Data assimilation (DA) optimally fuses observational data with mathematical models, serving as a core computational framework for forecasting complex dynamical systems like the weather. Because manipulating large-scale high-rank error covariances is classically intractable, conventional DA is forced into severe structural compromises such as artificial localization or static parametrizations that destroy genuine cross-variable correlations. Future fault-tolerant quantum computing (FTQC) could offer transformative advantages to overcome these classical computational limits. While quantum linear system solvers theoretically provide exponential speedups for matrix inversion, the practical mapping of large-scale, uncompromised DA onto quantum architectures remains largely unexplored. Our framework builds upon two emerging technologies: FTQC hardware and efficient block-encoded oracles of the error covariance and observation operators, which we envision being supplied by future artificial intelligence surrogate models. Under this premise, we identify a potential bottleneck in the quantum implementation. We show that a direct mapping of the DA equations leads to a quadratic increase in the subnormalization factor (α) associated with block encoding when typical nonlocal observations are utilized. To mitigate this algorithmic overhead, we propose a quantum-ready, combined state-observation space formulation. By reconfiguring the DA problem into an expanded saddle-point block-matrix system, our approach avoids the explicit multiplication of nonlocal observation operators. This maintains a linear scaling of α and confines the conditioning of the quantum solver to that of the observation error covariance, decoupled from the severely ill-conditioned prior. Numerical verification using the chaotic Lorenz-96 model demonstrates that our formulation achieves perfect fidelity with the uncompromised DA solution. Although reading out the full analysis state reduces the exponential speedup to a polynomial one, the framework retains a substantial advantage over the classical matrix inversion. This work bridges computational geosciences and quantum information science, providing the essential algorithmic foundation for large-scale DA to become a compelling application for FTQC.
One of the surprising, and potentially very useful, capabilities of analog quantum computers, such as D-Wave quantum annealers, is sampling from the Boltzmann, or Gibbs, distribution defined by a classical Hamiltonian. In this study, we thoroughly examine the ability of D-Wave quantum annealers to sample from the Boltzmann distribution defined by a canonical type of competing magnetic frustration J_{1}-J_{2} model, the one-dimensional ANNNI (axial next-nearest-neighbor Ising) model. Boltzmann sampling error rate is quantified for standard linear-ramp anneals ranging from 5 ns annealing times up to 2000 µs on two different D-Wave quantum annealing processors. Interestingly, we find some analog hardware parameters that result in a very high accuracy (down to a total variation distance of 0.0003) and low-temperature sampling (down to β=32.2) in a frustrated region of the ANNNI model magnetic phase diagram. This bolsters the viability of current analog quantum computers for thermodynamic sampling applications of highly frustrated magnetic spin systems.
Resolving the ultrafast decay of metastable electronic states into channels associated with spin-orbit-split ionization thresholds is a long-standing goal of attosecond photoelectron spectroscopy. Here, we use a variant of the rainbow reconstruction of attosecond beating by interference of two-photon transitions technique to study, experimentally and theoretically, the ultrafast dynamics, resolved in photoelectron energy and emission angle, of the autoionizing states comprised in the narrow 177 meV energy gap between the 3p^{−1} ^{2}P_{3/2}^{o} and ^{2}P_{1/2}^{o} thresholds in argon. The scheme employs three pulses: an XUV attosecond pulse train (pump), generated as odd harmonics of a fundamental IR frequency ω; a weak replica of the IR field (driver) that copropagates phase-locked with the pump; and a second IR pulse (probe) with controllable delay τ with respect to the pump. Two harmonics excite bound states below the ^{2}P_{3/2}^{o} threshold and the continuum above the ^{2}P_{1/2}^{o} threshold, and their overlapping sideband populates even-parity resonant states between the two thresholds, giving rise to resonant signals beating at both ω and 2ω. From the photoemission cross section and the β_{2} and β_{4} asymmetry parameters, we resolve both the nf and the np resonant series. In both theory and experiment, the relative weight of the ω and 2ω beatings changes significantly across the interthreshold gap, an evolution that we trace back to higher-order probe-photon processes. The resonant photoelectron emission is found to be strongly localized in small spots within the (β_{2},β_{4}) region admissible for two-photon transitions.
