We investigate the impact of an isotropic antiferromagnetic Heisenberg perturbation on the toric code, focusing on the resulting quantum phase transition and the nature of the phase that emerges beyond topological order. Using neural-network quantum states, we compute ground states over a wide range of Heisenberg couplings while fully respecting the exact symmetries of the model. In the weak-coupling regime, the numerical results are in excellent agreement with an effective low-energy description derived from a Schrieffer-Wolff (SW) transformation, providing analytic control over the perturbative breakdown of topological order. We show that the Heisenberg perturbation only renormalizes local operators at low orders, whereas mixing between topological sectors occurs only at a perturbative order proportional to the system size. At intermediate values of the Heisenberg interaction, the topological phase breaks down. We estimate the critical point through a combination of the fidelity susceptibility and the logarithmic susceptibility of noncontractible Wilson loops for various system sizes. Furthermore, we utilize the topological entanglement entropy to provide a comprehensive characterization of the phase transition. Beyond the transition, an antiferromagnetic $\pm X/\pm Z$ Néel phase emerges, characterized by a fourfold-degenerate symmetry-broken manifold, which is explicitly probed using staggered-magnetization-based diagnostics. Our results show how local two-spin interactions, which naturally arise in realistic implementations of the toric code, drive the breakdown of topological order. Moreover, we establish the SW approach as a systematic framework for analyzing such perturbations in combination with variational many-body methods.

Biomolecular condensates frequently form near surfaces, including lipid membranes. However, the effect of a surface on phase separation within a cell, a confined system, remains elusive. In this work, we study surface phase separation under the constraint of a finite number of molecules in a confined space and identify three wetting states: thin, intermediate, and thick. Notably, the intermediate state, which is unstable in a fixed-chemical-potential system, can be stabilized in confinement below a critical width. Intriguingly, in wider systems, the intermediate solution becomes unstable due to a negative relationship between the chemical potential and particle number, leading to partial-wetting or prewetting droplets. Importantly, as the particle volume fraction increases from a lower value starting from a homogeneous surface, droplets form when the average volume fraction reaches the threshold of the intermediate state, which can be much lower than the threshold of bulk spinodal decomposition. Our theory elucidates the kinetic pathways of droplet formation in a confined system, providing crucial insights into how biomolecular condensates near surfaces respond to cellular events, such as the synthesis of biomolecules.

Quantum machine learning is an emergent field that continues to draw significant interest for its potential to offer improvements over classical algorithms in certain areas. However, training quantum models remains a challenging task, largely because of the difficulty in establishing an effective inductive bias when solving high-dimensional problems. In this work, we propose a training framework that prioritizes informative data points over the entire training set. This approach draws inspiration from classical techniques such as curriculum learning and hard example mining to introduce an additional inductive bias through the training data itself. By selectively focusing on informative samples, we aim to steer the optimization process toward more favorable regions of the parameter space. This data-centric approach complements existing strategies such as warm-start initialization methods, providing an additional pathway to address performance challenges in quantum machine learning. We provide theoretical insights into the benefits of prioritizing informative data for quantum models, and we validate our methodology with numerical experiments on selected recognition tasks of quantum phases of matter. Our findings indicate that this strategy could be a valuable approach for improving the performance of quantum machine learning models.

Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution time. To address this challenge, we establish a fundamental scaling limit of critical quantum metrology with respect to the total evolution time. We find that the effective winding number of the system's phase-space trajectory determines the scaling bound of quantum Fisher information. Furthermore, we demonstrate that the exponential scaling of the quantum Fisher information can be obtained, and for this, it is necessary to increase the effective winding number by the total evolution time. Based on the topological nature of the effective winding number, we explicitly derive an optimal time-dependent control whose form is, surprisingly, a simple on-off scheme. We highlight that such an exponential scaling of quantum Fisher information remains valid even without reaching the critical point and in the presence of thermal dissipation, albeit with a decreased exponent.

