To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansätze. We perform variational energy minimization with respect to a quantum annealing Hamiltonian and utilize randomness by embedding the approaches in the metaheuristic iterated local search (ILS). The resulting quantum-inspired ILS algorithms are benchmarked on maximum cut problems of up to 50 000 variables. We show that they can outperform traditional (M)PS methods, classical ILS, the quantum approximate optimization algorithm, and other variational quantum-inspired solvers.

Long-distance entanglement generation at a high rate is a major quantum technological goal yet to be fully realized, with the promise of many interesting applications, such as secure quantum computing on remote servers and quantum cryptography. One possible implementation is using a variant of the scheme proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) [Duan et al., Nature (London) 414, 413 (2001)] by combining atomic-ensemble memories and linear optics with spontaneous parametric down-conversion (SPDC) sources. As we edge closer to the realization of such a technology, the complete details of the underlying components become crucial. In this paper, we consider the impact of the multimode emission from the SPDC source on quantum repeaters based on the DLCZ scheme. We consider two cases, driving the SPDC using short Gaussian pulses and driving the SPDC continuously. For pulsed driving, we find that the use of very narrow laser pulses to drive the SPDC source is crucial to obtain high-fidelity end-to-end entangled states, but this puts demands on the peak intensity. By introducing a maximally allowed laser intensity, we find optimal pulse widths for each swap depth. For continuous driving, we find the temporal acceptance window of clicks relative to the heralding time to be a crucial parameter, and we can similarly optimize the acceptance window for each swap depth. For both cases, we thus identify optimal parameters given experimental limitations and aims. We have thus provided helpful knowledge toward the realization of long-distance entanglement generation using the DLCZ scheme.

Localized growth in driven materials is often governed by intermittent failure, yet how a material's history biases failure sites remains poorly understood. Using pause-restart experiments on chemical precipitate membranes, we quantify the probability of age-dependent breaching. We show that the kinetics follow a stretched-exponential aging law with parameters that obey one-parameter scaling. As the system approaches a critical concentration, the stretching exponent $\beta$ tends to zero, signaling a crossover to scale-free, power-law behavior. A stochastic cellular automaton based on this aging rule reproduces the emergent filaments and their concentration-dependent thickening. Our findings identify aging-controlled failure with long-lived but decaying memory as a general route to pattern formation in far-from-equilibrium systems.

We analyze the metastability of Bose-Hubbard condensates for finite-size one-dimensional ring lattices and open chains, using a semiclassical tomographic perspective that emphasizes the relation of the many-body spectrum to the underlying classical phase-space structures. In order to address quantum ergodicity in far-from-equilibrium scenarios of experimental interest, we inspect both local aspects (via Bogoliubov analysis) and global aspects (mixed regular-chaotic dynamics). In particular, we highlight the roles of the two parameters that control metastability, clarify the essential differences between low- and high-dimensional chaos, and show how the dynamical instabilities diminish in the limit of the Gross-Pitaevskii equation. It is somewhat frustrating that with more degrees of freedom, the dynamically metastable islands become better distinct from the ergodic sea, while their borders become ill-defined topologically. This stands in opposition to the very structured phase space of two-degree-of-freedom systems, as reflected in the tomographic quantum spectrum.

Superlattice engineering, the introduction of periodic potentials to a material, can induce selective scattering events that modify the electrical properties of the material in predictable ways. Extending superlattice engineering to three-dimensional (3D) electronic materials can expand the tunability of their transport properties beyond traditional means such as doping. Here, we show that magnetotransport can be modified by superlattices in 3D materials based on the relative symmetry between the Fermi surface and nanostructured superlattice. We demonstrate commensuration oscillations in the ballistic transport regime of a nanostructured 3D material with the Weyl semimetal NbP. The oscillations encode information about the shared properties between the quasiparticles at the Fermi surface—including their momentum, charge, mass, and rotational symmetry—and the structure of the superlattice. These results point toward methods to engineer quantum transport in 3D electronic materials based on the mutual properties of the superlattice and Fermi surface.

The non-Hermitian skin effect (NHSE), characterized by the accumulation of a macroscopic number of bulk states at system boundaries, is a hallmark of non-Hermitian physics. However, in higher dimensions, achieving deterministic control over where skin modes accumulate remains a major challenge. Here, we propose a versatile route to program the skin-mode localization site in two-dimensional non-Hermitian lattices by combining disorder with a static electric field. While the electric field alone suppresses the NHSE in a clean system, the introduction of disorder induces transverse wave-packet transport perpendicular to the field. In nonreciprocal lattices, when the nonreciprocal hopping is misaligned with the electric field, the hopping component perpendicular to the field guides wave-packet propagation and produces boundary localization. By tuning the relative orientation between the electric field and the nonreciprocal hopping direction, the boundary localization position can be continuously and arbitrarily controlled. We further demonstrate distinct geometry-dependent manipulation of skin modes in reciprocal lattices, where controllable boundary localization emerges solely from the lattice geometry. Our results establish a robust and broadly applicable route to engineer boundary accumulation and directed transport along prescribed directions in two-dimensional non-Hermitian systems, enabling reconfigurable wave routing in classical platforms and programmable transport functionalities in quantum settings.