The Lieb-Robinson correlation function can be used to characterize the propagation of quantum information in Ising chains. Considerable work has been done to establish bounds on this correlation function in various circumstances. To actually calculate the value of the correlation function directly typically requires a state space that grows exponentially with system size, and so is intractable for all but relatively small systems. We employ a recently developed method that enables direct calculation of the Lieb-Robinson correlation function and that scales linearly with system size. This enables the computation for systems with more than a thousand qubits, revealing the propagation of quantum information down the chain. We extend this technique to the problem of Ising chains with randomly disordered coupling strengths. Increasing disorder causes localization of the quantum correlations and halts propagation of quantum information down the chain. We see light-cone isocontours therefore becoming vertical. The decay of correlations down the chain is characterized by a correlation length that in the paramagnetic phase increases quadratically with mean coupling strength and inverse quadratically with disorder level. The correlation length peaks at the phase transition. We map our general expression for the correlation function in the Ising system onto the probability density in the single-particle tight-binding Su-Schrieffer-Heeger model for a specific initial condition.
Despite extensive experimental efforts over the past two decades, topological superconductivity and Majorana fermions have remained elusive. By shifting focus from superconductors—whose topological nature is often debated—to the well-established p-wave superfluid ^{3}He, we propose an experimental approach designed to identify quantum Hall nature of the chiral superfluid ^{3}He-A phase. The method exploits the interaction between surface waves and the induced current transverse to varying density of the superfluid. It allows one to quantitatively measure this Hall current and thus to directly evaluate whether the Hall current is quantized or not. As the quantum Hall effect is a hallmark of topological condensed matter, such an experiment would offer direct evidence of nontrivial topology of superfluid ^{3}He. With the advent of microscopic superfluid resonators coupled to optical cavities, this proposal is both realistic and promising, potentially opening the door to future experiments ranging from topological acoustics to fault-tolerant quantum computing.
Quantum networks promise scalable distributed quantum information processing. Realizing this potential depends critically on the efficient use of nonclassical resources. Sequential sharing of quantum nonlocality provides a resource-efficient route for recycling entanglement across multiple observers. In network settings, however, such recycling is typically constrained by a trade-off between the number of active branches and the achievable sharing depth. Here, we investigate this problem in star networks using probabilistic projective measurements. We establish an explicit entanglement threshold above which nonlocality can be shared across all branches up to any target depth, and below which we determine the optimal trade-off between the number of active branches and the achievable number of sequential rounds. We further analyze the protocol’s robustness to noise and its experimental observability, clarifying its practical feasibility. These results establish quantitative design principles and entanglement requirements for scalable nonlocality recycling in quantum networks.
Biological cells and synthetic analogues use liquid-liquid phase separation to dynamically compartmentalize their environment for various applications. In many cases, multiple droplets need to coexist, and their size needs to be controlled, which is challenging because large droplets tend to grow at the expense of smaller ones. Chemical reactions can, in principle, control droplet sizes, but there are no clear guidelines on how to robustly achieve size control. To provide guidelines, we consider a binary fluid model driven out of equilibrium by chemical reactions. We reveal two different classes of size-controlled droplets, depending on the ratio of droplet radius to the reaction-diffusion length. Moreover, we determine parameter regimes in which droplets become small. Taken together, our theory allows us to separately predict the chemical reactions necessary for maintaining droplets of a given class or size.