A Bernoulli factory is a model for randomness manipulation that transforms an initial Bernoulli random variable into another Bernoulli variable by applying a predetermined function relating the output bias to the input one. In literature, quantum-to-quantum Bernoulli factory schemes have been proposed, which encode both the input and output variables using qubit amplitudes. This fundamental concept can serve as a subroutine for quantum algorithms that involve Bayesian inference and Monte-Carlo methods, or that require data encryption, like in blind quantum computation. In this work, we present a characterization of the complexity of the quantum-to-quantum Bernoulli factory by providing a lower bound on the required number of qubits needed to implement the protocol, an upper bound on the success probability, and the quantum circuit that saturates the bounds. We also formalize and analyze two different variants of the original problem that address the possibility of increasing the number of input biases or the number of functions implemented by the quantum-to-quantum Bernoulli factory. The obtained results can be used as a framework for randomness manipulation via such an approach.

Machine-learning surrogates are increasingly used to accelerate computational fluid dynamics (CFD), yet their robustness to small, structured input perturbations remains insufficiently characterized. Conventional adversarial training is largely impractical for artificial intelligence for CFD (AI4CFD), since perturbed inputs alter the underlying partial differential equation (PDE) solutions and require costly resimulation for valid labels. We propose a systematic post hoc robustness audit and apply it to the Fourier neural operator (FNO) and UNet on three canonical two-dimensional flows—laminar tube flow, transient dam break, and cylinder wake—using Gaussian, random, and fast gradient sign method (FGSM) perturbations together with normalized mean-squared error, attack gain, and signed-bias diagnostics. Adversarial vulnerability is found to arise from a coupling between flow physics and architectural inductive bias: The transient dam break exhibits heavy-tailed gains with rare amplification of order ${10}^2$, while steadier flows remain bounded. A spectral analysis with a proposed attack separability index shows that FNO behaves like a spectral solver with global mode coupling, whereas UNet acts as a dissipative low-pass scheme, with the distinction modulated by PDE type. A physical-realizability audit, including a divergence-free Helmholtz projection control, rules out continuity violation and distributional shift, indicating that the vulnerability is intrinsic to the learned operator rather than a generalization artifact. We therefore argue that robustness auditing should accompany accuracy reporting in AI4CFD, and provide a practical three-step audit protocol.

The one-way quantum computation utilizing bosonic modes of light offers unmatched scalability of light modes, and it has seen rapid experimental development recently. Scalability requires robust and low-error gates and measurements. Squeezing gate is one of the necessary Gaussian operations. We find the optimal squeezing gate in cluster-state architecture. Our approach newly uses amplitude transmission coefficients of unbalanced beam splitters and homodyne detection with subsequent unity-gain feedforward to squeeze the input state. The approach outperforms the current method based on optimally rotated homodyne detection but fixed balanced beam splitters. The performance of both cluster-state squeezers is evaluated for Gaussian and non-Gaussian input states. We use different metrics to benchmark the quality of squeezed output states. The result opens a road to low-noise squeezing gates in experimentally achievable cluster states.

Cilia and flagella are highly conserved biological motors that drive the motility of diverse eukaryotic cells. In the microscopic world, an organism's swimming kinematics are generally assumed to be a direct, instantaneous proxy for its underlying motor force output. However, as organisms scale in size—such as during the evolutionary transition to multicellularity—this fundamental assumption may break down. Using the multicellular alga Volvox as a model biophysical system, we perform direct, time-resolved force measurements during free-swimming collisions to deconvolve a swimmer's inertial impact force from its motor's propulsive force. We discover a $\sim 30\mathrm{Hz}$ propulsive pulse, which serves as the mechanical signature of collective ciliary action and hydrodynamic synchronization. Crucially, we demonstrate that while this high-frequency motor output drives a fluctuating velocity in the smaller V. carteri, it is mechanically filtered by the inertia of the larger V. ferrisii, resulting in a smooth swimming trajectory. Our work reveals that as organisms grow larger, their own mass acts as a mechanical low-pass filter. This fundamentally decouples high-frequency motor dynamics from whole-organism swimming kinematics, highlighting how physical constraints shape the mechanobiology of motility as organisms evolve toward complex multicellularity.

