Soft solids and their surface deformations control the response of many natural and artificial systems. Yet, their underlying properties are vigorously debated, particularly for polymer networks. While molecular-scale theories predict no interfacial changes with macroscopic deformation, multiple experiments suggest otherwise. To settle this issue, we measure displacement fields near the interface of a silicone gel, in the limit of small deformations. We discover an unexpected multiscale response. The shear modulus decreases smoothly by half with $20\mathrm{\mu }\mathrm{m}$ of the interface. At the same time we observe a surface excess elasticity, that depends on history and outer medium composition. These results reveal the fundamentally multiscale nature of polymeric surfaces, and call for further experimental and theoretical investigations into the basic understanding of soft solid interfaces.

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

The relaxation dynamics of glass-forming liquids shows at a temperature $T_c$, somewhat above the glass-transition temperature $T_g$, a crossover, indicating the conjunction of two different dynamical regimes. For temperatures slightly above $T_c$, experiments and computer simulations have extensively probed this dynamics on the particle level and identified several universal scaling laws that are often compatible with the predictions of ideal mode coupling theory, while for temperatures below $T_c$, the nature of the relaxation dynamics, and hence the reason for the crossover, has so far remained elusive. Here we use large-scale computer simulations to investigate how in the low-temperature regime the relaxation mechanism differs from the one at higher temperatures. Our analysis reveals unexpected scaling laws that allow us to give a surprisingly simple description of the relaxation dynamics at very low $T$’s. Space-time correlation functions show that the cage-escape process involves rare but large particle displacements. These displacements give rise to distinctive subdiffusive power laws in the mean squared displacement and the intermediate scattering function, and also rationalize the origin of the universal excess wing found in the dynamic susceptibility. This insight advances our understanding on the dynamics of glass-forming systems at temperatures that are close to the experimental glass transition.

The tin-vacancy center in diamond (SnV) has emerged as a compelling building block for realizing next-generation quantum networks thanks to its excellent optical and spin properties. Coupling to photonic crystal cavities (PCCs) promises to further enhance the SnV light-matter interface and unlock a diverse range of entanglement generation protocols. Recent pioneering experiments showing Purcell enhancement of SnV centers in PCCs underscore this potential. However, optical coupling that is coherent—the key ingredient for use in quantum protocols—has so far remained elusive. Here, we demonstrate above-unity coherent cooperativity of SnV centers embedded in photonic crystal cavities. We fabricate free-standing PCCs using a quasi-isotropic undercut. Across two samples, we conduct room-temperature characterizations, measuring resonances for 327 cavities, with an average quality factor exceeding $Q=1.1(4)\times {10}^4$. Two cavity-coupled emitters are examined in detail, exhibiting quality factors up to $Q=25.4(4)\times {10}^3$ and Purcell-reduced lifetimes corresponding to cooperativities up to $C=20.3(11)$. Furthermore, the single SnVs are observed to strongly modulate the cavity transmission with an extinction contrast up to 98.8(4)%% on resonance. Finally, SnV linewidth measurements reveal above-unity coherent cooperativities in both devices, with the highest value being $C_{\mathrm{coh}}=8.3(12)$. These results open the door to using cavity-coupled SnV centers as efficient, coherent light-matter interfaces for future quantum networks.

BosonSampling is the leading candidate for demonstrating quantum computational advantage in photonic systems. While we have recently seen many impressive experimental demonstrations, there is still a formidable distance between the complexity-theoretic hardness arguments and current experiments. One of the largest gaps involves the ratio of particles to modes—all current hardness evidence assumes a “dilute” regime in which the number of linear optical modes scales at least quadratically in the number of particles. By contrast, current experiments operate in a “saturated” regime with a linear number of modes. In this paper, we bridge this gap, bringing the hardness evidence for experiments in the saturated regime to the same level as had been previously established for the dilute regime. This involves proving a worst-to-average-case reduction for computing the permanent, which is robust both to large numbers of row repetitions and also to distributions over matrices with correlated entries. We also apply similar arguments to give evidence for hardness of Gaussian BosonSampling in the saturated regime.

