A major challenge of AI plus science lies in its inherent incompatibility: Today’s AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold networks (KANs) and science. The framework highlights KANs’ usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in pykan: (1) MultKAN, KANs with multiplication nodes, (2) kanpiler, a KAN compiler that compiles symbolic formulas into KANs; (3) tree converter, convert KANs (or any neural networks) into tree graphs. Based on these tools, we demonstrate KANs’ capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

This work rigorously establishes a universal lower bound $z\ge 2$ for the dynamical exponent in frustration-free quantum many-body systems whose ground states exhibit power-law decaying correlations. The derivation relies on the Gosset-Huang inequality, providing a unified framework applicable across various lattice structures and spatial dimensions, independent of specific boundary conditions. Remarkably, our result can be applied to prove bounds for dynamics of classical stochastic processes. Specifically, we utilize a well-established mapping from the time evolution of local Markov processes with detailed balance to that of frustration-free quantum Hamiltonians, known as Rokhsar-Kivelson Hamiltonians. This proves $z\ge 2$ for such Markov processes, which is an improvement over existing bounds. Beyond these applications, the quantum analysis of the $z\ge 2$ bound is further broadened to include systems exhibiting hidden correlations, which may not be evident from purely local operators.

Because of the large-period superlattices emerging in moiré two-dimensional (2D) materials, electronic states in such systems exhibit low energy flat bands that can be used to simulate strongly correlated physics in a highly tunable setup. While many investigations have thus far focused on moiré flat bands and emergent correlated electron physics in triangular, honeycomb, and quasi-one-dimensional lattices, tunable moiré realizations of square lattices subject to strong correlations remain elusive. Here we propose a feasible scheme to construct moiré square lattice systems by twisting two or more layers of 2D materials in a rectangular lattice by 90°. We demonstrate the concept with twisted $\mathrm{GeX}/\mathrm{SnX}$ ($\mathrm{X}=\mathrm{S}$, Se) moiré superlattices and calculate their electronic structures from first principles. We show that the lowest conduction flat band in these systems can be described by a square lattice Hubbard model with parameters which can be controlled by varying the choice of host materials, number of layers, and external electric fields. In particular, twisted double bilayer GeSe realizes a square lattice Hubbard model with strong frustration due to the next-nearest-neighbor hopping that could host unconventional superconductivity, in close analogy to the Hubbard model for copper-oxygen planes of cuprate high-temperature superconductors. The presented scheme uses 90° twisted 2D materials with rectangular unit cells as a promising platform for realizing the physical phenomena of square lattice Hubbard models, establishing a new route for studying its rich phase diagram of magnetism, charge order, and unconventional superconductivity in a highly tunable setting.

Premelting plays a key role across physics, chemistry, materials, and biology sciences but remains poorly understood at the atomic level due to surface characterization limitations. We report the discovery of an amorphous ice layer (AIL) preceding the quasiliquid layer during ice premelting, enabled by a machine learning framework integrating atomic force microscopy (AFM) with molecular dynamics simulations. This approach overcomes AFM’s depth and signal limitations, allowing for three-dimensional surface structure reconstruction from AFM images. It further enables structural exploration of premelting interfaces across a wide temperature range that are experimentally inaccessible. We identify the AIL present between 121 and 180 K displaying a disordered two-dimensional hydrogen-bond network with solidlike dynamics. Our findings refine the ice premelting phase diagram and offer new insights into the surface growth dynamic, dissolution, and interfacial chemical reactivity. Methodologically, this work establishes a novel framework for AFM-based 3D structural discovery, marking a significant leap in our ability to probe complex disordered interfaces with unprecedented precision and paving the way for future disciplinary research, including surface reconstruction, crystallization, ion solvation, and biomolecular recognition.

