Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes to deliver reliable parameter estimation and model selection from coarsely sampled time series, without requiring analytical solutions. Crucially, we couple mechanistic stochastic models with their inference procedures to quantify how experimental design—specifically, sampling frequency and dataset size—governs estimator precision and model distinguishability. This analysis reveals optimal sampling regimes and sharp, resolution-dependent limits beyond which competing models become empirically indistinguishable. We validate the approach across four disparate systems—trajectories of optically trapped particles, human microbiome dynamics, social-media topic mentions, and forest population time series—recovering parameters and identifying when inference is fundamentally constrained by measurement resolution, thereby clarifying ongoing debates about dominant noise sources in these systems. Together, these results establish path-based Monte Carlo as a practical, general tool for inference and model discrimination in complex systems and provide principled guidelines for designing measurements that maximize information under real-world constraints.

For four decades, statistical physics has been providing a framework to analyze neural networks. A long-standing question remained on its capacity to tackle deep-learning models capturing rich feature-learning effects, thus going beyond the narrow networks or kernel methods analyzed until now. We positively answer through the study of the supervised learning of a multilayer perceptron. Importantly, (i) its width scales as the input dimension, making it more prone to feature learning than ultrawide networks and more expressive than narrow ones or ones with fixed embedding layers, and (ii) we focus on the challenging interpolation regime where the number of trainable parameters and data are comparable, which forces the model to adapt to the task. We consider the matched teacher-student setting. Therefore, we provide the fundamental limits of learning random deep neural-network targets and identify the sufficient statistics describing what is learned by an optimally trained network as the data budget increases. A rich phenomenology emerges with various learning transitions. With enough data, optimal performance is attained through the model’s “specialization” toward the target, but it can be hard to reach for training algorithms, which get attracted by suboptimal solutions predicted by the theory. Specialization occurs inhomogeneously across layers, propagating from shallow toward deep ones but also across neurons in each layer. Furthermore, deeper targets are harder to learn. Despite its simplicity, the Bayes-optimal setting provides insights into how the depth, nonlinearity, and finite (proportional) width influence neural networks in the feature-learning regime that are potentially relevant in much more general settings.

Turbulence follows a few well-known organizational principles, rooted in conservation laws. One such principle states that a system conserving two sign-definite invariants self-organizes into large-scale structures. Ordinary three-dimensional turbulence does not fall within this paradigm but is profoundly altered when subject to rotation. In rotating turbulence, 3D inertial waves coexist alongside emergent two-dimensional structures, which tend to take the form of domain-scale flows called condensates. This interplay raises a fundamental question: Why and when are 2D flows sustained if only 3D waves are excited? We develop a quasilinear wave-kinetic theory to answer this question. We show that near-resonant interactions between 3D waves and a large-scale 2D flow impose an additional conservation law: Waves must conserve their helicity separately for each helicity sign. This emergent sign-definite invariant constrains the waves to transfer their energy to large-scale 2D motions, which maintains the latter in statistical steady state. We derive analytical expressions for the 3D-2D energy transfer as a function of rotation, Reynolds number, and domain geometry in a rotation-dominated regime and compare them with extensive numerical simulations of the rotating 3D Navier-Stokes equations. As rotation increases, the energy transfer from the waves to the 2D flow progressively vanishes as the two decouple, leading to a transition between distinct classes of turbulence: from 2D-dominated to 3D-dominated wave turbulence. Our theory shows that this gradual transition is caused by a depletion of modes satisfying the resonance conditions and exhibits good agreement with numerical simulations when the number of near-resonant modes is not too small. We discuss such limitations of our theory, as well as the validity range of its underlying assumptions. Together, these results suggest a mechanism underlying two-dimensionalization in rotating turbulence and, more broadly, illustrate how nonlinear systems sustaining waves can self-organize into anisotropic, zero-frequency structures.

