demonstrate that bulk ferromagnetism can be achieved in delafossite oxides while preserving their structural integrity, positioning hydrogenated delafossites as a versatile platform for exploring correlated quantum effects and designing multifunctional devices.

Elucidating fundamental limitations inherent in physical systems is a central subject in physics. For important thermodynamic operations such as information erasure, cooling, and copying, resources like time and energetic cost must be expended to achieve the desired outcome within a predetermined error margin. In the context of cooling, the unattainability principle of the third law of thermodynamics asserts that infinite “resources” are needed to reach absolute zero. However, the precise identification of relevant resources and how they jointly constrain achievable error remains unclear within the frameworks of stochastic and quantum thermodynamics. In this work, we introduce the concept of separated states, which consist of fully unoccupied and occupied states, and formulate the corresponding thermokinetic cost and error, thereby establishing a unifying framework for a broad class of thermodynamic operations. We then uncover a three-way trade-off relation between time, cost, and error for thermodynamic operations aimed at creating separated states, simply expressed as $\tau \mathcal{C}{ϵ}_{\tau }\ge 1-\eta$. This fundamental relation is applicable to diverse thermodynamic operations, including information erasure, cooling, and copying. It provides a profound quantification of the unattainability principle in the third law of thermodynamics in a general form. Building upon this relation, we explore the quantitative limitations governing cooling operations, the preparation of separated states, and a no-go theorem for exact classical copying. Furthermore, we extend these findings to the quantum regime, encompassing both Markovian and non-Markovian dynamics. Specifically, within Lindblad dynamics, we derive a similar three-way trade-off relation that quantifies the cost of achieving a pure state with a given error. The generalization to general quantum dynamics involving a system coupled to a finite bath implies that the dissipative cost becomes infinite as the quantum system is exactly cooled down to the ground state or perfectly reset to a pure state, thereby resolving an open question regarding the thermodynamic cost of information erasure.

${\mathrm{TiSe}}_2$ has long been considered one of the best candidate materials to host the elusive excitonic insulator (EI) phase. However, a finite coupling to the lattice can generically be expected, while a lack of “smoking-gun” signatures for the importance of the electron-hole interaction in driving the phase transition has rendered it challenging to distinguish the EI from the conventional charge-density wave (CDW) phase. Here, we demonstrate a new approach, exploiting the susceptibility of excitons to dielectric screening. We combine mechanical exfoliation with molecular-beam epitaxy to fabricate ultraclean van der Waals heterostructures of monolayer (ML) ${\mathrm{TiSe}}_2$/graphite and ML ${\mathrm{TiSe}}_2/h$-BN. We observe how the modified substrate screening environment drives a renormalization of the quasiparticle band gap of the ${\mathrm{TiSe}}_2$ layer, signifying its susceptibility to Coulomb engineering. The temperature-dependent evolution of its electronic structure, however, remains unaffected, indicating that excitons are not required to drive the CDW transition in ${\mathrm{TiSe}}_2$.

Most emulsions ripen with an average droplet size increasing in time. In chemically active emulsions, coarsening can be absent, leading to a nonequilibrium steady state with monodisperse droplet sizes. By considering a minimal model for phase separation and chemical reactions maintained away from equilibrium, we show that there is a supercritical transition controlled by the conserved quantity between two classes of chemically active droplets: intensive and extensive active droplets. While intensive droplets reach a stationary size mainly controlled by the interplay between reactions and diffusion, the size of an extensive active droplet scales with the system size. For intensive droplets, growth arrests at a finite size. Thus, they can be far apart from each other and evolve independently from other droplets in an active emulsion. The growth of extensive droplets, however, arrests due to the presence of other droplets in the emulsion. In both cases, monodisperse emulsions can emerge. We show how the supercritical transition between intensive and extensive active droplets affects shape instabilities, including the division of active droplets, paving the way for the observation of successive division events in chemically active emulsions.

Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited. GNNs can encounter difficulties in gathering information from nodes that are far apart by iterated aggregation steps. This situation is partly caused by so-called oversmoothing; and overcoming it is one of the practically motivated challenges. We consider the situation where information is aggregated by multiple steps of convolution, leading to graph convolutional networks (GCNs). We analyze the generalization performance of a basic GCN, trained for node classification on data generated by the contextual stochastic block model. We predict its asymptotic performance by deriving the free energy of the problem, using the replica method, in the high-dimensional limit. Calling depth the number of convolutional steps, we show the importance of going to large depth to approach the Bayes optimality. We detail how the architecture of the GCN has to scale with the depth to avoid oversmoothing. The resulting large depth limit can be close to the Bayes optimality and leads to a continuous GCN. Technically, we tackle this continuous limit via an approach that resembles dynamical mean-field theory with constraints at the initial and final times. An expansion around large regularization allows us to solve the corresponding equations for the performance of the deep GCN. This promising tool may contribute to the analysis of further deep neural networks.

Continuous-variable cat codes are encodings into a single photonic or phononic mode that offer a promising avenue for hardware-efficient fault-tolerant quantum computation. Protecting information in a cat code requires measuring the mode’s occupation number modulo two, but this can be relaxed to a linear occupation-number constraint using the alternative two-mode pair-cat encoding. We construct multimode codes with similar linear constraints using any two integer matrices satisfying a Calderbank-Shor-Steane-like homological condition of a quantum rotor code. Just like the pair-cat code, syndrome extraction can be performed in tandem with stabilizing dissipation using current superconducting-circuit designs. The framework includes codes with various finite- or infinite-dimensional code spaces and codes with finite or infinite Fock-state support. It encompasses two-component cat, pair-cat, dual-rail, two-mode binomial, various bosonic repetition codes, and aspects of $\chi$-squared encodings, while also yielding codes from homological products, lattices, generalized coherent states, and algebraic varieties. Among our examples are analogs of repetition codes, the Shor code, and a surface-code-like construction that is not a concatenation of a known cat code with the qubit surface code. Code words are coherent states projected into a Fock-state subspace defined by an integer matrix, and their overlaps are governed by Gelfand-Kapranov-Zelevinsky hypergeometric functions.

We consider the universal aspects of two problems: (i) the singular value structure of a product $M_t=m_t{m}_{t-1}\dots m_1$ of many large independent random matrices and (ii) the slow purification of a large number of qubits by repeated quantum measurements. The time-evolution operator in the latter case is again a product of matrices $m_i$, representing time steps in the evolution, but the $m_i$ are now nontrivially correlated as a result of Born’s rule. Both processes are associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product. We argue that, for a broad class of models, each process is described by universal scaling forms for purification and that (i) and (ii) represent distinct “universality classes” with distinct scaling functions. Using the replica trick, these universality classes correspond to effective one-dimensional statistical mechanics models for a gas of “kinks,” representing domain walls between elements of the permutation group. This is an instructive low-dimensional limit of the effective statistical mechanics models for random circuits and tensor networks. These results apply to longtime purification in spatially local monitored circuit models on the entangled side of the measurement phase transition.

A major hurdle for building a large-scale quantum computer is increasing the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be achieved by moving subregisters consisting of a few ions across the processor. Here, we focus on an architecture, which we refer to as the quantum spring array (QSA), that is based on a rectangular two-dimensional lattice of linear strings of ions. Connectivity between adjacent ion strings can be controlled by adjusting their separation. This requires control of trapping potentials along two directions, one along the axis of the ion string and one radial to it. In this work, we investigate key elements of the QSA architecture along both directions: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to electrical noise, both being key requisites for fast and high-fidelity quantum gate operations. The coherence of the coupling is assessed and an entangling gate between qubits stored in radially separated trapping regions is demonstrated. Moreover, we demonstrate control over radio-frequency signals to adjust the radial separation, and thus the coupling rate, between strings. We further present constructions for the implementation of parallelized, transversal gate operations, and map the QSA architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale operation.

Recently, several notions of entanglement in time have emerged as a novel frontier in quantum many-body physics, quantum field theory, and gravity. We propose a systematic prescription to characterize temporal entanglement in relativistic quantum field theory in a general state for an arbitrary subregion on a flat, constant time slice in a flat spacetime. Our prescription starts with the standard entanglement entropy of a spatial subregion and amounts to transporting the unchanged subregion to boosted time slices all the way across the light cone when it becomes, in general, a complex characterization of the corresponding temporal subregion. For holographic quantum field theories, our prescription amounts to an analytic continuation of all codimension-two bulk extremal surfaces satisfying the homology constraint and picking the one with the smallest real value of the area as the leading saddle point. We implement this prescription for holographic conformal field theories in thermal states on both a two-dimensional Lorentzian cylinder and three-dimensional Minkowski space, and we show that it leads to results with self-consistent physical properties of temporal entanglement.

