Antiferromagnets that break both space-time reversal and translation-spin-rotation symmetries were recently predicted [L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Phys. Rev. B 102, 014422 (2020)] to possess splitting between the otherwise spin-degenerate energy bands even without the relativistic spin-orbit coupling (SOC). Here, we point out that such nonrelativistic spin splitting (NRSS)—in particular, “spin splitting type 4” (SST-4) symmetry-broken antiferromagnets—can be divided into subgroups having distinct patterns of spin splitting and spin textures, depending on additional auxiliary symmetries of spin interconversion and polarity. These SST-4 subgroups include the $\alpha$-type (no spin-interconverting symmetry) having spin splitting at the Brillouin zone center, as well as the $\beta$ subgroup in which a rotation symmetry is applied and determines the alternating spin texture and the $\gamma$ subgroup having exclusively reflection spin-interconverting symmetry. Unlike ferrimagnets, the $\alpha$-type compounds are shown to have tiny net magnetization at finite temperature and thus avoid the adverse effect of the stray field. The $\alpha$ and $\beta$ subgroups can be either polar or nonpolar, whereas the $\gamma$ subgroup is polar only, providing a basis for possible switching by external fields. The combination of NRSS-enabling and auxiliary symmetries is used here as a filter for identifying previously synthesized compounds as specific prototypes. Their characteristic splitting and spin polarization are calculated by density functional theory to the benefit of potential future experimental testing. Interesting results are as follows: (i) SOC-independent NRSS can exceed the magnitude of the SOC-induced Rashba and Dresselhaus spin splitting in semiconductors. (ii) Examples of predicted $\alpha$-type insulating compounds include ${\mathrm{BiCrO}}_3$ (nonpolar) and ${\mathrm{Mn}}_2{\mathrm{ScSbO}}_6$ (polar), the latter having spin splitting of 158 meV and 160 meV in the valence and conduction bands, respectively. (iii) The $\beta$-type (${\text{Cu}}_2{\text{Y}}_2{\text{O}}_5$ and ${\text{FeF}}_2$) and $\gamma$-type compounds (${\text{Mn}}_4{\text{Nb}}_2{\text{O}}_9$ and ${\text{FeScO}}_3$) are distinguished both by their auxiliary symmetries and polarity. The spin textures of $\gamma$-type compounds are mirror reflected with spin degeneracy of the wave vectors on that mirror. These observations will likely broaden the experimental playing field of NRSS physics significantly.

Quantum communication is needed to build powerful quantum computers and establish reliable quantum networks. At its basis lies the ability to generate and distribute entanglement to separate quantum systems, which can be used to run remote quantum operations on them or teleport quantum states from one system to another with the help of classical channels. To this end, it is useful to harness the resource of continuous-variable (CV) entanglement, since it can be efficiently and unconditionally produced by squeezing light in a nonlinear medium and can be easily manipulated, distributed, and measured using standard components. While various aspects of CV-based quantum communication have been successfully demonstrated in the optical domain, some key capabilities, such as entanglement swapping, have been lacking in the microwave domain. Here, we demonstrate three key elements of CV-based microwave quantum communication: (i) a Josephson mixer operating as a nondegenerate two-mode entangler with maximum measured logarithmic negativity $E_N=1.5$, (ii) a quantum teleportation apparatus, capable of teleporting vacuum and coherent states with a maximum fidelity of 73%, which exceeds the 50% classical limit and is mainly limited by intermediate losses in the setup, and (iii) an entanglement-swapping system which generates entanglement between two remote noninteracting modes via entanglement-swapping operations applied to input vacuum and coherent states with maximum measured logarithmic negativity $E_N=0.53$. Such hardware-efficient CV entanglement building blocks that are based on nondegenerate Josephson mixers could enable wide-ranging applications in modular quantum computation, quantum cryptography, and quantum communication.