In nonlinear transport, the quantum-geometric effects can generate higher-harmonic voltages in response to a driving current, which has defined a fast-moving field of intense interest. However, in realistic materials where disorder scattering also contributes to nonlinear transport, identifying the geometric mechanisms remains a challenge. In particular, a theoretical framework for data analysis is still lacking for nonlinear transport at any order. Here, we develop a mechanism-resolved and symmetry-guided framework for identifying mechanisms of third-order nonlinear transport in disordered materials. We find a total of 20 mechanisms of third-order nonlinear transport, by treating quantum-geometric and disorder-mediated mechanisms on an equal footing. More importantly, we propose a protocol of data analysis that combines symmetry diagnosis of magnetic point groups and scaling law of relation between the third-order nonlinear Hall conductivity and linear longitudinal conductivity. We identify characteristic fingerprints in the scaling-law weights, which allow the mechanisms to be quantitatively distinguished in experiments. We have applied the protocol to identify the geometric mechanisms in materials with and without time-reversal symmetry, including 2D materials, topological materials, and altermagnets. The theory can be generalized to arbitrary orders of nonlinear transport, further promoting nonlinear transport as a probe of geometric effects and phase transitions in quantum materials.

Heavy polar molecules are sensitive probes of physics beyond the standard model. However, uncontrolled external electromagnetic fields pose challenges to achieving precise and accurate measurements. Minimizing susceptibility to these fields is therefore critical and has played an important role in all precision experiments of this type. Here we devise and demonstrate clock transitions engineered to realize robust symmetry violation searches in the polyatomic molecule YbOH. Sensitivities to external fields can be suppressed by orders of magnitude while preserving high sensitivity to the electron electric dipole moment. We perform Ramsey measurements on these clock transitions and observe suppression of electric and magnetic sensitivities by at least factors of 700 and 200, respectively, and demonstrate the robustness of their spin coherence against large electromagnetic-field fluctuations. We further identify and employ selected quantum states to make sensitive measurements of external magnetic and electric fields, another critical feature for highly accurate measurements. This approach of molecular engineering is broadly applicable to diverse molecular species and states, including those with complex nuclei and those that are compatible with state-of-the-art cooling and trapping techniques, thereby offering the potential to significantly improve experimental sensitivity to a wide range of new physics while expanding the chemical design space for molecular quantum science.

Solving large-scale quadratic unconstrained binary optimization (QUBO) problems is critical in various fields, including physics, finance, and engineering. However, these problems remain intractable on conventional computing architectures. Alternative solvers, such as Ising machines (IMs) based on networks of coupled electronic, mechanical, or photonic parametric oscillators (POs), have recently been developed. PO-based IMs aim to find the ground state of an Ising Hamiltonian, which encodes the solution to a QUBO problem. However, their analog nature and their energy-minimization process based on gradient descent make PO-based IMs inherently susceptible to identifying inaccurate solutions. In this work, we introduce and validate a QUBO solver—the analog Floquet solver (AFS)—which enhances the dynamics of PO-based IMs by leveraging Floquet states that emerge spontaneously in POs coupled to high-quality-factor resonances. These states enable the AFS to embed periodic time modulation into its energy-minimization process, allowing it to escape local minima during the search for QUBO problem solutions. As a result, the AFS significantly increases the likelihood of identifying accurate solutions compared to conventional PO-based IMs. More generally, this work defines a new paradigm in analog computing—spanning both classical and quantum realms—that can be physically realized with existing technologies across diverse physical domains.

