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 ${\mathrm{CO}}_2$ 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.

Recently proposed analog solvers based on dynamical systems, such as Ising machines, are promising platforms for large-scale combinatorial optimization. Yet, given the heuristic nature of the field, there is very limited insight on optimality guarantees of the solvers, as well as how parameter schedules shape dynamics and outcomes. Here, we develop a dynamical mean-field framework to analyze Ising-machine dynamics for finding the ground-state energy of the Sherrington-Kirkpatrick (SK) model of spin glasses and identify mechanisms that enable rapid convergence to provably near-optimal energies. For a fixed target energy density $E_c$, we show that solutions are typically reached within $O\left(1\right)$ matrix vector multiplications, indicating constant time complexity. We further delineate theoretical limitations arising from different parameter-scheduling trajectories and demonstrate a pronounced benefit of temperature-only annealing for the coherent Ising machine. Building on these insights, we propose a general framework for designing optimized parameter schedules, thereby improving the practical effectiveness of Ising machines for complex optimization tasks. The superior performance of the dynamical solvers is illustrated by the attainment of the ground-state energy of the SK model.

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 $\sim 22\%$ reduction in force and an $\sim 40$ reduction in energy prediction error relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

Active matter generates order or patterns through nonequilibrium dynamics. An open research challenge is to determine how efficiently a nonequilibrium self-organizing system can convert consumed energy into macroscopic order. We study an information-theoretic quantity that directly addresses this challenge by estimating the entropy reduction induced by a small control-parameter perturbation, relative to the generalized work required for the perturbation. This quantity has previously been considered mainly in an equilibrium or near-equilibrium context, and here we extend this framework and apply it to two nonequilibrium self-organizing systems: persistent and active Ising models. We observe that the thermodynamic efficiency of nonequilibrium systems maximizes at phase transitions, as in equilibrium systems. Furthermore, we compare thermodynamic efficiency and inferential efficiency across control parameters. While these two quantities are equal in equilibrium as a consequence of the fluctuation-dissipation theorem, we report that they diverge out of equilibrium, and the gap serves as a phenomenological signature of broken detailed balance.

There is widespread interest in many-body quantum systems that exhibit limit-cycle or time-crystalline behavior. An ideal quantum limit cycle would be realized using fully coherent driving (to minimize noise) and also have a continuous internal symmetry (to ensure generation of monochromatic radiation). While these two requirements may seem incompatible, we introduce in this work a large class of multimode bosonic limit-cycle models based on coherent parametric driving, which possess an $\text{O}\left(N\right)$ continuous symmetry. Surprisingly, the full quantum dissipative steady state of these models can be found exactly. They exhibit rich physics, including steady-state entanglement, reduced phase diffusion, and the possibility of realizing quantum limit tori. The basic mechanism we identify provides a unified way to understand how coherent parametric driving can yield symmetry-enriched limit cycles, and also helps us understand related models where the relevant symmetries are weakly broken. The models we study are compatible with a range of different experimental platforms, including quantum optical setups and superconducting quantum circuits.

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 ${\mathrm{CsBi}}_2$, 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.

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.

We reinterpret publicly available $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ 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 $|{\left(F_V\right)}_{\mathrm{sd}}\left({\mu }_K\right)|>1.6\times {10}^{12}\mathrm{GeV}$. 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, $f_a>4.9\times {10}^4\mathrm{GeV}$. These results provide the strongest accelerator-based constraints on axion-induced $d\leftrightarrow s$ transitions and establish a robust lower bound on $f_a$, complementary to astrophysical limits.

Entangling gates between neighboring physical qubits are essential for quantum error correction. Implementing them in an all-microwave manner simplifies signal routing and control apparatus of superconducting quantum processors. We propose and experimentally demonstrate an all-microwave controlled-Z (CZ) gate that achieves high fidelity while suppressing residual ZZ interactions. Our approach utilizes a fixed-frequency transmon coupler and multipath coupling, thereby sufficiently reducing the net transverse interaction between data transmons to suppress residual ZZ interactions. The controlled phase arises from the dispersive frequency shift of the $|gf\rangle –|eg\rangle$ transition between the coupler and one of the data transmons conditioned on the state of the other data transmon. Driving the transitions at the midpoint of two dispersively shifted resonance frequencies induces state-dependent geometric phases to achieve the CZ gate. Crucially, with this scheme, we can maintain a small net transverse interaction between two data transmons while increasing the coupling between the data and coupler transmons to accelerate the CZ-gate speed. Additionally, we measure the coupler state after the gate to detect a subset of decoherence-induced failures that occur during the gate operation. These events constitute erasure errors with known locations, enabling erasure-aware quantum error-correcting codes to improve future logical qubit performance.