Understanding the physics of the two-dimensional Hubbard model is widely believed to be a key step in achieving a full understanding of high-$T_{\mathrm{c}}$ cuprate superconductors. In recent years, progress has been made by large-scale numerical simulations at finite doping and, on the other hand, by microscopic theories able to capture the physics of individual charge carriers. In this work, we study single pairs of dopants in a cylindrical system using the density-matrix renormalization group algorithm. We identify two coexisting charge configurations that couple to the spin environment in different ways: a tightly bound configuration featuring (next-)nearest-neighbor pairs and a stripelike configuration of dopants on opposite sides of the cylinder, accompanied by a spin domain wall. Thus, we establish that the interplay between stripe order and uniform pairing, central to the models’ phases at finite doping, has its origin at the single-pair level. By interpolating between the Hubbard and the related $t\text{−}J$ model, we are able to quantitatively understand discrepancies in the pairing properties of the two models through the three-site hopping term usually omitted from the $t\text{−}J$ Hamiltonian. This term is closely related to a next-nearest-neighbor tunneling $t^{\prime }$, which we observe to upset the balance between the competing stripe and pair states on the two-dopant level.

We initiate the study of state complexity for continuous-variable quantum systems. Concretely, we consider a setup with bosonic modes and auxiliary qubits, where available operations include Gaussian one- and two-mode operations and single- and two-qubit operations as well as qubit-controlled phase-space displacements. We define the (approximate) complexity of a bosonic state by the minimum size of a circuit that prepares an approximation to the state in trace distance. We propose a new circuit which prepares an approximate Gottesman-Kitaev-Preskill (GKP) state $|{\mathsf{G}\mathsf{K}\mathsf{P}}_{\kappa ,\mathrm{\Delta }}⟩$. Here, ${\kappa }^{-2}$ is the variance of the envelope, and ${\mathrm{\Delta }}^2$ is the variance of the individual peaks. We show that the circuit accepts with constant probability and—conditioned on acceptance—the output state is polynomially close in $(\kappa ,\mathrm{\Delta })$ to the state $|{\mathsf{G}\mathsf{K}\mathsf{P}}_{\kappa ,\mathrm{\Delta }}⟩$. The size of our circuit is linear in $(\log 1/\kappa ,\log 1/\mathrm{\Delta })$. To our knowledge, this is the first protocol for GKP-state preparation with fidelity guarantees for the prepared state. We also show converse bounds, establishing that the linear circuit-size dependence of our construction is optimal. This fully characterizes the complexity of GKP states.

The estimation of continuous parameters from measured data plays a central role in many fields of physics. A key tool in understanding and improving such estimation processes is the concept of Fisher information, which quantifies how information about unknown parameters propagates through a physical system and determines the ultimate limits of precision. With artificial neural networks gradually becoming an integral part of many measurement systems, it is essential to understand how they process and transmit parameter-relevant information internally. Here, we present a method to monitor the flow of Fisher information through an artificial neural network performing a parameter estimation task, tracking it from the input to the output layer. We show that optimal estimation performance corresponds to the maximal transmission of Fisher information and that training beyond this point results in information loss due to overfitting. This provides a model-free stopping criterion for network training—eliminating the need for a separate validation dataset. To demonstrate the practical relevance of our approach, we apply it to a network trained on data from an imaging experiment, highlighting its effectiveness in a realistic physical setting.

Anticoncentration describes how an ensemble of quantum states spreads over the allowed Hilbert space, leading to statistically uniform output probability distributions. In this work, we investigate the anticoncentration of random Clifford circuits toward the overlap distribution of random stabilizer states. Using exact analytical techniques and extensive numerical simulations based on Clifford replica tensor networks, we demonstrate that random Clifford circuits fully anticoncentrate in logarithmic circuit depth; namely, higher-order moments of the overlap distribution converge to those of random stabilizer states. Moreover, we investigate the effect of introducing a controlled number of non-Clifford (magic) resources into Clifford circuits. We show that inserting a polylogarithmic in qudit number of $T$ states is sufficient to drive the overlap distribution toward the Porter-Thomas statistics, effectively recovering full quantum randomness. In short, this fact presents doped tensor networks and shallow Clifford circuits as pseudomagic quantum states. Our results clarify the interplay between Clifford dynamics, magic-state injection, and quantum complexity, with implications for quantum circuit sampling, many-body quantum physics, and the benchmarking of quantum computational advantage.