Abrupt learning, long performance plateaus followed by rapid convergence, is a common phenomenon in recurrent neural networks (RNNs) trained on working-memory tasks. In such cases, the networks develop transient slow regions in state space that extend the effective timescales of computation. However, the mechanisms driving sudden performance improvements and their causal role remain unclear, largely because we lack an analytical dynamical-systems framework. To address this gap, we introduce the ghost mechanism, a general process by which finite-dimensional continuous-time dynamical systems exhibit transient slowdown near the remnant of a saddle-node bifurcation. By reducing the high-dimensional dynamics near ghost points, we derive a one-dimensional canonical form that analytically captures learning as a process controlled by a single scale parameter. Using this model, we study a form of abrupt learning emerging from ghost points and identify a critical learning rate that scales as an inverse power law with the timescale of the learned computation. Beyond this rate, learning collapses through two interacting modes: (i) vanishing gradients and (ii) oscillatory gradients near minima. These features can lock the system into high confidence but incorrect predictions when parameter updates trigger a no-learning zone, a region of parameter space where gradients vanish. We validate these predictions in low-rank RNNs, where ghost points precede abrupt transitions and further demonstrate their generality in full-rank RNNs trained on canonical working-memory tasks. Our theory offers two approaches to address these learning difficulties: Increasing trainable ranks stabilizes learning trajectories, while reducing output confidence mitigates entrapment in no-learning zones. Overall, the ghost mechanism reveals how the computational demands of a task constrain the optimization landscape, demonstrating that well-known learning difficulties in RNNs partly arise from the dynamical systems they must learn to implement.

The paradigm of considering open quantum systems—i.e., focusing only on the system of interest, and treating the rest of the world as an effective environment—has proven to be a highly effective way to understand a range of quantum systems, across areas of study such as quantum optics, cold atoms, superconducting qubits, and impurities in solid-state systems. A common approach in many of these contexts has been to consider simplified approaches based on the Born and Markov approximations. While these approximations are indeed often appropriate in contexts such as quantum optics, the widespread application of these approximations has been driven more by simplicity than by accuracy. In particular, these Markovian treatments will fail in many cases, such as when coupling to the environment is not weak, when the environment is structured and has resonances, when the system couples to low-frequency modes of the environment, or when the questions of interest involve the propagation of information through the environment. Despite the fact that many real problems are non-Markovian, the Markov approximation is still widely used, as it is often assumed that a fully non-Markovian treatment is too complex to be practical. In this Perspective we discuss a recently developed set of techniques that address this challenge. Centering our discussion around the notion of the process tensor, we demonstrate that the generality of the process tensor concept, coupled with efficient tensor-network methods, opens the door to the description of a wide range of observable non-Markovian processes in a wide range of open quantum systems.

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analog quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system and further extract multipoint correlations from the output strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of ${10}^{19}$ and outpacing the most powerful supercomputer in terms of sampling rate by 3 orders of magnitude. The volume law scaling of the Rényi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multipoint correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fail to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.

We introduce a nonperturbative framework for quantizing chiral solitons in interacting quantum spin chains. This approach provides a direct lattice extension of the well-established $S$-duality between the sine-Gordon and Thirring models, thereby bridging the gap between continuum dualities and their lattice counterparts. By constructing the quantum chiral-soliton operators explicitly, we show how their unconventional dynamics appear in the excitation spectrum and correlation functions across the full Brillouin zone. A key result is that the dominant soliton tunneling amplitude alternates in sign, $\mathrm{sgn}(t_{1+})=(-1{)}^{2S+1}$, sharply distinguishing half-odd-integer from integer spin chains. We further identify characteristic signatures of these chiral excitations in the dynamical spin structure factor, demonstrating their visibility in inelastic neutron scattering. Our results open a route to experimentally probing nonperturbative features of dual quantum field theories in condensed-matter settings.

The fuzzy-sphere regularization is a powerful tool to study conformal field theories (CFT) in three spacetime dimensions. In this paper, we extend its scope to CFTs with local fermionic operators. We realize the free-Majorana-fermion CFT on a setup with one flavor of bosons and one flavor of fermions on the lowest Landau level with a $1/2$ angular momentum mismatch and allow conversion between two bosons and two fermions, and use a relative chemical potential as the tuning parameter. On the phase diagram, we observe two continuous transitions described, respectively, by a free Majorana fermion and a gauged Ising CFT. We numerically confirm the emergent conformal symmetry through the operator spectrum and the two-point correlation function of the local Majorana fermion. We further establish a correspondence between the fuzzy-sphere models and the field-theory Lagrangians, and extend it to an interacting fermionic CFT—the super-Ising theory with emergent superconformal symmetry.