Locally noncentrosymmetric materials are attracting significant attention due to the unique phenomena associated with sublattice degrees of freedom. The recently discovered heavy-fermion superconductor ${\mathrm{CeRh}}_2{\mathrm{As}}_2$ has emerged as a compelling example of this class, garnering widespread interest for its remarkable temperature-magnetic-field phase diagram, which features a field-induced first-order superconductor-to-superconductor phase transition with nontrivial dependence on the field direction and high critical fields, as well as antiferromagnetic and potentially higher multipole orders. To investigate the complex interplay of the ordered phases in ${\mathrm{CeRh}}_2{\mathrm{As}}_2$, we develop a theoretical framework based on symmetry analysis applied to a Bogoliubov–de Gennes Hamiltonian and Landau methods. This approach allows us to propose probable symmetries of the superconducting states and elucidate their close relationship with magnetism. Among other results, we find that the near degeneracy of two pairing symmetries is naturally explained if and only if intralayer spin-orbit coupling is large compared to interlayer hopping. Intriguingly, we find that the first-order transition can be interpreted as a transition between coexistence phases of the same superconducting order parameters, albeit with distinct admixtures. This line may end in a critical end point below the superconducting critical temperature. Our approach accurately reproduces current experimental phase diagrams for varying temperature as well as out-of-plane and in-plane magnetic field, both if the transition to a magnetic phase occurs below the superconducting critical temperature and if it occurs above. Furthermore, we calculate the magnetic susceptibility and the specific heat and compare these quantities to recent experimental results.

Mounting evidence indicates that some of the gravitational wave signals observed by ground-based observatories might arise from eccentric compact object binaries, increasing the urgency for accurate waveform models for such systems. While for noneccentric binaries, surrogate models are efficient and accurate, the additional features due to eccentricity have posed a challenge. In this work, we present a method for decomposing eccentric numerical relativity waveforms, making them amenable to surrogate modeling techniques. We parametrize the inspiral in the radial-phase domain, factoring out eccentricity-induced dephasing and thus enhancing compressibility and accuracy. This is combined with a second surrogate for the merger ringdown in the time domain and a technique to take advantage of the approximate periodicity with radial oscillations during the inspiral. We apply this procedure to the (2, 2) mode for nonspinning black hole binaries and demonstrate that the resulting surrogate, NRSurE_q4NoSpin_22, is able to faithfully reproduce the underlying numerical relativity waveforms, with maximum mismatches of $6\times {10}^{-4}$ and median mismatches of $4\times {10}^{-5}$. This technique paves the way for high-accuracy parameter estimation with eccentric models, a key ingredient for astrophysical inference and tests of general relativity.

Muon spin rotation (${\mu }^{+}\mathrm{SR}$) was used to investigate the magnetic properties of cobalt-intercalated $2H-{\mathrm{NbSe}}_2$ (${\mathrm{Co}}_{1/4}{\mathrm{NbSe}}_2$). ${\mathrm{Co}}_{1/4}{\mathrm{NbSe}}_2$ is predicted to be an altermagnet, and while neutron diffraction has proposed its magnetic structure, the microscopic details of this remain unclear. Therefore, a local probe investigation of the magnetism in ${\mathrm{Co}}_{1/4}{\mathrm{NbSe}}_2$ is essential. Our results reveal a sharp second-order transition to a full-volume-fraction, homogeneous magnetic order below $T_{\mathrm{N}}=168\mathrm{K}$. The moments are aligned antiparallel along the $c$ axis, consistent with neutron diffraction and altermagnetism. ${\mu }^{+}\mathrm{SR}$ reveals that the state remains stable under a $c$-axis magnetic field up to $0.78\mathrm{T}$, with magnetization measurements suggesting that this robust regime extends to at least 5 T. Within the time sensitivity of ${\mu }^{+}\mathrm{SR}$, no precursor slow magnetic fluctuations were detected above $T_{\mathrm{N}}$, which is important for interpreting the band splitting in the paramagnetic state reported by photoemission studies.

Electron-phonon interactions play a central role in determining charge and heat transport in condensed matter systems, but in disordered and low-dimensional materials, this coupling can be strongly suppressed, leading to nontrivial transport phenomena. One striking manifestation is the appearance of bistable current-voltage ($I\text{−}V$) characteristics, where an imbalance between electrical heating and electron-phonon cooling yields multiple nonequilibrium steady states. In this work, we experimentally investigate this phenomenon in amorphous $a\text{−}{\mathrm{Y}}_x{\mathrm{Si}}_{1-x}$ thin films, where disorder can be tuned by thermal annealing. We identify the critical disorder at which bistability emerges and characterize the associated jumps in nonlinear $I\text{−}V$ curves. To interpret these results, we develop a microscopic derivation of the phenomenological hot-electron model and extend it by incorporating electric-field-assisted hopping and phonon-mediated intergrain transitions, allowing quantitative agreement with experimental data across different disorder regimes. Complementary numerical simulations confirm the robustness of our extended framework. Our combined experimental, analytical, and numerical results provide a comprehensive description of electron-phonon decoupling and its impact on transport in disordered systems, offering a platform for studying nonequilibrium phases.