Two-dimensional electron systems (2DESs) have represented an ever-expanding frontier in condensed matter physics. Over the past two decades, this growth has primarily been propelled by the emergence of novel 2DESs, exemplified by graphene and other two-dimensional (2D) crystals, each exhibiting distinctive properties. In this study, we synthesize high-quality $\beta$-phase bismuth thin films on exfoliated hexagonal boron nitride (hBN) and establish that bismuth surface states form a high-mobility 2DES with strong spin-orbit coupling (SOC). The extreme two dimensionality of the 2DES is characterized by an out-of-plane to in-plane effective-mass-anisotropy lower bound exceeding ${10}^3$. We further demonstrate that the spin degeneracy of the hole pockets is completely lifted, providing unambiguous transport evidence that they originate from Rashba states induced by strong SOC in the bismuth thin film. Under magnetic fields up to 40 Tesla, electrostatic gating drives the carriers into the lowest Landau levels, revealing signatures of rotational symmetry breaking and electronic nematicity. These findings position the bismuth 2DES as a compelling platform for exploring topological quantum phenomena in systems with strong SOC and high carrier mobility.

Charged particle reconstruction, the identification and characterization of particles from collision data, is fundamental to nearly all research at particle colliders like the Large Hadron Collider (LHC). With the High-Luminosity upgrade (HL-LHC), particle multiplicities will increase substantially, overwhelming traditional track reconstruction algorithms and presenting computational bottlenecks. Here, we introduce a proof of concept for a powerful new method for charged particle reconstruction inspired by state-of-the-art machine learning (ML) approaches in computer vision. Our model leverages transformer neural networks to efficiently filter relevant signals and fully reconstruct particle trajectories, directly tackling the computational complexity that traditional methods face. Evaluated on the widely used TrackML dataset, our approach achieves state-of-the-art tracking efficiency (97%) and a low fake rate (0.7%), requiring just 97 ms to reconstruct on average 1300 particle trajectories from 55,000 detector hits for particles with transverse momentum above 750 MeV. These results represent a significant milestone in both performance and speed, demonstrating a shift toward unified, scalable ML solutions that offer substantial improvements for collider experiments.

Geometrically frustrated magnetic systems, such as those based on the Shastry-Sutherland lattice (SSL), offer a rich playground for exploring unconventional magnetic states. The delicate balance between competing interactions in these systems leads to the emergence of novel phases. We present the characterization of ${\mathrm{Er}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$, an SSL compound with ${\mathrm{Er}}^{3+}$ ions forming orthogonal dimers separated by nonmagnetic layers whose structure is invariant under the $P\overline{4}{2}_{1}m$ space group. Neutron scattering reveals an antiferromagnetic dimer structure at zero field, typical of Ising spins on that lattice and consistent with the anisotropic magnetization observed. However, magnetization measurements exhibit fractional plateaus at $1/4$ and $1/2$ of saturation, in contrast to the expected $1/3$ plateau of the SSL Ising model. By comparing the energy of candidate states with ground-state lower bounds we show that this behavior requires spatially anisotropic interactions, leading to an anisotropic Shastry-Sutherland Ising model symmetric under the $Cmm2$ space group. This anisotropy is consistent with the small orthorhombic distortion observed with single-crystal neutron diffraction. The other properties, including thermodynamics, which have been investigated theoretically using tensor networks, point to small residual interactions, potentially due to further couplings and quantum fluctuations. This study highlights ${\mathrm{Er}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$ as a promising platform for investigating exotic magnetic phenomena.

Efficient, low-noise, and high-bandwidth transduction between optical and microwave photons is key to long-range quantum communication between distant superconducting quantum processors. Recent demonstrations of microwave-optical transduction using the broadband direct electro-optic (Pockels) effect in optical thin films made of AlN or ${\mathrm{LiNbO}}_3$ have shown promise. To improve efficiency and added noise, materials with larger Pockels coefficients, such as the soft ferroelectrics ${\mathrm{BaTiO}}_3$ or ${\mathrm{SrTiO}}_3$, are needed. However, these materials require adapted designs and fabrication approaches due to their nonlinear and, in some cases, hysteretic electro-optic response. Here, we engineer an on-chip, triply resonant transducer comprising low-loss ${\mathrm{BaTiO}}_3$-on-${\mathrm{SiO}}_2$ waveguides monolithically integrated with a superconducting microwave resonator made of Nb. We demonstrate bidirectional microwave-optical transduction and reach total off-chip efficiencies of $1\times {10}^{-6}$ using pulsed pumping. The device design permits in situ poling of the ferroelectric material without introducing excess microwave loss, exploiting superconducting air bridges fabricated using only subtractive patterning steps. In addition, we investigate optically induced heating, revealing fast thermalization and quasiparticle resilience of the microwave resonator. Our transducer concept and fabrication process are applicable to other materials with a large bias-induced Pockels effect like ${\mathrm{SrTiO}}_3$ and pave the way for efficient, low-power quantum interconnects.