We investigate the nonequilibrium glassy dynamics of dense, topologically constrained ring-polymer systems subjected to instantaneous thermal quenches, using large-scale molecular dynamics simulations. We show that the onset of dynamical arrest is strongly controlled by polymer stiffness, with increasing rigidity enhancing configurational constraints and shifting the estimated glass transition temperature to higher values. Below this threshold temperature, the system exhibits clear aging behavior, manifested through the waiting-time dependence of two-time correlation functions, with the corresponding structural relaxation approximately displaying a simple aging scenario. A key feature of these systems is the emergence of long-lived threaded rings, upon quenching, which act as persistent topological constraints, and the threading relaxation is shown to be correlated with aging dynamics. At the collective level, persistent threading leads to pronounced spatial heterogeneity, manifested as clustering of centers of mass of the rings. Cluster formation is maximized near the glass transition and is enhanced by polymer stiffness, while aging primarily affects the kinetics of cluster participation rather than their characteristic size. Overall, our study establishes a direct connection between polymer stiffness, topological constraints, spatial heterogeneity, and aging dynamics in ring-polymer glasses.

Some atomic nuclei exhibit enhanced octupole collectivity, reflected in finite reflection-asymmetric multipole correlations rather than necessarily in a rigid static pear-shaped ground state. Low-energy studies indicate finite octupole strength in uranium-238, commonly interpreted as soft or vibrational in nature, in addition to its large prolate quadrupole collectivity [F. K. McGowan and W. T. Milner, Nucl. Phys. A 571, 569 (1994).; T. Kibédi and R. H. Spear, At. Data Nucl. Data Tables 80, 35 (2002)]. Here, we investigate how such octupole correlations can be encoded in the initial geometry of relativistic heavy-ion collisions and mapped to final-state flow observables. Using state-of-the-art hydrodynamic calculations, we demonstrate quantitative sensitivity to octupole-induced features encoded in the initial-state geometry and suggest a modest effective octupole-correlation strength in uranium-238 that is compatible with the latest high-energy experimental measurements [B. E. Aboona et al. (STAR), Rep. Prog. Phys. 88, 108601 (2025)]. These findings provide a complementary probe of odd-order nuclear collectivity and help constrain quark-gluon plasma initial conditions.

As a nontrivial state of solid, Schwarz crystal manifests itself in extremely refined nanograins and triply periodic minimal surface (TPMS) grain boundaries, and therefore exceptional thermal and mechanical stability. However, it remains unexploited how the structural units interact and thermal transport is influenced by such complex atomic structures. Here, we investigate Schwarz crystals of Cu and Pt using neutron scattering and thermal transport measurements. Pair distribution function analysis reveals the coexistence of compressed grains and expanded TPMS grain-boundary regions, forming a spatially confined atomic environment. This leads to an unusual phonon hardening suggested by inelastic neutron scattering. As bulk materials, Schwarz crystals exhibit a quasilinear temperature dependence of thermal conductivity, which was previously only observed in low-dimensional materials. This contrast indicates that the spatial confinement of the Schwarz crystals plays a crucial role in determining the unique thermal conductivity, which also provides an emergent route to regulate thermal properties in bulk materials.

We propose and analyze a scheme to generate squeezed light by storing a classical probe pulse in a Bose-Einstein condensate (BEC) and exploiting the nonlinear evolution caused by atom-atom collisions during the storage time. A $\mathrm{\Lambda }$-type optical memory interface maps a chosen temporal probe mode onto a single phase-matched collective spin wave; for a coherent input, this prepares a tunable coherent spin state of a two-component BEC, with its initial spin orientation set by the stored mean excitation number and the phase relation between the probe and control fields. Collisional interactions during storage then implement one-axis-twisting dynamics and generate spin squeezing in the atomic ensemble. We account for realistic loss and finite memory and retrieval efficiencies, and model readout as a single-mode beam-splitter mapping that transfers the atomic quadrature squeezing onto a propagating optical mode. The model identifies optimal storage times and predicts that, under realistic conditions, several decibels of squeezing can be transferred to the retrieved light.

We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive semidefinite estimators, the sampling error at each site can be rigorously bounded relative to the mean via the Markov inequality, overcoming the lack of self-averaging and enabling accurate estimates even under strong spatial fluctuations. The approach extends to nondiagonal observables, such as local currents, through local unitary transformations and its effectiveness is showcased by benchmark calculations in the disordered two-dimensional $\pi$-flux model, where the local density of states and steady-state current maps are computed. This method will enable simulations of disorder-driven mesoscopic physics in realistically large lattices and accelerate real-space self-consistent mean-field calculations.

