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.

We report the discovery of super-resonance—a new regime of resonant behavior in which a mode’s out-of-phase response persists far beyond its classical bandwidth. This effect emerges from a coiled phononic structure composed of a locally resonant elastic metamaterial and architected to support multiple internal energy pathways. These pathways converge at an effectively single spatial location, enabling extended modal dominance and significantly broadening the frequency range over which a resonant phase is sustained. We demonstrate by direct numerical simulations the implications of this mechanism in the context of flow instability control, where current approaches are inherently constrained by the characteristically narrow spectral bandwidth of conventional resonances. Using a super-resonant phononic subsurface structure interfacing with a channel flow, we show passive simultaneous suppression of four unstable flow perturbations across a frequency range more than 5 times wider than that is attainable with a standard resonance in an equivalent uncoiled structure. By enabling broadband control of flow instabilities, super-resonance overcomes a long-standing limitation in laminar flow control strategies. More broadly, it introduces a powerful new tool for phase-engineered wave-matter interaction. The ability to preserve out-of-phase modal response across wide spectral ranges establishes a fundamental advance in the physics of resonance, with far-reaching implications for suppressing fully developed turbulent flows and beyond.

The charged anyons of a fractional quantum Hall fluid are necessarily dispersionless due to the continuous magnetic translation symmetry. Neutral anyons, however, can disperse, resulting in a much richer space of possible “daughter” states when doped to finite density. We discuss a natural realization of such physics in quantum Hall bilayers, where a finite density of excitons with fractional statistics is argued to give rise to “anyonic exciton superfluidity,” the charge-neutral analog of anyon superconductivity. In a balanced bilayer of two Laughlin $\nu =1/3$ states, the minimal interlayer exciton carries anyonic exchange statistics. A finite density of these excitons is argued to yield an exciton superfluid stitched to a specific bulk topological order and edge spectrum. Such a superfluidity should be most robust near the direct transition into the Halperin (112) state, and near analogous transitions in the bilayer Jain sequence at total filling ${\nu }_{\mathrm{T}}=2\times [n/(2n+1)]$. These topological transitions can be described by Chern-Simons ${\mathrm{QED}}_3$, from which we derive several novel and general properties of anyon superfluidity near such transitions, including an anomalously large superfluid stiffness of ${\kappa }_{\mathrm{s}}\propto |\delta \nu {|}^{1/2}$ at layer imbalance fraction $\delta \nu$. A notable feature of the phase diagrams we construct is the prevalence of spatial symmetry breaking driven by an underlying composite Fermi surface. Our results can be directly tested with currently available experimental techniques. We compare our theory with existing data and make concrete predictions for future measurements, including higher-pseudospin exciton superfluids when doping higher Jain fractions.

Kagome spin ice is an intriguing class of spin systems constituted by in-plane Ising spins with ferromagnetic interaction residing on the kagome lattice, theoretically predicted to host a plethora of magnetic transitions and excitations. In particular, different variants of kagome spin ice models can exhibit different sequences of symmetry breaking upon cooling from the paramagnetic to the fully ordered ground state. Recently, it has been demonstrated that the frustrated intermetallic HoAgGe stands as a faithful solid-state realization of kagome spin ice. However, whether any of the established symmetry-breaking pathways apply to this material remains unaddressed. Here, we use single-crystal neutron diffuse scattering to map the spin ordering of HoAgGe at various temperatures more accurately; surprisingly, we find that the ordering sequence appears to be different from previously known scenarios: From the paramagnetic state, the system first enters a partially ordered state with fluctuating magnetic charges, in contrast to a charge-ordered paramagnetic phase, before reaching the fully ordered state. Through Monte Carlo simulations and scaling analyses using an extended three-dimensional (3D) spin model for the distorted kagome spin ice in HoAgGe, we elucidate a single 3D XY phase transition into the ground state with broken time-reversal symmetry (TRS). However, the 3D XY transition has a long crossover tail before the fluctuating magnetic charges fully order. More interestingly, we find, both experimentally and theoretically, that the TRS-breaking phase of HoAgGe features an unusual, hysteretic response: Despite their vanishing magnetization, the two time-reversal partners are distinguished and selected by a nonlinear magnetic susceptibility tied to the kagome ice rule. Our discovery not only unveils a new symmetry-breaking hierarchy of kagome spin ice but also demonstrates the potential of TRS-breaking frustrated spin systems for information technology applications.

Physical qubits in a quantum computer are often represented by superposition states of single particles or excitations. Decay of the excitation itself is a fundamental error channel that is difficult to overcome via external drive or control techniques. Quantum error correcting codes, which encode information in superpositions involving multiple excitations, provide a path to preserve information beyond the capacity of individual excitations, but typically require exquisite active operations on the system. Here, we demonstrate a steady-state driven-dissipative quantum system, composed of a superconducting cavity and a transmon ancilla, that preserves a logical qubit beyond the photon-lifetime limit by about 5% using a binomial encoding. This realization of continuous quantum error correction at the breakeven point highlights the quantitative competitiveness of passive correction strategies, while circumventing some demanding hardware requirements of its active counterparts.

