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 ${}^3\mathrm{He}$, we propose an experimental approach designed to identify quantum Hall nature of the chiral superfluid ${}^3\mathrm{He}-A$ 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 ${}^3\mathrm{He}$. 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.

Understanding the entanglement dynamics in quantum many-body systems under steady-state transport conditions is an actively pursued challenging topic. Hydrodynamic equations, akin to transport equations for charge or heat, would be of great interest but face severe challenges because of the inherent nonlocality of entanglement and the difficulty of identifying conservation laws. We show that progress is facilitated by using information as a key quantity related to—but distinct from—entanglement. Employing the recently developed “information lattice” framework, we formulate general continuity equations governing the flow of spatially and scale-resolved information currents in nonequilibrium open quantum systems. To illustrate our theory, we consider noninteracting fermion chains coupled to dissipative reservoirs, using Lindblad master equations. By relating the information lattice to a noise lattice constructed from particle-number fluctuations, we show that information is experimentally accessible via noise measurements. Similarly, local information currents can be obtained by measuring particle currents, on-site occupations, and covariances of particle numbers and/or particle currents. Using the fermionic negativity to quantify bipartite entanglement, we also study transport-induced entanglement and its relation to information currents. For a clean particle-hole symmetric chain, we find that information currents are shielded from entering the information lattice. Impurities or particle-hole asymmetry break this effect, causing information current flow and entanglement between end segments of the chain. Our work opens the door to systematic investigations of information transport and entanglement generation in driven open quantum systems far from equilibrium.

Remote state preparation (RSP) allows one party to remotely prepare a known quantum state on another party's qubit using entanglement. This can be used in quantum networks to perform applications such as blind quantum computing or long-distance quantum key distribution (QKD) with quantum repeaters. Devices to perform RSP, referred to as a client, ideally have low hardware requirements, such as only sending photonic qubits. A weak coherent pulse source offers a practical alternative to true single-photon sources and is already widely used in QKD. Here, we introduce two protocols to the previously known protocol for RSP with a weak-coherent-pulse-based device. The known technique uses a double-click (DC) protocol, where a photon from both the server and the client needs to reach an intermediate Bell state measurement. Here, we add to that a single-click (SC) RSP protocol, which requires only one photon to reach the Bell state measurement, allowing for better performance in certain regimes. In addition, we introduce a double-single-click (DSC) protocol, where the SC protocol is repeated twice, and a cnot gate is applied between the resulting qubits. DSC mitigates the need for phase stabilization in certain regimes, lowering technical complexity while still improving performance compared to DC in some regimes. We compare these protocols in terms of fidelity and rate, finding that SC consistently achieves higher rates than DC and, interestingly, does not suffer from an inherently lower fidelity than DC, as is the case for entanglement generation. Although SC provides stronger performance, DSC can still show performance improvements over DC, and it may have reduced technical complexity compared to SC. Finally, we show how these protocols can be used in long-distance QKD using quantum repeaters.

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 $F\left(\mathrm{\Delta }\right)=exp[-{(\mathrm{\Delta }/\alpha )}^{\beta }]$, where $\mathrm{\Delta }$ is the spectral detuning from the band edge, and an exponent $\beta \approx 1$ 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 $\alpha$ 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.

We study the triangular lattice optical Su-Schrieffer-Heeger (SSH) model using determinant quantum Monte Carlo. By varying the model's carrier concentration $\langle n\rangle$, electron-phonon coupling strength, and phonon energy $\mathrm{\Omega }$, we identify two doping regimes of interest. At one-quarter filling ($\langle n\rangle =0.5$), corresponding to the case of a circular noninteracting Fermi surface, we find evidence for a metal to insulating bond-order-wave (BOW) phase transition that breaks a local $C_6$ rotational symmetry. Conversely, at three-quarter filling ($\langle n\rangle =1.5$), corresponding to a hexagonal Fermi surface, we find evidence for transitions to a metallic BOW phase for small $\mathrm{\Omega }$ and an $s$-wave superconducting phase for sufficiently large $\mathrm{\Omega }$. This tendency toward pairing appears to be associated with the possibility of a sign change in the effective nearest-neighbor intersite hopping, which can occur for sufficiently large lattice displacements. We also find no evidence for enhanced magnetic correlations in the model, contrary to what has been reported for some square lattice SSH models.

We present a native realization of iSWAP and parametrized exchange gates for neutral-atom quantum processing units. Our approach leverages strong dipole-dipole interactions between two different dipole-coupled Rydberg states, employing optimal control techniques to design high-fidelity, time-efficient gate pulses. To minimize experimental complexity, we utilize global driving fields acting identically on all atoms and apply pulse smoothing techniques. While detrimental van der Waals interactions pose a significant challenge, we demonstrate that for both ${}^{133}\mathrm{Cs}$, as a representative alkali atom, and ${}^{88}\mathrm{Sr}$, an alkaline-earth species, high-fidelity pulses can nevertheless be obtained over a broad range of parameters. We identify candidate protocols with reduced susceptibility to noise and analyze their performance under realistic conditions, accounting for atomic motion, Rydberg decay, and experimentally motivated laser frequency and intensity noise. Crucially, we demonstrate that in both Alkali and alkaline-earth-based systems, we can obtain fast iSWAP gates with fidelities of $99.9\%$ under realistic experimental conditions. These results pave the way for expanding the neutral-atom gate set beyond conventional Rydberg-blockade-based entangling gates.

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.