We present a quantum dynamical study of pulsed few-photon scattering from a single artificial atom, consisting of a two-level system (TLS) or qubit, in a waveguide-quantum electrodynamics system, directly comparing and contrasting two different quantum theoretical simulation methods: (1) an input-output scattering approach that uses frequency-dependent scattering matrices, and (2) a matrix product states (MPS) approach, which uses quantum noise operators in discretized time bins and a tensor network technique to directly solve the time-dependent observables for the entire quantum waveguide-qubit system. Beginning with pulsed quantum-field excitation, using one-photon and two-photon Fock-state pulses, we first show how to compute time-dependent observables with a scattering matrix approach, in terms of frequency integrals that encode the pulse spectrum, including how to extract population dynamics of the excited quantum emitter, as well as the linear and nonlinear contributions. We present solutions for both symmetric and chiral TLS coupling. We then show how to compute the qubit and field observables in a more direct way using MPS, and obtain the characteristic birdlike shape for the two-photon correlation function at two times, which has been observed in recent experiments. We compare and contrast both of these methods, for one-photon and two-photon excitation pulses, and show excellent agreement. We also present a study of the linear and nonlinear contributions, which can easily be calculated using scattering theory, and which show the important role of pulse duration. Finally, we demonstrate the clear advantages of MPS by easily going to higher $N$-photon excitations, and show selected example population dynamics of up to eight-photon Fock-state pulses, manifesting in nonlinear population oscillations during the pulse interaction, similar to classical Rabi oscillations, but with quantum input fields that have a vanishing electric field expectation value.

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 $\zeta$ 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.

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.

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 ${\mathbb{Z}}_{2q}$ 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.

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.

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 ${}^4\mathrm{He}$ 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 ${}^4\mathrm{He}$ not seen in classical fluids.

We introduce a chiral Schrödinger cat qubit, a bosonic quantum code generalizing Kerr cat qubits that exploits higher-order nonlinearities. Compared to standard Kerr cats, the chiral cat qubit allows additional correction of bit-flip errors within the Hilbert space of a single bosonic oscillator. This property results from optical bistability, i.e., the simultaneous presence of multiple long-lived states. Two of them define the code logical basis and two define an error manifold. Thanks to the chiral structure of the phase space of this system, the error manifold can be engineered to “capture” bit-flip events in the code space (a bit-flip trap), without affecting the quantum information stored in the system. Therefore, it is possible to perform detection and correction of errors. We demonstrate how this topological effect can be particularly efficient in the presence of large dephasing. We provide concrete examples of the performance of the code and show the possibility of applying quantum operations rapidly and efficiently. Beyond the interest in this single technological application, our work demonstrates how the topology of phase space can enhance the performance of bosonic codes.

Quantum query complexity studies the number of queries needed to learn some property of a black box. A closely related question is how well an algorithm can succeed with this learning task using only a fixed number of queries. In this work, we propose measuring an algorithm's performance using the mutual information between the output and the actual value. The task of optimizing this mutual information using a single query is similar to a basic task of quantum communication, where one attempts to maximize the mutual information of the sender and receiver. We make this analogy precise by splitting the algorithm between two agents, obtaining a communication protocol. The oracle's target property plays the role of a message that Alice encodes into a quantum state, which is subsequently sent over to Bob. The first part of the algorithm performs this encoding, and the second part measures the state and aims to deduce the message from the outcome. Moreover, we formally consider the oracle as a separate subsystem, whose state records the unknown oracle identity. Within this construction, Bob's optimal measurement basis minimizes the quantum correlations between the two subsystems. We also find a lower bound on the mutual information, which is related to quantum coherence. These results extend to multiple-query nonadaptive algorithms. As a result, we describe the optimal nonadaptive algorithm that uses at most a fixed number of queries, for any oracle classification problem. Crucially, this mutual-information perspective was shown elsewhere [A. Levi et al., Quantum Sci. Technol. 11, 015029 (2026)] to have practical utility for algorithmic design, providing the theoretical foundation to optimize iterative subroutines in hybrid quantum-classical schemes. Within the present work, we apply this framework to analyze the stage-by-stage information flow and track partial progress in several standard quantum algorithms, including the Deutsch-Jozsa, Bernstein-Vazirani, and Shor-Kitaev algorithms.

We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.

Optical clocks have achieved remarkable estimated fractional frequency uncertainties reaching the ${10}^{-18}$ level and below, enabling applications in fundamental physics, general relativity, and geodesy. However, the challenge of verifying the international consistency of optical clocks remains critical as efforts intensify toward redefining the SI second based on an optical transition or transitions. We report on a two-month international clock comparison campaign involving seven optical clocks in four national metrology institutes (INRIM, LNE-OP, NPL, and PTB) connected via the optical fiber network established in Europe. The campaign resulted in optical frequency ratios with uncertainties ranging from $7.7\times {10}^{-18}$ to $6.1\times {10}^{-17}$. Among the results, the ${}^{171}\mathrm{Yb}^{+}\left(\mathrm{E}3\right)$ clocks at NPL and PTB demonstrated agreement within an uncertainty of $7.7\times {10}^{-18}$, marking the first international verification of two independently developed optical clocks below one part in ${10}^{17}$. The operation of the ${}^{199}\mathrm{Hg}$ clock at LNE-OP (formerly LNE-SYRTE) resulted in frequency ratios with improved uncertainties with ${}^{171}\mathrm{Yb}^{+}\left(\mathrm{E}3\right), {}^{171}\mathrm{Yb}$, and ${}^{87}\mathrm{Sr}$ optical clocks. These results provide input for the redefinition of the second and underscore how fiber-linked clock networks can advance metrology and scientific applications.