The interplay among electronic correlation, topology, and time-reversal symmetry often leads to exotic quantum states of matter, as highlighted by the discoveries of fractional Chern insulators in twisted bilayer ${\mathrm{MoTe}}_2({\mathrm{tMoTe}}_2)$. Among the fractional Chern insulators (FCIs) in ${\mathrm{tMoTe}}_2$, the most robust is at a hole filling factor of $\mathit{\nu }=-\frac{2}{3}$ per moiré unit cell. Here, employing pump-probe circular dichroism measurement on ${\mathrm{tMoTe}}_2$ at twist angles $\theta =3.9°$ and 3.7°, we show that a correlated state at $\mathit{\nu }=-\frac{4}{3}$ exhibits an unusual Ising antiferromagnet behavior. The $\mathit{\nu }=-\frac{4}{3}$ state with no net magnetization undergoes first order phase transitions at extremely low magnetic fields of $|{\mu }_{0}H|\sim 2–6\mathrm{mT}$ to partially valley polarized states. This behavior is notably absent for all other correlated states in ${\mathrm{tMoTe}}_2$ and also disappears for $\mathit{\nu }=-\frac{4}{3}$ at higher or lower twist angles ($\theta =4.0°$ or 3.3°). The observed magnetic signature is consistent with a theoretically proposed fractional topological insulator (FTI), consisting of two copies of ${\mathit{\nu }}_{\pm }=-\frac{2}{3}$ FCIs with opposite chirality in the ${\mathit{K}}^{\pm }$ valleys. The experimental results are supported by interacting continuum model calculations that reveal the extreme closeness in energy ($\mathrm{\Delta }\mathrm{E}<1\mathrm{meV}$) between the putative FTI (${\mathit{\nu }}_{\pm }=-\frac{2}{3}$ and ${\mathit{\nu }}_{\mp }=-\frac{2}{3}$) and partially valley polarized states (${\mathit{\nu }}_{\pm }=-1$ and ${\mathit{\nu }}_{\mp }=-\frac{1}{3}$). Our findings present a candidate FTI with time-reversal symmetry and call for advanced transport and imaging measurements to establish the quantized helical edge modes.

The discovery of superconductivity in bulk bilayer nickelates under high pressure, and its subsequent stabilization in compressively strained thin films at ambient pressure, has established a new platform for exploring high-$T_{\mathrm{c}}$ superconductivity beyond the cuprates. Central to this development is the prominent role of the $3d_z^2$ orbital in shaping the low-energy electronic structure, imposing constraints on microscopic theories and fueling debate over the superconducting mechanism. Here we report a systematic in situ angle-resolved photoemission spectroscopy study of compressively strained bilayer nickelate thin films spanning Ca doping, oxygen stoichiometry and film thickness. Despite variations in oxygen-vacancy disorder and surface termination, the electronic structure remains robust and exhibits a systematic strain-driven evolution consistent with an intermediate-correlation regime. In particular, we demonstrate a Ca-doping-induced electronic structure evolution that is consistent with Fermi-level crossing of the $\gamma$ band and is decoupled from the presence of superconductivity, suggesting that, while important for the $\gamma$ band to be near the Fermi level, the debated $\gamma$ crossing and the resulting Fermi pocket may not be a prerequisite for superconductivity. Together, our results establish key spectroscopic constraints on the minimal fermiology and correlation strength relevant to superconductivity in bilayer nickelates, providing an experimental foundation for microscopic theories of their pairing mechanism.

We introduce configuration space path integrals for quantum fields interacting with classical fields. We show that this can be done consistently by proving that the dynamics are completely positive directly, without resorting to master equation methods. These path integrals allow one to readily impose space-time symmetries, including Lorentz invariance or diffeomorphism invariance. They generalize and combine the Feynman-Vernon path integral of open quantum systems and the stochastic path integral of classical stochastic dynamics while respecting symmetry principles. We introduce a path integral formulation of general relativity where the space-time metric is treated classically. The theory is a candidate for a fundamental theory that reconciles general relativity with quantum mechanics. The theory is manifestly covariant, and may be inequivalent to the theory derived using master equation methods. We prove that entanglement cannot be created via the classical field, reinforcing proposals to test the quantum nature of gravity via entanglement generation.

Knits and crochets are mechanical metamaterials with a long history that can typically be produced from a single yarn. Despite the simplicity of the manufacturing process, they exhibit a wide range of structural configurations with diverse mechanical properties and application potentials. Although there has been recent growing interest in textile-based metamaterials, a rigorous topological characterization of what makes a structure knittable has been lacking. Here, we introduce a general criterion based on topological constraints that distinguish knits and crochets from other textile structures. We demonstrate how the introduction of topological defects and their propagation makes this classification practical. Our approach highlights a fundamental link between manufacturing processes and structural fragility. Within this framework, we show how the rationalization of defect propagation unlocks the design of fabrics with controllable damage resistance.