Flat electronic bands, which amplify electron correlations by quenching kinetic energy, provide an ideal foundation for exotic quantum phases. However, prevailing strategies—including geometrically frustrated lattices, moiré superlattices, and heavy-fermion systems—often suffer from inherent trade-offs among robustness, tunability, and orbital control, thereby limiting their broad applicability. Here, we report the experimental discovery of intrinsic orbital-selective flat bands in the layered transition-metal oxyhalide family $MO{X}_2$ ($M=\mathrm{Nb}$, Ta; $X=\mathrm{Cl}$, Br, I), directly observed by angle-resolved photoemission spectroscopy at room temperature. Importantly, this materials platform exhibits pronounced tunability: The flat-band bandwidth and correlation strength can be systematically tuned via halogen substitution, while the Fermi level is controllable through electrostatic gating and surface charge transfer. Remarkably, the flat band remains stable upon dimensional reduction, persisting from the bulk crystal down to the few-layer limit. Our theoretical analysis reveals that this flat band transcends simple lattice geometry, originating instead from an orbital-driven synergetic Su-Schrieffer-Heeger-Lieb mechanism: a cooperative interplay between quasi-one-dimensional $M\text{−}{d}_{z^2}$ Su-Schrieffer-Heeger chains and a two-dimensional $M\text{−}{d}_{x^2-y^2}$ Lieb-like sublattice, reinforced by Peierls dimerization. Together, these findings establish layered transition-metal oxyhalides as a versatile materials-by-design platform for systematically engineering intrinsic flat bands via chemical, electronic, and dimensional control, which provides a robust pathway to exploring room-temperature flat-band physics.

Among the thriving quantum computation and quantum simulation platforms based on arrays of Rydberg atoms, those using circular Rydberg atoms are particularly promising. These atoms uniquely combine the strong dipole-dipole interactions typical of Rydberg states with long lifetimes. However, low-angular-momentum ($\ell$) laser-accessible Rydberg levels have been so far mostly used, because circular Rydberg atoms have no optical transitions, hindering their individual detection and manipulation. We remove this limitation with a hybrid platform, combining an array of data laser-trapped circular Rydberg atoms of rubidium with an auxiliary array of Rb ancilla atoms transiently excited to a low-$\ell$ Rydberg level. We perform a quantum nondemolition detection of the data qubit with the ancilla, through the blockade of the ancilla optical excitation induced by a Förster resonance. Conversely, we locally manipulate the data qubit through the excitation of the ancilla. This dual-Rydberg platform is highly promising for quantum computation and simulation. It adds to the circular-atom toolbox the midcircuit measurements, essential for error correction. More strikingly, it gives access to time correlations in long-term quantum simulations, uniquely accessible to circular Rydberg atoms.

Continuous-variable quantum key distribution holds the potential to generate high secret key rates, making it a prime candidate for high-rate metropolitan quantum network applications. However, despite these promising opportunities, the realization of high-rate continuous-variable quantum key distribution systems with composable security remains an elusive goal. Here, we report a discrete-modulated continuous-variable quantum key distribution system with a composable secret key rate of 18.93 Mbps against collective attacks over a 25-km fiber channel. This record-breaking rate is achieved through the probability-shaped 16 quadrature amplitude modulation-modulated protocol, which employs semidefinite programming to ensure its composable security. Furthermore, we have employed a fully digital and precise quantum signal processing technique to reduce excess noise to extremely low levels, thereby facilitating efficient broadband system operation. While ensuring low complexity and cost, our system achieves a performance advantage of over an order of magnitude compared to previous continuous-variable quantum key distribution systems, providing a promising solution for future deployment of quantum key distribution.

Pathwise observables—functionals of stochastic trajectories—are at the heart of time-averaged statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation bounds. They provide a means of thermodynamic inference in the typical situation, when not all dissipative degrees of freedom in a system are experimentally accessible. So far, theories focusing on pathwise observables have been developing in two major directions, diffusion processes and Markov-jump dynamics, in a virtually disjoint manner. Moreover, even the respective results for diffusion and jump dynamics were derived with a patchwork of different approaches that are predominantly indirect. Stochastic calculus was recently shown to provide a direct approach to pathwise observables of diffusion processes, while a corresponding framework for jump dynamics remained elusive. In our work, we develop, in an exact parallelism with continuous-space diffusion, a complete stochastic calculus for pathwise observables of Markov-jump processes. We formulate a “Langevin equation” for jump processes, define general pathwise observables, and establish their covariation structure, whereby we fully account for transients and time-inhomogeneous dynamics. We prove the known kinds of thermodynamic inequalities in their most general form and discuss saturation conditions. We determine the response of pathwise observables to general (including thermal) perturbations and introduce a corresponding response-function formalism. We carry out the continuum limit to achieve the complete unification of diffusion and jump dynamics. In addition, we connect the framework to quantum unraveling and the Belavkin equation for open quantum systems, associating quantum and classical descriptions of thermal systems. Our results open avenues in the direction of discrete-state analogs of generative diffusion models and the learning of stochastic thermodynamics from fluctuating trajectories.