The divergence of the electron density of states (DOS) plays an important role in enhancing many-body interactions and inducing various quantum phases in low-dimensional systems. However, such unique electronic structures remain experimentally elusive in three-dimensional (3D) systems, particularly those with strong spin-orbit coupling (SOC). Using angle-resolved photoemission spectroscopy and first-principles calculations for a Laves-phase superconductor CsBi_{2}, which features a Bi-pyrochlore 3D network with strong SOC, we identify two characteristic electronic structures with a large DOS. One is a quasiflat band within a topologically nontrivial band sector with p-orbital character, locally formed around the U-K line, which enhances DOS near the Fermi level. The other involves type-I and type-II saddle points connected by a quasiflat band, which cooperatively produce an enhancement in the DOS. Our findings lay a foundation for exploring exotic phenomena driven by the interplay of multiple singularities with a large DOS, nontrivial topology, and strong SOC in 3D pyrochlores.
Point defects play a central role in driving the properties of materials. First-principles methods are widely used to compute defect energetics and structures, including at scale for high-throughput defect databases. However, these methods are computationally expensive, making machine learning force fields (MLFFs) an attractive alternative for accelerating structural relaxations. Most existing MLFFs are based on graph neural networks (GNNs), which can suffer from oversmoothing, oversquashing, and poor representation of long-range interactions. Both of these issues are especially of concern when modeling point defects. To address these challenges, we introduce the Accelerated Deep Atomic Potential Transformer (ADAPT), an MLFF that replaces graph representations with a direct coordinates-in-space formulation and explicitly considers all pairwise atomic interactions. Atoms are treated as “tokens,” with a transformer encoder modeling their interactions. Applied to a dataset of silicon point defects, ADAPT achieves an ∼22% reduction in force and an ∼40 reduction in energy prediction error relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.
Disorder in photonic lattices creates localized states inside the photonic band gap. The energy distribution of these states is often described as a Lifshitz tail, even though it is inconsistent with Lifshitz statistics near the band edge. Here, we show that in photonic-crystal waveguides with intentionally engineered anisotropic disorder, the band-edge tail accessible experimentally follows an Urbach law, with cumulative statistics F(Δ)=exp[−(Δ/α)^{β}], where Δ is the spectral detuning from the band edge, and an exponent β≈1 independent of disorder strength and orientation. In contrast to Lifshitz behavior, the density of states is maximal at the band edge and decays into the gap. Crucially, we find that the Urbach energy α is anisotropic, with a pronounced directional splitting and qualitatively different scaling for disorder parallel and perpendicular to the waveguide axis. These conclusions are supported by quantitative agreement between optical measurements of GaAs photonic-crystal waveguides and full-vector simulations. The anisotropic Urbach energy emerges as a sensitive probe of the coupling between structural disorder and the guided Bloch mode, and a practical metric to characterize structural disorder in photonic devices.
This article is part of a Physical Review Collection on the Physics in a Changing Climate. The Atlantic Meridional Overturning Circulation (AMOC) has been identified as a tipping element in the Earth system. Under the current climate change scenarios, it is urgent to develop robust methods for determining the probability of future AMOC transitions. Recent studies using an Earth system model of intermediate complexity (EMIC) have revealed the importance of an AMOC edge state, located on the boundary of the attraction basin of the collapsed state, in AMOC transitions. Here, we provide a characterization of this edge state through climate networks, using instantaneous temporal correlations between geographical locations to define the network links. We apply the climate network analysis to a set of EMIC simulations with CO_{2} forcing according to an intermediate climate change scenario (SSP2-4.5), which exhibit qualitatively different AMOC responses as a result of interaction with the edge state. We show that network measures, specifically the normalized degree centrality, reveal the presence of teleconnections across the equator as the AMOC approaches the edge state. A similar result is obtained for an Earth system model (ESM) simulating AMOC collapse or recovery, suggesting that climate networks could be used to detect an AMOC instability in ESMs and observations.