We introduce an unsupervised machine-learning framework that discovers optimally compressed representations of quantum many-body ground states. Using an autoencoder neural network architecture on reduced density matrix data from $L$-site Fermi-Hubbard models, we identify minimal latent spaces with a sharp reconstruction quality threshold at $L-1$ latent dimensions, matching the system's intrinsic degrees of freedom. We demonstrate the use of the trained decoder as a differentiable variational ansatz to minimize energy directly within the latent space. Crucially, this approach circumvents the $N$-representability problem, as the learned manifold implicitly restricts the optimization to physically valid quantities.

Alternating shear rotations in dense suspensions have recently shown the ability to reduce both viscosity and dissipation per strain (at a fixed global shear rate). Here, we study alternating shear rotations, with extensive numerical simulations, at various angles and up to their corresponding jamming points. For increasing shear rotation angles, we find that the jamming point is continuously shifted to higher packing fractions for frictional particles, while it remains constant for frictionless particles. As a consequence, the alternating shear rotation is unable to reduce the dissipation per strain for suspensions composed of frictionless particles. We detail the individual contributions, hydrodynamic or contact, to the shear stress, which are uncharted for this protocol. As the angle of rotation increases, the average contact stress decreases. However, we find that the hydrodynamic stress shows the opposite trend, instead increasing with increasing angle. Hence, hydrodynamic stress will dominate up to much higher packing fractions as the angle of rotation increases. In addition, we report how the microstructure varies and establish a one-to-one mapping between the contact number and its contribution to the total stress for both frictionless and frictional particles.

Cells control their size to cope with noise during growth and division. Eukaryotic cells exhibiting “sizer” control (targeting a specific size before dividing) may rely on molecular concentration thresholds, but simple implementations of this strategy are not stable. We derive a general criterion for concentration-based sizer control and demonstrate it with a mechanistic model that resolves the instability by using multistage progression toward division. We show that if molecular dynamics in one stage satisfy the sizer criterion, then sizer control follows for the whole progression. We predict that perturbations to the molecular dynamics in nonsizer stages shift the size statistics without disrupting sizer control, consistent with recent experiments in fission yeast.

The kinetic energy dissipation rate is of central importance for small-scale statistics in turbulent flows. Here, we report a transition to the dilatation-dominated regime of three-dimensional isothermal fully compressible, homogeneous, isotropic turbulence by moments of energy dissipation and its components up to order 4 for root-mean-square (rms) Mach numbers $0.1\le M_{\mathrm{rms}}\le 10$ and for Reynolds numbers $100\le \text{Re}\le 2400$. Our high-resolution numerical simulations show a crossover from incompressible to $M_{\mathrm{rms}}$-independent, Burgers turbulencelike scaling of energy dissipation rate moments with respect to Reynolds number $\text{Re}$. This confirms the statistical dominance of shocks for rms Mach numbers $M_{\mathrm{rms}}\gtrsim 1$.

We propose a quantum sensor for electric fields based on networks of Rydberg atoms. The sensing mechanism exploits the strong dependence of the Rydberg blockade on the applied electric field near a Förster resonance. In this regime, variations of the electric field across the array lead to local changes in the blockade radius. Therefore, owing to its spatially distributed architecture, the device can operate as a gradiometer. Our analysis shows that our scheme enables detection of spatial variations in the electric field with a resolution of few micrometers. We analyze the dynamics of Rydberg excitations for systems with different spatial geometries and electric field configurations to establish the relation between the applied field and the blockade response. For spatially inhomogeneous fields, we also provide another observable, density-density correlations, that can probe the field’s spatial structure.

Quantum Monte Carlo (QMC) methods are uniquely capable of providing exact simulations of quantum many-body systems. Unfortunately, the applications of a QMC simulation are limited because extracting dynamic properties requires solving the analytic continuation problem. Across the many fields that use QMC methods, there is no universally accepted analytic continuation algorithm for extracting dynamic properties, but many publications compare to the maximum entropy method. We investigate when entropy maximization is an acceptable approach. We show that stochastic sampling algorithms reduce to entropy maximization when the Bayesian prior is near to the true solution. We investigate when is Bryan’s controversial optimization algorithm [Bryan, Eur. Biophys. J. 18, 165 (1990)] for entropy maximization (sometimes known as the maximum entropy method—MEM) appropriate to use. We show that Bryan’s algorithm is appropriate when the noise is near zero or when the Bayesian prior is near the true solution. We also investigate the mean squared error, finding a better scaling when the Bayesian prior is near the true solution than when the noise is near zero. Together, these three results indicate that enhancing the quality of the Bayesian prior enhances the validity of the MEM and has better return on investment than reducing the noise. We point to examples of improved data-driven Bayesian priors that have already leveraged this advantage. We support these results by solving the double Gaussian problem using both Bryan’s algorithm and the newly formulated dual approach to entropy maximization [Chuna et al., J. Phys. A: Math. Theor. 58, 335203 (2025)].

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.