Successful development from a single cell to a complex, multicellular organism requires that cells differentiate in a coordinated and organized manner in response to a variety of signaling modalities. While the molecular underpinnings may be complex, the resulting phenomenon, in which a cell decides between one fate or another, is relatively simple. A body of work—rooted in dynamical systems theory—has formalized this notion of cellular decision making as flow in a Waddington-like landscape, in which cells evolve according to gradientlike dynamics within a potential that changes shape in response to a number of signals. We present a framework leveraging neural networks as universal function approximators to infer such a parametrized landscape from gene expression data. Inspired by the success of physics-informed machine learning in data-limited contexts, we enforce principled constraints motivated not by physical laws but by this phenomenological understanding of differentiation. Our data-driven approach infers a governing landscape atop a manifold situated within expression space, thereby describing the dynamics of interest in a biologically meaningful context. The resulting system provides an intuitive, visualizable, and interpretable model of cellular differentiation dynamics.

We study novel itinerant phases that can be accessed by doping a fractional quantum anomalous Hall (FQAH) insulator, with a focus on the experimentally observed Jain states at lattice filling $\nu =p/(2p+1)$. Unlike in the lowest Landau level, where charge motion is confined into cyclotron orbits, the charged excitations in the FQAH occupy Bloch states with well-defined crystal momenta. At a nonzero doping density, this feature enables the formation of itinerant states of the doped anyons just beyond the FQAH plateau region. Focusing on the vicinity of $\nu =2/3$, we describe a few possible itinerant states, including a topological superconductor with chiral neutral fermion edge modes as well as a more exotic pair density wave (PDW) superconductor with non-Abelian topological order. A Fermi liquid metal with a doping-induced period-3 charge density wave also occurs naturally in our analysis. This Fermi liquid (as well as the PDW) arises from pairing instabilities of a composite Fermi liquid metal that can emerge near filling $2/3$. Though inspired by the theory of anyon superconductivity, we explain how our construction is qualitatively different. At a general Jain filling $\nu =p/(2p+1)$, the same analytical framework leads to a wider variety of phases, including higher-charge superconductors and generalized composite Fermi liquids. We predict unusual physical signatures associated with each phase and analyze the crossover between different temperature regimes. These results provide a proof-of-principle that exotic itinerant phases can be stabilized by correlations intrinsic to the FQAH setup.

Time estimation is a fundamental task that underpins precision measurement, global navigation systems, financial markets, and the organization of everyday life. Many biological processes also depend on time estimation by nanoscale clocks, whose performance can be significantly impacted by random fluctuations. In this work, we formulate the problem of optimal time estimation for Markovian stochastic processes, and present its general solution in the asymptotic (longtime) limit. Specifically, we obtain a tight upper bound on the precision of any time estimate constructed from sustained observations of a classical, Markovian jump process. This bound is controlled by the mean residual time, i.e., the expected wait before the first jump is observed. As a consequence, we obtain a universal bound on the signal-to-noise ratio of arbitrary currents and counting observables in the steady state. This bound is similar in spirit to the kinetic uncertainty relation but provably tighter, and we explicitly construct the counting observables that saturate it. Our results establish ultimate precision limits for an important class of observables in nonequilibrium systems and demonstrate that the mean residual time, not the dynamical activity, is the measure of freneticity that tightly constrains fluctuations far from equilibrium.