Entanglement can improve the measurement precision of quantum sensors beyond the shot noise limit. Neutral atoms, the basis of some of the most precise and accurate optical clocks and interferometers, do not naturally exhibit the all-to-all interactions traditionally used to generate such entangled states. On the other hand, these systems exhibit exceedingly high degrees of experimental control over parameters such as temperature, spatial entropy, and itinerancy. In this work, we investigate spin squeezing in a highly coherent itinerant system of neutral atoms with magnetic dipole-dipole interactions. We achieve 7.1 dB of metrologically useful squeezing using finite-range spin-exchange interactions in an erbium quantum gas microscope, and we demonstrate that introducing atomic motion, realizing a dipolar $t\text{−}J$ model, protects the spin sector coherence at low fillings, significantly improving the achievable spin squeezing in a 2D dipolar system. This work’s protocol can be implemented with most neutral atoms, opening the door to quantum-enhanced metrology in other itinerant dipolar systems, such as molecules or optical lattice clocks, and serves as a novel method for studying itinerant quantum magnetism with long-range interactions.

In the past couple of decades, there have been significant advances in measuring quantum properties of light, such as quadratures of squeezed light and single-photon counting. Here, we explore whether such tools can be leveraged to probe electronic correlations in the many-body quantum regime. Specifically, we show that it is possible to probe certain spin, charge, and topological orders in an electronic system by measuring the correlation functions of scattered photons. We construct a mapping from the correlators of the scattered photons to those of a correlated insulator, particularly for Mott insulators described by a single-band Fermi-Hubbard model at half filling. We show that frequency filtering before photodetection plays a crucial role in determining this mapping. We find that if the ground state of the insulator is a gapped spin liquid, a photon-pair correlation function, i.e., $G^{(2)}$, can detect the presence of anyonic excitations with fractional mutual statistics. Moreover, we show that correlations between electromagnetic quadratures can be used to detect expectation values of static spin chirality operators on both the kagome and triangular lattices, thus being useful in detecting chiral spin liquids. More generally, we show that a series of hitherto unmeasured spin-spin and spin-charge correlation functions of the material can be extracted from photonic correlations. This work opens up access to probe correlated materials, beyond the linear-response paradigm, by detecting quantum properties of scattered light.

Studies of the dynamics of nonlinear recurrent neural networks often assume independent and identically distributed couplings, but large-scale connectomics data indicate that biological neural circuits exhibit markedly different connectivity properties. These include rapidly decaying singular-value spectra and structured singular-vector overlaps. Here, we develop a theory to analyze how these forms of structure shape high-dimensional collective activity in nonlinear recurrent neural networks. We first introduce the random-mode model, a random-matrix ensemble related to the singular-value decomposition that enables control over the spectrum and right-left mode overlaps. Then, using a novel path-integral calculation, we derive analytical expressions that reveal how connectivity structure affects features of collective dynamics: the dimension of activity, which quantifies the number of high-variance collective-activity fluctuations, and the temporal correlations that characterize the timescales of these fluctuations. We show that connectivity structure can be invisible in single-neuron activities, while dramatically shaping collective activity. Furthermore, despite the nonlinear, high-dimensional nature of these networks, the dimension of activity depends on just two connectivity parameters—the variance of the couplings and the effective rank of the coupling matrix, which quantifies the number of dominant rank-one connectivity components. We contrast the effects of single-neuron heterogeneity and low-dimensional connectivity, making predictions about how $z$-scoring data affects the dimension of activity. Finally, we demonstrate the presence of structured overlaps between left and right modes in the Drosophila connectome, incorporate them into the theory, and show how they further shape collective dynamics.

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g., the computational basis). Our approach is based upon the intuition that noise exponentially damps nonlocal correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by keeping track of only the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasipolynomial time, so long as the distribution anticoncentrates. A number of implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: For constant noise rates, any quantum circuit for which error mitigation succeeds in polynomial-time on most input states can also be classically simulated in polynomial-time on most input states. Our algorithms scale exponentially in the inverse noise rate, which is fundamental and makes them impractical for current quantum devices.