Recently, a host of exciting magnetic textures such as topologically protected skyrmion lattices has been discovered in several bulk metallic lanthanide compounds. In addition to hosting skyrmion phases, a hallmark of this class of materials is the appearance of numerous spin textures characterized by superposition of multiple magnetic modulations: spin moiré superlattices. In order to understand the multitude of complex phases often present in these materials, we require a general-purpose experimental and theoretical framework. Here, we demonstrate such an approach in ${\mathrm{EuAg}}_4{\mathrm{Sb}}_2$ by comprehensively characterizing and modeling its three complex zero-field magnetic textures. Systematic symmetry-breaking experiments using uniaxial strain determine that the ground-state incommensurate magnetic phase (ICM1) is single $q$, meaning the magnetic moments modulate along one magnetic propagation vector. In contrast, ICM2 and ICM3 are both double $q$, meaning they are formed from the superposition of two sinusoidal spin modulations, i.e., spin moiré superlattices. Further, through application of polarized small-angle neutron scattering and spherical neutron polarimetry, we demonstrate that ICM1 is a single-$q$ cycloid and ICM2 and ICM3 are double-$q$ vortex lattices. Despite the quasi-two-dimensional nature of ${\mathrm{EuAg}}_4{\mathrm{Sb}}_2$, the modulations propagate out of the ab plane, leading to a shift of the spin texture between triangular lattice planes. Further, the ICM3 to ICM2 transition includes an unusual 45° rotation of the magnetic vortex lattice. Motivated by the coexistence of such drastically different phases in this compound, we conclude by developing a phenomenological model that sheds light on the energetic origins of these varied phases. Our experimental probes and theoretical modeling definitively characterize three different and tunable phases in one material and provide insight for the design of topological spin-texture materials.

Dirac magnons, the bosonic counterparts of Dirac fermions in graphene, provide a versatile platform to explore symmetry-protected band crossings and quantum geometry in magnetic insulators while promising high-velocity, low-dissipation spin transport for next-generation magnonic technologies. However, their stability under realistic, finite-temperature conditions remains an open question. Here, we develop a microscopic theory of thermal magnon-magnon interactions in van der Waals honeycomb ferromagnets, focusing on both gapless and gapped Dirac magnons. Using nonlinear spin-wave theory with magnon self-energy corrections and a $T$-matrix resummation that captures two-magnon bound states, we quantitatively reproduce temperature- and momentum-dependent energy shifts and linewidths observed experimentally in the gapless Dirac magnon material ${\mathrm{CrBr}}_3$, even near the Curie temperature. Our approach provides a consistent interpretation of theoretical predictions and experiment shedding light on the role of bound states in enhancing magnon damping at low temperatures. For gapped Dirac magnon materials such as ${\mathrm{CrI}}_3$, ${\mathrm{CrSiTe}}_3$, and ${\mathrm{CrGeTe}}_3$, we find a thermally induced reduction of the topological magnon gap, while no indication of thermally driven topological phase transitions is observed within the considered parameter range. Classical atomistic spin-dynamics simulations corroborate the gap’s robustness up to the Curie temperature. Furthermore, we establish a practical criterion for observing topological gaps by determining the minimum ratio of Dzyaloshinskii-Moriya interaction to Heisenberg exchange required to overcome thermal broadening throughout the ordered phase, typically around 5%. Taken together, our results elucidate the interplay between thermal many-body effects and topology in low-dimensional magnetic systems and provide a controlled framework for the interpretation of spectroscopic measurements.

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size, which makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling, and (ii) dissipative preparation through collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

Collision-resistant hash functions are a fundamental cryptographic primitive that rely on the computational hardness of finding two inputs that produce the same output. Motivated by this problem, we study the complexity of finding collisions in a family of neural networks with oscillating activation functions. A neural network trained on a classification task is specified by a set of weights assigning a label to each data point, and a collision is defined as two distinct weight configurations that produce the same labeling. We show that, within this class of neural networks, the space of collisions exhibits an overlap gap property, whereby certain overlap values between distinct solutions are forbidden. This property is a geometric feature of the solution landscape in high-dimensional random constraint satisfaction problems that has recently emerged as a powerful indicator of algorithmic barriers. Our analysis predicts a regime in which efficient algorithms fail to find collisions. This prediction is supported by numerical experiments using approximate message passing algorithms, which cease to return collisions well below the threshold predicted by theory. Neural networks, therefore, provide a class of candidate collision-resistant functions that, for suitable parameter choices, depart from existing constructions based on lattices. Beyond their cryptographic relevance, our results reveal forms of computational hardness in large neural networks that may be of independent interest.