The Středa formula establishes a fundamental physical connection between the topological invariants characterizing the bulk of topological matter and the presence of gapless edge modes. In this work, we extend the Středa formula to periodically driven systems, providing a rigorous framework to elucidate the unconventional bulk-boundary correspondence of Floquet systems while offering a physically grounded link between Floquet winding numbers and tractable response functions. Using the Sambe representation of periodically driven systems, we analyze the response of the unbounded Floquet density of states to a magnetic perturbation. This Floquet-Středa response is regularized through Cesàro summation, yielding a well-defined, quantized result within spectral gaps. The response features two physically distinct contributions: a quantized charge flow between edge and bulk and an anomalous energy flow between the system and the drive, offering new insight into the nature of anomalous edge states. This fundamental result rigorously connects Floquet winding numbers to the orbital magnetization density of Floquet states and holds broadly, from clean to disordered and inhomogeneous systems. This is further supported by providing a real-space formulation of the Floquet-Středa response, which introduces a local topological marker suited for periodically driven settings. In translationally invariant systems, the framework yields a remarkably simple expression for Floquet winding numbers involving geometric properties of Floquet-Bloch bands. A concrete experimental protocol is proposed to extract the Floquet-Středa response via particle-density measurements in systems coupled to engineered baths. Finally, by expressing the topological invariants through the magnetic response of the Floquet density of states, this approach opens a promising route toward the topological characterization of interacting driven phases.

Hybrid multiterminal Josephson junctions (JJs) are expected to harbor a novel class of Andreev bound states (ABSs), including topologically nontrivial states in four-terminal devices. In these systems, topological phases emerge when ABSs depend on at least three superconducting phase differences, resulting in a three-dimensional (3D) energy spectrum characterized by Weyl nodes at zero energy. Here, we realize a four-terminal JJ in a hybrid $\mathrm{Al}/\mathrm{InAs}$ heterostructure, where ABSs form a synthetic 3D band structure. We probe the energy spectrum using tunneling spectroscopy and identify spectral features associated with the formation of a tri-Andreev molecule, a bound state whose energy depends on three superconducting phases and, therefore, is able to host topological ABSs. The experimental observations are well described by a numerical model. The calculations predict the appearance of four Weyl nodes at zero energy within a gap smaller than the experimental resolution. These topological states are theoretically predicted to remain stable within an extended region of the parameter space, well accessible by our device. These findings establish an experimental foundation to study high-dimensional synthetic band structures in multiterminal JJs and to realize topological Andreev bands.

Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard techniques, both in the continuum and in the lattice frameworks. However, classical methods have limitations, particularly when attempting to extrapolate the continuum limit from the study of lattice gauge theories. Complementing classical computations or combining them with quantum computational methods, to improve the predictions toward the continuum limit with current quantum resources, is a formidable open challenge. In this paper, we propose a resource-efficient method to compute the running of the coupling in non-Abelian gauge theories beyond one spatial dimension. We first represent the Hamiltonian on periodic lattices in terms of loop variables and conjugate loop electric fields, exploiting the Gauss law to retain the gauge-independent ones. Then, we identify a local basis for small and large loops variationally to minimize the truncation error while computing the running of the coupling on small tori. Our method enables computations at arbitrary values of the bare coupling and lattice spacing with current quantum computers, simulators, and tensor-network calculations, in regimes otherwise inaccessible.

“Strange” metals that do not follow the predictions of Fermi liquid theory are prevalent in materials that feature superconductivity arising from electron interactions. In recent years, it has been hypothesized that spatial randomness in electron interactions must play a crucial role in strange metals for their hallmark linear-in-temperature ($T$) resistivity to survive down to low temperatures where phonon and umklapp processes are ineffective, as is observed in experiments. However, a clear picture of how this happens has not yet been provided in a realistic model free from artificial constructions, such as large-$N$ limits and replica tricks. We study a realistic model of two-dimensional metals with spatially random antiferromagnetic interactions in a nonperturbative regime, using numerically exact high-performance, large-scale hybrid Monte Carlo simulation and exact averages over the quenched spatial randomness. Our simulations reproduce strange metals’ key experimental signature of linear-in-$T$ resistivity with a universal “Planckian” transport scattering rate ${\mathrm{\Gamma }}_{\mathrm{tr}}\sim k_{B}T/\hslash$ that is independent of coupling constants. We further find that strange metallicity in these systems is not associated with a quantum critical point and, instead, arises from a phase of matter with gapless antiferromagnetic fluctuations that lacks long-range correlations and spans an extended region of parameter space: A feature that is also observed in several experiments. These gapless antiferromagnetic fluctuations take the form of spatially localized overdamped modes, whose presence could possibly be detected using recently developed nanoscale magnetometry methods. Our work paves the way for an eventual microscopic understanding of the role of spatial disorder in determining important properties of correlated-electron materials.