The behavior of charged vesicle suspensions, commonly encountered in biological and industrial contexts, is largely governed by screened electrostatic repulsions. However, the addition of depletants such as polymers can induce attractive interactions and lead to gel formation. Here, we investigate the rheology and yielding behavior of such a vesicle gel, relevant to a class of consumer products. The combination of experiments and Brownian dynamics simulations enables us to establish connections between macroscopic rheology and microstructural features. Oscillatory tests reveal a predominantly elastic response at small deformations, followed by yielding upon increasing the strain amplitude. With increasing shear rate, the flow curves feature a yield stress regime, followed by shear thinning and, eventually, a Newtonian-like response (viscosity plateau). We find that, in both oscillatory and shear-rate-controlled tests, the yielding transition is accompanied by nonmonotonic trends in structural heterogeneity. Fitting the flow curves with the recently introduced three-component model reveals that structural heterogeneity peaks near the crossover from the yield stress plateau to shear thinning, while homogeneity is recovered in the Newtonian-like regime. Numerical creep tests exhibit rich phenomenology, including Andrade-like deformation, delayed yielding, and resolidification, whose persistence even above the dynamic yield stress highlights the ductile nature of gels with competing attractive and repulsive interactions. Overall, our study highlights distinctive rheological and structural features of gels with competing attractive and repulsive interactions, providing insight into how microscopic heterogeneity controls yielding and flow.

We propose a quantum algorithm for computing one-quasiparticle excitation energies in the thermodynamic limit by combining numerical linked-cluster expansions (NLCEs) and the variational quantum eigensolver (VQE). Our approach uses VQE to block diagonalize the cluster Hamiltonian through a single-unitary transformation. This unitary is then postprocessed using the projective cluster-additive transformation (PCAT) to ensure cluster additivity, a key requirement for NLCE convergence. We benchmark our method on the transverse-field Ising model (TFIM) in one and two dimensions, and with longitudinal field, computing one-quasiparticle dispersions in the high-field polarized phase. We compare two cost function classes, trace minimization and variance based, demonstrating their effectiveness with the Hamiltonian variational ansatz (HVA). For pure TFIM, $\lceil N/2\rceil$ layers of HVA suffice: $\mathrm{NLCE}+\mathrm{VQE}$ matches exact diagonalization. For TFIM with longitudinal field, where parity symmetry breaks and PCAT becomes essential, both $\lceil N/2\rceil$ and $N$ layers of HVA converge with increasing cluster size, with $N$ layers providing improved accuracy. Our results establish PCAT as a cluster-additive framework that extends variational quantum algorithms to excited-state calculations in the thermodynamic limit via NLCE. While demonstrated with VQE, the PCAT postprocessing approach, which requires only low-energy eigenspace information, applies to any quantum eigenstate preparation method.

We establish a quantitative relation between the altermagnetic spin splitting and different higher-order multipoles of the charge and magnetization density around the magnetic atoms. Magnetic multipoles such as octupoles or triakontadipoles have been suggested as potential ferroic order parameters for $d$- and $g$-wave altermagnetism, respectively, based mainly on qualitative symmetry arguments. We use first-principles-based electronic structure calculations to establish a clear quantitative relation between the strength of the altermagnetic spin splitting and the magnitude of certain local multipoles. We vary the magnitude of these multipoles either by applying an appropriate constraint on the charge density or by varying a corresponding structural distortion mode, using two simple perovskite materials, ${\mathrm{SrCrO}}_3$ and ${\mathrm{LaVO}}_3$, as model systems. Our analysis indicates that in general the altermagnetic spin splitting is not exclusively determined by the lowest-order nonzero magnetic multipole, but results from a superposition of contributions from different multipoles with comparable strength, suggesting the need for a multicomponent order parameter to describe altermagnetism. We also discuss different measures to quantify the overall spin splitting of a material, without relying on features that might be specific to only individual bands.