There is a received wisdom about where to draw the boundary between classical and nonclassical for various types of quantum processes. For multipartite states, it is the divide between separable and entangled; for channels, the divide between entanglement breaking and not; for sets of measurements, the divide between compatible and incompatible; for assemblages, the divide between unsteerable and steerable. However, these choices have not been motivated by any unified notion of what it means to be classically explainable. One well-motivated notion of classical explainability is the one based on generalized noncontextuality: A set of circuits is classically explainable if a generalized-noncontextual ontological model can realize the statistics they generate. In this work, we show that this notion can be leveraged to define a classical-nonclassical divide for individual quantum processes of arbitrary type. A set of measurements, for example, is judged to be classical if and only if a particular set of circuits—the one obtained by contracting these measurements with every possible quantum state—is classically explainable in the sense just articulated. We begin the task of characterizing where the classical-nonclassical divide lies according to this proposal for a variety of different types of processes. In particular, we show that all of the following are judged to be nonclassical: every entangled state, every set of incompatible measurements, every non-entanglement-breaking channel, and every steerable assemblage. Our proposal differs from the received wisdom, however, insofar as it also judges certain subsets of the complementary classes to be nonclassical, including certain separable states, compatible sets of measurements, entanglement-breaking channels, and unsteerable assemblages. Finally, we prove structure theorems characterizing the classical-nonclassical divide based on whether a process admits of a specific type of frame representation.

Full coherent control and generation of nonclassical superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology, and continuous-variable quantum computation. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear interactions with midcircuit spin measurements that herald the probabilistic preparation of superpositions of squeezed, trisqueezed, and quadsqueezed states, which have not previously been experimentally demonstrated. We achieve independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full-state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.

Physical links are fundamental to the structure, function, and ultimately the understanding of many networked systems. Erroneously identified, such direct cause-effect relations undermine the understanding of the system’s dynamics and can impede effective intervention. To address the long-standing challenge of distinguishing direct from indirect links in observational data from complex dynamical networks, we introduce a general inference framework tailored to networked dynamical systems. Our approach combines cross mapping with a novel, physics-informed technique for incremental variable construction that leverages temporal delay effects to identify relevant variables and eliminate indirect links. We validate our method across a diverse set of noisy benchmark and real-world systems, including brain networks, gene regulation, synthetic gene circuits, and biosphere-atmosphere interactions. The method achieves particularly strong gains on mesoscale networks ($n\approx 5–20$), consistently outperforming existing approaches under diverse noise conditions. Although designed for small- to medium-sized systems, it continues to outperform competing methods even in larger networks, demonstrating both robustness and broad applicability.

An attractive approach for stabilizing entangled many-body spin states is to employ engineered dissipation. Most existing proposals either target relatively simple collective spin states or require numerous independent and complex dissipative processes. Here, we show a surprisingly versatile scheme for many-body reservoir engineering that relies solely on fully collective single-excitation decay, augmented with local Hamiltonian terms. Crucially, all these ingredients are readily available in cavity QED setups. Our method is based on splitting the spin system into groups of subensembles and provides an easily tunable setup for stabilizing a broad family of pure, highly entangled states with closed-form analytic descriptions. Our results have immediate application to multiensemble quantum metrology, enabling Heisenberg-limited sensing of field gradients and curvatures. Notably, our approach solves an important challenge in differential quantum sensing by providing an example of Heisenberg-limited differential sensing immune to common-mode noise and accessible with only simple one-body measurements. The same setup also allows the stabilization of an entire family of entangled states in a one-dimensional chain of spin ensembles with symmetry-protected topological order and has a direct connection to the outputs of sequential unitary circuits. A special case of our protocol efficiently stabilizes the celebrated Affleck-Kennedy-Lieb-Tasaki state.

Symmetry breaking underlies various nonreciprocal transport phenomena. A well-known example is the semiconductor $p\text{−}n$ junction diode, a cornerstone of modern electronics. Its superconducting counterpart—the superconducting diode effect (SDE)—has recently attracted intense interest due to its potential in ultra-low-power superconducting circuits. While most SDEs reported so far involve either explicit or spontaneous breaking of time-reversal symmetry (TRS), a comprehensive theoretical framework remains elusive. Moreover, a general mechanism enabling TRS-preserving SDEs with minimal dependence on material or device architecture has yet to be established. Here, we report polarity-tunable SDEs without breaking TRS, realized in superconducting $n\text{−}n$, $p\text{−}n$, and $p\text{−}p$ homojunctions defined via local protonic gates in multilayer ${\mathrm{NbSe}}_2$. The local gates induce partial proton intercalation, generating a built-in proton concentration gradient across the transition zone between the gated and ungated regions—closely resembling the depletion layer in conventional semiconductor diodes. We find that the observed SDE arises from electric-field-driven variation of the proton concentration gradient in the transition region, which asymmetrically modulates the critical current: suppressing it in one direction and enhancing it in the other. This local-gate-driven, TRS-preserving mechanism offers a general and scalable strategy for realizing nonreciprocal superconducting transport. Our findings establish a material-agnostic platform for SDEs, broadly applicable across two-dimensional (2D) superconductors.