We reinterpret publicly available K^{+}→π^{+}νν[over ¯] data collected by NA62 from 2016 to 2024 to constrain the fundamental vectorial coupling of the QCD axion to down and strange quarks. Using a fully reproducible likelihood analysis and a complete renormalization-group evolution of the axion couplings from the Peccei-Quinn (PQ) scale to the kaon scale, we translate the experimental limit into bounds on both the low-energy flavor-violating coupling and the fundamental UV parameters. In the generic regime where strong contributions dominate the decay amplitude, we obtain |(F_{V})_{sd}(μ_{K})|>1.6×10^{12}GeV. The coexistence of parametrically suppressed weak contributions implies a second, conceptually distinct constraint: The fact that weak-amplitude dominance arises from highly tuned UV coupling configurations translates into a conservative general lower limit on the PQ scale, f_{a}>4.9×10^{4}GeV. These results provide the strongest accelerator-based constraints on axion-induced d↔s transitions and establish a robust lower bound on f_{a}, complementary to astrophysical limits.
Morphogenesis involves complex shape changes of biological tissues. Yet, tissue shape changes depend on tissue rheology, which in turn arises from the interplay of large numbers of cells. Here, we link cell- and tissue-scale mechanics by constructing mean-field rheological relations for the vertex model. In contrast to past work in the field, we study a vertex model with an explicit viscous friction. We also include two different cellular mechanisms creating active, anisotropic stresses. Our mean-field model accounts for cell shape and the nonlinear elastic and viscoplastic regimes. We validate our results by predicting the response to large-amplitude oscillatory shear. There are several vertex model variants, and comparing to results from the literature, we show that their rheology depends on a number of model details. Our approach should be sufficiently general to construct nonlinear mean-field constitutive relations for any cell-based tissue model.
Recently, there has been considerable interest in studying quantum sensing near the critical points of a system evolving unitarily and undergoing a phase transition. However, there are many quantum systems in which dissipation is very important. The quantum phase transition in such systems results as a result of competition between nonlinearity, drive, and dissipation. These quantum phase transitions belong to the class of nonequilibrium phase transitions. In this work, we present a detailed study of quantum sensing of the system parameters near the critical points of a dissipative phase transition. We illustrate the key results by considering a coherently driven nonlinear Kerr medium interacting with environment. The first-order quantum phase transition is characterized by the closing of the gap in eigenvalues of the underlying Liouvillian. The steady-state sensing away from the critical point has standard quantum limit scaling with respect to the effective system size, whereas Heisenberg scaling is found at the critical point. The latter is subject to a critical slowing down. We have also examined sensing of system parameters using the metastable states and find better sensing performance at intermediate timescales, i.e., when the system has not yet settled in steady state. Detailed results on the scaling behavior in different time domains are given.
Droplets are ubiquitous in nature and industry, yet their behavior is not yet fully understood, particularly for extreme conditions not typically encountered in viscous classical fluids. In this study, we investigated the oscillations of a superfluid ^{4}He pendant droplet formed beneath a cup by superfluid film flow. We controlled the mobility of the droplet's edge by attaching cylinders of varying diameter to the underside of the cup, so that the droplet was suspended from the bottom of the cylinder. For wide cylinders or in the absence of a cylinder, the lowest point of the droplet oscillated vertically, while the edge oscillated along the surface, with only a slight dependence of the oscillation period on the droplet volume, which contradicts the common assumption in classical fluids that larger droplets oscillate with a longer period. For narrow cylinders, the droplet oscillated vertically, while the edge remained fixed at the cylinder's edge, and the oscillation period increased monotonically with increasing droplet volume, displaying the expected behavior. These observations demonstrate that free motion of the droplet's edge contributes to anomalous volume-independent oscillation of pendant droplets. We propose that the marginal volume dependence arises from the stability of superfluid pendant droplets in a region between two instabilities. This behavior is significant only for fluids that completely wet the substrate and possess a mobile edge, a condition rarely observed in classical fluids but naturally occurring in superfluids. Hence, these findings reveal unique properties of droplets in superfluid ^{4}He not seen in classical fluids.