Recent progress in tabletop experiments offers the opportunity to show, for the first time, that gravity is not compatible with a classical description. In all current experimental proposals, such as the generation of gravitationally induced entanglement between two quantum sources of gravity, gravitational effects can be explained solely with the Newton potential, namely, in a regime that is consistent with the weak-field limit of general relativity and does not probe the field nature of gravity. Hence, the Newtonian origin of the effects is a limitation to the conclusions on the nature of gravity that can be drawn from these experiments. Here, we identify two effects that overcome this limitation: They cannot be reproduced using the Newton potential, and they are independent of graviton emission. First, we show that the interaction between two generic quantum sources of gravity, e.g., in wide Gaussian states, cannot be reproduced with the Newton potential nor with a known classical theory of gravity. Second, we show that the quantum commutator between the gravitational field and its canonically conjugate momentum appears as an additional term in the relative phase of a generic quantum source interacting with a test particle. Observing these two effects would give further quantitative information and stronger evidence, compared to experiments only involving the Newton potential, to show that gravity is nonclassical. More broadly, identifying stronger quantum aspects of gravity than those reproducible with the Newton potential is crucial to prove the nonclassicality of gravity and to plan a new generation of experiments testing quantum aspects of gravity in a broader sense than what has been proposed so far.

We report on a single-shot longitudinal phase-space reconstruction diagnostic for electron beams in a laser wakefield accelerator via the experimental observation of distinct periodic modulations in the angularly resolved spectra. Such modulated angular spectra arise as a result of the direct interaction between the ultrarelativistic electron beam and the laser driver in the presence of the wakefield. A constrained theoretical model for the coupled oscillator, assisted by a genetic algorithm, can recreate the experimental electron spectra and, thus, fully reconstructs the longitudinal phase-space distribution of the electron beam with a temporal resolution of approximately 1.3 fs. In particular, it reveals the slice energy spread of the electron beam, which is important to measure for applications such as x-ray free electron lasers. In our experiment, the root-mean-square slice energy spread retrieved is bounded at 9.9 MeV, corresponding to a 0.9%–3.0% relative spread, despite the overall GeV energy beam having approximately 100% relative energy spread.

The mechanical properties of biological materials are spatially heterogeneous. Typical tissues are made up of a spanning fibrous extracellular matrix in which various inclusions, such as living cells, are embedded. While the influence of embedded inclusions on the stiffness of common elastic materials such as rubber has been studied for decades and can be understood in terms of the volume fraction and shape of inclusions, the same is not true for disordered filamentous and fibrous networks. Recent work has shown that, in isolation, such networks exhibit unusual viscoelastic behavior indicative of an underlying mechanical phase transition controlled by network connectivity and strain. How this behavior is modified when inclusions are present is unclear. Here, we present a theoretical and computational study of the influence of rigid inclusions on the mechanics of disordered elastic networks near the connectivity-controlled central-force rigidity transition. Combining scaling theory and coarse-grained simulations, we predict and confirm an anomalously strong dependence of the composite stiffness on inclusion volume fraction, beyond that seen in ordinary composites. This stiffening exceeds the well-established volume-fraction-dependent stiffening expected in conventional composites, e.g., as an elastic analog of the classic volume-fraction-dependent increase in the viscosity of liquids first identified by Einstein. We show that this enhancement is a consequence of the interplay between interparticle spacing and an emergent correlation length, leading to an effective finite-size scaling imposed by the presence of inclusions. We outline the expected scaling of the linear shear modulus and strain fluctuations with the inclusion volume fraction and network connectivity, confirm these predictions in simulations, and discuss potential experimental tests and implications for our predictions in real systems.