Twisted bilayer ${\mathrm{MoTe}}_2$ (${\mathrm{tMoTe}}_2$) is an emergent platform for exploring exotic quantum phases driven by the interplay between nontrivial band topology and strong electron correlations. Direct experimental access to its momentum-resolved electronic structure is essential for uncovering the microscopic origins of the correlated topological phases therein. Here, we report angle-resolved photoemission spectroscopy measurements of ${\mathrm{tMoTe}}_2$, revealing pronounced twist-angle-dependent band reconstruction shaped by orbital character, interlayer coupling, and moiré potential modulation. Density functional theory captures the qualitative evolution, yet underestimates key energy scales across twist angles, highlighting the importance of electronic correlations. Notably, the hole effective mass at the $K$ point exhibits a nonmonotonic dependence on twist angle, peaking near 2°, consistent with band flattening at the magic angle predicted by continuum models. Via electrostatic gating and surface dosing, we further visualize the evolution of electronic structure versus doping, enabling direct observation of the conduction band minimum and confirm ${\mathrm{tMoTe}}_2$ as a direct band gap semiconductor. These results establish a spectroscopic foundation for modeling and engineering emergent quantum phases in this moiré platform.

By combining ab initio downfolding with cluster dynamical mean-field theory, we study the degree of correlations in monolayer, bilayer, and bulk breathing-mode kagome van der Waals materials ${\mathrm{Nb}}_3(\mathrm{F},\mathrm{Cl},\mathrm{Br},\mathrm{I}{)}_8$. Our new material-specific many-body model library shows that in low-temperature bulk structures the Coulomb correlation strength steadily increases from I to Br, Cl, and F, allowing us to identify ${\mathrm{Nb}}_3{\mathrm{I}}_8$ as a weakly correlated insulator whose gap is only mildly affected by the local Coulomb interaction. ${\mathrm{Nb}}_3{\mathrm{Br}}_8$ and ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$ are strongly correlated insulators, whose gaps are significantly influenced by Coulomb-induced vertex corrections. ${\mathrm{Nb}}_3{\mathrm{F}}_8$ is a prototypical bulk Mott insulator whose gap is initially opened by strong correlation effects. Angle-resolved photoemission spectroscopy measurements comparing ${\mathrm{Nb}}_3{\mathrm{Br}}_8$ and ${\mathrm{Nb}}_3{\mathrm{I}}_8$ allow us to experimentally confirm these findings by revealing spectroscopic footprints of the degree of correlation. Our calculations further uncover how the thickness and the stacking affect the degree of correlations and predict that the entire material family can be tuned into correlated charge transfer or Mott-insulating phases upon electron or hole doping. Our magnetic property analysis based on our model parameter library additionally confirms that interlayer magnetic interactions likely drive the lattice phase transition to the low-temperature structures. The accompanying bilayer hybridization through interlayer dimerization yields magnetic singlet-like ground states in the Cl, Br, and I compounds. We further prove that all low-temperature compounds are dynamically stable and that electron-phonon coupling to the low-energy subspace is suppressed. Our findings establish ${\mathrm{Nb}}_3{\mathrm{X}}_8$ as a robust, versatile, and tunable class for van der Waals-based Coulomb and Mott engineering with a rich phase diagram and allow us to speculate on the symmetry-breaking effects necessary for the recently observed Josephson diode effect in ${\mathrm{NbSe}}_2/{\mathrm{Nb}}_3{\mathrm{Br}}_8/{\mathrm{NbSe}}_2$ heterostructures.