We provide, to our knowledge, first and unambiguous evidence of the existence of cluster crystals formed by a binary mixture of ultrasoft, cluster-forming particles. In an effort to reduce the high dimensionality of the parameter space of binary mixtures, we have restricted ourselves to a symmetric, equimolar system, introducing as the pivotal parameter the scaling factor ζ that characterizes the cross interaction. Our investigations are based on a commonly used model for ultrasoft particles and on classical density functional theory, which, within a mean-field framework, allows for mixed clusters composed of particles of both species. Minimizing the free energy functional predicts three competing cluster crystal structures, namely, a bcc and a tetragonal lattice that reduces under certain conditions to an fcc lattice. The emerging phase diagram is rather intricate, but is well understood in terms of an energetic competition between the two sublattices. Complementary molecular dynamics simulations confirm the stability of the predicted structures and allow to trace the particles in their migration processes through the crystal.
The quantum geometric tensor sets the local relation between variations of external parameters and distances between states in Hilbert space. Its real and imaginary parts are, respectively, the quantum Fisher information matrix, which determines the ultimate precision bound in parameter estimation, and the Berry curvature. We study the geometry of SU(1,1) Hamiltonian eigenstates and propose two dynamical methods for extracting the components of the SU(1,1) quantum geometric tensor. A time-separated quench method extracts both the real and imaginary parts of the quantum geometric tensor from transition probabilities following two sudden parameter changes separated by free evolution, while a weak resonant modulation method relates quasiparticle production to the same geometric tensor. These results provide an operational method for measuring the local geometry of single-mode squeezed states and, in particular, for extracting the quantum Fisher information matrix directly from experimental observables.
Crystallites form in supercooled liquids as particles rearrange into ordered structures, driven by thermal fluctuations or external stimuli. While the thermodynamics of heterogeneous crystallization under boundary constraints is well described by classical nucleation theory, the kinetics of symmetry formation—particularly in systems far from the transition point—remains poorly understood. In this study, we investigate the heterogeneous crystallization of a colloidal system across a wide range of effective supercooling degrees by varying the volume fraction. Using confocal microscopy, we capture the motion and local structures of particles in situ with high spatial and temporal resolution. Our results reveal a consistent crystallization pathway across different supercooling levels: Rotational symmetry forms prior to translational symmetry, with normal modes of local structures playing distinct roles in each stage of crystallization. Notably, the liquid-to-precursor transformation is robust even under deep supercooling, suggesting minimal influence of supercooling on rotational order development. In contrast, the precursor-to-solid transformation is significantly accelerated in denser systems, indicating that translational order is strongly governed by the degree of supercooling. These findings provide insights into the interplay between thermodynamics and kinetics in heterogeneous crystallization and offer guidance for controlling phase transitions across a broad range of disciplines.
We construct a model of a three-dimensional helical second-order topological superconductor formed by an array of weakly coupled Rashba nanowires. We identify the parameter regime in which there are energy gaps in both the bulk and surface energy spectra, while a pair of helical Z_{2q} parafermionic modes (with q being an odd integer) remains gapless along a closed path of one-dimensional hinges. The precise trajectory of these hinge modes is dictated by the hierarchy of interwire couplings and the boundary termination of the sample. In the noninteracting limit q=1, the system hosts gapless Majorana hinge modes.
Inorganic structural chemistry leads naturally to a theory for crystal structure prediction formalized by a generalized disjunctive programming, which is formulated using continuous and Boolean variables to involve the algebraic equations, disjunctions, and logic propositions. Since the feasibilities of continuous variables change drastically depending on Boolean variables and vice versa, iterative optimization of continuous and Boolean variables efficiently transforms a randomly generated initial structure into an optimal solution. Boolean variables are introduced to elucidate the “combinatorial backbone” of the original continuous optimization problem, which corresponds to the graphs describing crystal structures with clear chemical meanings. Since many subgraphs are discovered in numerous graphs generated through structural optimizations, on-the-fly learning of the feasibilities of them accelerates the discovery of the optimal solutions. This theory enables designing a wide variety of crystal structures with small computations based on only the atomic radii and feasible coordination numbers of each atom.