The distribution of entanglement across distant qubits is a central challenge for the operation of scalable quantum computers and large-scale quantum networks. Existing approaches rely on deterministic state transfer, or probabilistic protocols that require active control or measurements and postselection. Here, we demonstrate a fundamentally different, fully autonomous process, where two remote qubits are entangled through their coupling to a quantum-correlated photonic reservoir. In our experiment, a Josephson parametric converter produces a Gaussian, continuous-variable entangled state of propagating microwave fields that drives two spatially separated superconducting transmon qubits into a stationary, discrete-variable entangled state. We also show how qubit tomography unlocks a direct and sensitive verification of two-mode squeezing in the microwave domain. These results establish networks of qubits interfaced with distributed continuous-variable entangled states as a powerful platform for foundational studies and quantum-technology applications.

Remote entanglement between widely separated qubits is a fundamental quantum phenomenon and a critical resource for quantum information applications. Generating entanglement between independent qubits separated by arbitrary, potentially large distances requires propagating quantum states and is typically achieved using pulsed protocols combining distinct steps of local entanglement generation followed by distribution. This necessity raises an intriguing question: Can remote entanglement be stabilized indefinitely, instead of periodically regenerated and redistributed only after decay? Here, we demonstrate that this is indeed possible, reporting autonomous stabilization of entanglement between two separate superconducting-qubit devices. Combining nonreciprocal waveguide coupling and local driving, we experimentally realize a symmetry-based coherent quantum-absorber scheme in a cascaded network. We quantify the degree of entanglement through quantum state tomography, finding that the protocol’s entangling power is severely limited by imperfections that break the required symmetry. We show, however, that a modified protocol based on an alternate symmetry is far more robust, enabling us to achieve a concurrence approaching 0.5, a limit set by only local loss in the network. Our results enable on-demand delivery of high-fidelity entanglement in modular quantum processors and networks and pave the way for autonomously protecting distributed quantum information.

Recent studies of two-dimensional layered materials under external electric fields have gained significant attention, as such fields offer a powerful, noninvasive approach to actively modulate surface interactions at the molecular level, enabling real-time and reversible tuning of material properties. In this article, we use fully atomistic molecular dynamics simulations based on machine-learning potentials to predict the dependence of chemifriction on external electric fields in defected layered contacts. By controlling the rate of polar bond formation and rupture, friction can be either increased or decreased depending on the field strength and direction. To extend these atomistic insights to the experimentally relevant low-velocity regime, we develop a physically motivated stochastic model that bridges atomic-scale mechanisms with macroscopic friction behavior. Although demonstrated for hexagonal boron nitride junctions, the proposed mechanism of electrotunable chemifriction is expected to be general and applicable to a broad range of layered materials with polar interlayer bonding.

The quest to identify quantum advantages lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets attempting to foretell the future, yet the boundary between visionary insight and unfounded fantasy is perilously thin. In this Perspective, we examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, and communication. We explore five keystone properties, predictability, typicality, robustness, verifiability, and usefulness that define an ideal quantum advantage, and envision what new quantum advantages could arise in a future with ubiquitous quantum technology. We prove that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide, the ultimate power of quantum technologies may emerge from advantages we cannot yet conceive.

The process of scientific discovery relies on an interplay of observations, analysis, and hypothesis generation. Machine learning is increasingly being adopted to address individual aspects of this process. However, it remains an open challenge to fully automate the heuristic, iterative loop required to discover the laws of an unknown system by exploring it through experiments and analysis, without tailoring the approach to the specifics of a given task. Here, we introduce sciexplorer, an agent that leverages large language model tool-use capabilities to enable exploration of systems without any domain-specific blueprints and apply it to physical systems that are initially unknown to the agent. We test sciexplorer on a broad set of models spanning mechanical dynamical systems, wave evolution, and quantum many-body physics. Despite using a minimal set of tools, primarily based on code execution, we observe impressive performance on tasks such as recovering equations of motion from observed dynamics and inferring Hamiltonians from expectation values. The demonstrated effectiveness of this setup opens the door toward similar scientific exploration in other domains, without the need for fine-tuning or task-specific instructions.

We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose code space is stabilized by Clifford operators. We formulate a path-integral framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits. We also show an equivalence between our approach and prior proposals where a 2D array of qubits reproduces the action of a transversal gate in a 3D stabilizer code over time, thus establishing a connection between 3D codes and 2D non-Abelian topological phases. We prove a threshold theorem for our protocols under local stochastic circuit noise using a just-in-time decoder to correct the non-Abelian code.

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.