The classification of topological phases of matter is a fundamental challenge in quantum many-body physics, with applications to quantum technology. Recently, this classification has been extended to the setting of adaptive finite-depth local unitary (AFDLU) circuits, which allow global classical communication. In this setting, the trivial phase is the collection of all topological states that can be prepared via AFDLU. Here, we propose a complete classification of the trivial phase by showing how to prepare all solvable anyon theories that admit a gapped boundary via AFDLU, extending recent results on solvable groups. Our construction includes non-Abelian anyons with irrational quantum dimensions, such as Ising anyons, and more general acyclic anyons. Specifically, we introduce a sequential gauging procedure, with an AFDLU implementation, to produce a string-net ground state in any topological phase described by a solvable anyon theory with gapped boundary. In addition, we introduce a sequential ungauging and regauging procedure, with an AFDLU implementation, to apply string operators of arbitrary length for anyons and symmetry twist defects in solvable anyon theories. We apply our procedure to the quantum double of the group $S_3$ and to several examples that are beyond solvable groups, including the doubled Ising theory, the ${\mathbb{Z}}_3$ Tambara-Yamagami string net, and doubled $\mathrm{SU}(2{)}_4$ anyons.

Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent experimental and theoretical studies suggest that spontaneous translation symmetry breaking in some two-dimensional materials with nontrivial quantum geometry (e.g., rhombohedral pentalayer graphene) leads to a topologically nontrivial electron crystal state called the anomalous Hall crystal and characterized by a vanishing linear-response dc longitudinal conductivity and a nonvanishing Hall conductivity. In this work we present a theoretical investigation of the sliding dynamics of this new type of electron crystal, taking into account the system’s nontrivial quantum geometry. We find that when accelerated by an external electric field, the crystal acquires a transverse anomalous velocity that stems from not only the Berry curvature of the parent band but also the Galilean noninvariance of the crystal state (i.e., crystal states with different momenta are not related by simple momentum boosts). We further show that acceleration of the crystal modifies its internal current from the static crystal value that is determined by the Chern number of the crystal state. The net Hall conductance including contributions from center-of-mass motion and internal current is in general not quantized. As an experimentally relevant example, we present numerical results in rhombohedral pentalayer graphene and discuss possible experimental implications.

Nonequilibrium states of quantum materials can exhibit exotic properties and enable unprecedented functionality and applications. These transient states are inherently inhomogeneous, characterized by the formation of topologically protected structures, requiring nanometer spatial resolution on femtosecond timescales to resolve their evolution. Using ultrafast total x-ray scattering at a free electron laser and a sophisticated scaling analysis, we gain unique access to the dynamics on the relevant mesoscopic length scales. Our results provide direct evidence that ultrafast excitation of ${\mathrm{LaTe}}_3$ leads to formation of topological vortex strings of the charge density wave. These dislocations of the charge density wave exhibit anomalous, subdiffusive dynamics, slowing the equilibration process, providing rare insight into the nonequilibrium mesoscopic response in a quantum material. Our findings establish a general framework to investigate properties of topological defects, which are expected to be ubiquitous in nonequilibrium phase transitions and may arrest equilibration and enhance competing orders.

Magnetoelectric effects and their coupling to light helicity are important for both fundamental science and applications in sensing, communication, and data storage. Traditional approaches require complex device architectures, involving separate spin-injection, ferromagnetic, and optically active layers. Recently, the emergence of 2D semiconductor moiré superlattices with flat Chern bands and strong light-matter interactions has established a simple yet powerful platform for exploring the coupling between photon, electron, and spin degrees of freedom. Here, we report efficient current control of spontaneous ferromagnetism and associated helicity of light emission in moiré ${\mathrm{MoTe}}_2$ bilayer—a system which hosts a rich variety of topological phases, including newly discovered zero-field fractional Chern insulators. We show that the current control is effective over a wide range of doping of the first moiré Chern band, implying the uniformity of the Berry curvature distribution over the flat band. By setting the system into the anomalous Hall metal phase, a current as small as 10 nA is sufficient to switch the magnetic order, a substantial improvement over both conventional spin-torque architectures and other moiré systems. The realized current control of ferromagnetism leads to continuous tuning of trion photoluminescence helicity from left to right circular via spin-valley Hall torque at zero magnetic field. Our results pave the way for topological optospintronics based on semiconductors with synthetic flat Chern bands.