Understanding how the vibrational and thermal properties of solids are influenced by atomistic structural disorder is of fundamental scientific interest and paramount to designing materials for next-generation energy technologies. While several studies indicate that structural disorder strongly influences the thermal conductivity, the fundamental physics governing the disorder-conductivity relation remains elusive. Here we show that order-of-magnitude, disorder-induced variations of conductivity in network solids can be predicted from a “bond-network” entropy, an atomistic structural descriptor that quantifies heterogeneity in the topology of the atomic-bond network. We employ the Wigner formulation of thermal transport to demonstrate the existence of a relation between the bond-network entropy and observables such as smoothness of the vibrational density of states and macroscopic conductivity. We also show that the smoothing of the vibrational density of states encodes information about the thermal resistance induced by disorder and can be directly related to phenomenological models for phonon-disorder scattering based on the semiclassical Peierls-Boltzmann equation. Our findings rationalize the conductivity variations of disordered carbon polymorphs ranging from nanoporous electrodes to defective graphite used as a moderator in nuclear reactors.

Quantum processors based on neutral atoms trapped in arrays of optical tweezers have appealing properties, including relatively easy qubit number scaling and the ability to engineer arbitrary gate connectivity with atom movement. However, these platforms are inherently prone to atom loss, and the ability to replace lost atoms during a quantum computation is an important but previously elusive capability. Here, we demonstrate the ability to measure and reinitialize, and if necessary replace, a subset of atoms while maintaining coherence in other atoms. This allows us to perform logical circuits that include single- and two-qubit gates as well as repeated midcircuit measurement while compensating for atom loss. We highlight this capability by performing up to 41 rounds of syndrome extraction in a repetition code, and combine midcircuit measurement and atom replacement with real-time conditional branching to demonstrate heralded state preparation of a logically encoded Bell state. Finally, we demonstrate the ability to replenish atoms in a tweezer array from an atomic beam while maintaining coherence of existing atoms—a key step toward execution of logical computations that last longer than the lifetime of an atom in the system.

A central mystery in high-temperature cuprate superconductors is the coexistence of multiple exotic orders, which is presumably associated with strong electronic correlation. The ongoing interest in this enigmatic phenomenon is further energized when similar electronic orders and states emerge and coexist in less correlated kagome superconductors. Here, by utilizing angle-resolved photoemission spectroscopy (ARPES), nuclear magnetic resonance (NMR) spectroscopy, scanning tunneling microscopy (STM) and first-principles calculations, we reveal the sudden emergence of a distinct short-range charge stripe order in Sn-doped ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ kagome superconductors when the long-range $2\times 2$ charge density wave order in pristine ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ is suppressed. This short-range stripe order features a modulation vector of approximately $1/3$ along one of the three lattice directions, induces remarkable quasiparticle scattering between the original quasi-1D kagome $d$ bands and their replica of folding, and clearly suppresses the electron density of states at the Fermi level. Our first-principles calculations reveal that $3\times 1$ supermodulation represents a hidden secondary instability in pristine ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. This instability is further enhanced by in-plane chemical pressure induced by Sn substitution, and coupled to the electronic correlation, leading to a unique charge stripe order in the system. As such, our results reveal a new route toward emergent electronic orders via cooperative interactions between the lattice and electronic degrees of freedom.

From the vasculature of animals to the porous media making up batteries, the core task of flow networks is to transport solutes and perfuse all cells or media equally with resources. Yet, living flow networks have a key advantage over porous media: They are adaptive, and they self-organize their geometry for homogeneous perfusion throughout the network. Here, we show that artificial flow networks can also self-organize toward homogeneous perfusion by the versatile adaption of controlled erosion. Flowing a pulse of cleaving enzyme through a network patterned into an erodible hydrogel, with initial channels disparate in width, we observe a homogenization in channel resistances. Experimental observations are matched with numerical simulations of the diffusion-advection-sorption dynamics of an eroding enzyme within a network. Analyzing transport dynamics theoretically, we show that homogenization only occurs if the pulse of the eroding enzyme lasts longer than the time it takes any channel to equilibrate to the pulse concentration. The equilibration time scale derived analytically is in agreement with simulations. Lastly, we show both numerically and experimentally that erosion leads to the homogenization of complex networks containing loops. Erosion being an omnipresent reaction, our results pave the way for a very versatile self-organized increase in the performance of porous media.

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.