Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the underlying mathematical principles of these quantum models and find that the quantum neural network with amplitude encoding is equivalent to a weight-constrained neural network. Motivated by this discovery, we develop a classical weight-constrained neural network. We find that this approach can reduce the number of variables in a classical neural network by a factor of 135 while preserving its accuracy. In addition, we develop a dropout method to enhance the robustness of quantum machine learning models, which are highly susceptible to adversarial attacks. This technique can also be applied to improve the adversarial robustness of the classical weight-constrained neural network, which is essential for industry applications, such as self-driving vehicles. Our work offers an approach to reduce the complexity of large classical neural networks, addressing a critical challenge in machine learning.

The study of probabilistic models for the analysis of complex networks represents a flourishing research field. Among the former, exponential random graphs (ERGs) have gained increasing attention over the years. So far, only linear ERGs have been extensively employed to gain insight into the structural organization of real-world complex networks. None, however, is capable of accounting for the variance of the empirical degree distribution. To this aim, nonlinear ERGs must be considered. After showing that the usual mean-field approximation forces the degree-corrected version of the two-star model to degenerate, we define a fitness-induced variant of it. Such a “softened” model is capable of reproducing the sample variance, while retaining the explanatory power of its linear counterpart, within a purely canonical framework.

We propose using qumodes, quantum bosonic modes, for detecting high-frequency gravitational waves via the inverse Gertsenshtein effect, where a gravitational wave resonantly converts into a single photon in a magnetized cavity. For an occupation number $n$ of the photon field in a qumode, the conversion probability is enhanced by a factor of $n+1$ due to Bose-Einstein statistics. Unlocking this increased sensitivity entails the ability to continuously prepare the qumode and perform nondemolition measurement on the qumode-qubit system within the qumode coherence time. Our results indicate that, at microwave frequencies and with existing technology, the proposed setup can attain sensitivities within 1.7 orders of magnitude of the cosmological bound. With anticipated near-future improvements, it has the potential to surpass this limit and pave the way for the first exploration of high-frequency cosmological gravitational wave backgrounds. At optical frequencies, it can enhance the sensitivity of current detectors by one order of magnitude. That further enhances their potential in reaching the single-graviton level.

Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states—characterized by order in four-electron composite objects, termed electron quadrupling or composite order—can exist in materials, and if so, under what conditions they emerge and what properties they exhibit. These states lie beyond the scope of Bardeen-Cooper-Schrieffer theory, and a microscopic description of them remained elusive. In the first part of the paper, we provide a general microscopic framework to describe these and the other four-fermion composite states. In the second part of the paper, we derive and solve a specific fermionic model in two and three dimensions that hosts time-reversal symmetry-breaking electron quadrupling order. The fermionic microscopic theory is used to estimate the specific heat and electron density of states.

Electrochemical phenomena in biology often unfold in confined geometries where micrometer- to millimeter-scale domains coexist with nanometer-scale interfacial diffuse charge layers. We analyze a model lipid membrane-electrolyte system where an ion channellike current flows across the membrane while parallel electrodes simultaneously apply a step voltage, emulating an extrinsic electric field. Matched asymptotic expansions of the Poisson-Nernst-Planck equations show that, under physiological conditions, the diffuse charge layers rapidly reach a quasisteady state, and the bulk electrolyte remains electroneutral. As a result, all free charge is confined to the nanometer-scale screening layers at the membrane and electrode interfaces. The bulk electric potential satisfies Laplace's equation and is dynamically coupled to the interfacial layers through time-dependent boundary conditions. This multiscale coupling partitions the space-time response into distinct regimes. At sufficiently long times, we show that the system can be represented by an equivalent circuit analogous to those used in classical cable theory. We derive closed-form expressions of the transmembrane potential within each regime and verify them against nonlinear numerical simulations. Our results show how electrode-induced screening and confinement effects influence the electrochemical response over multiple length and timescales in biological systems.

The reproduction ratio $R$ is a central metric for monitoring infectious disease epidemics and guiding public health interventions. It is typically inferred from population-level surveillance data, but such estimates can be biased by the spatial structure of the underlying population and by complexities in disease natural history. Here, we develop a theoretical framework to study how the distribution of the generation time (the time from primary to secondary infection) interacts with spatial network structure of the host population, to shape epidemic dynamics and the accuracy of $R$ estimates. We show that the mean and dispersion of the generation time determine the contribution of subdominant epidemic modes, controlling the rate at which the system converges to its spatial equilibrium. Overdispersed generation times slow convergence near the epidemic threshold, whereas underdispersed distributions, common for respiratory pathogens, can markedly delay convergence at moderate and high transmissibility, producing long-lived biases in $R$. We evaluate the performance of an existing correction to incidence data that removes bias from spatial structure under simpified dynamical conditions. We demonstrate that it remains valid for arbitrary generation time distributions only if both mean and dispersion are accurately specified. Otherwise, substantial residual errors persist, especially when $R$ is above the threshold. We extend the framework to short-lived perturbations, both exogenous (e.g., extreme weather, mass gatherings, and mobility restrictions) and endogenous (e.g., behavioral changes), and show that realistic dispersions can amplify their impact on spatial distributions and prolong bias on $R$ far beyond the perturbation. We illustrate these mechanisms through a case study of a respiratory pathogen in Spain, using colocation-based mobility data, and identify the conditions under which surveillance-derived $R$ is reliable and when precise measurements of the generation time distribution are critical.

The $\alpha$(bcc)-$\varepsilon$(hcp) phase transition in polycrystalline Fe has been investigated under fast quasihydrostatic compression using piezoelectric actuator driven dynamic diamond anvil cells. X-ray diffraction data from Fe under intermediate strain rate compression were collected at megahertz repetition rates. Our results demonstrate, for the first time, the full evolution of the $\alpha \text{−}\varepsilon$ phase transition in powder and foil samples at strain rates of $\sim {10}^2{\mathrm{s}}^{-1}$. Under fast compression, the majority of the $\alpha$ phase transforms to $\varepsilon$-Fe in a timescale of tens of microseconds, with a corresponding coexistence pressure of $\sim 2\mathrm{GPa}$. The observed onset phase transition pressure of 13.4–14.4 GPa is in good agreement with the results of previous quasihydrostatic compression studies, suggesting that the transition is not influenced by compression rates up to $\sim 80\mathrm{TPa}{\mathrm{s}}^{-1}$.

We demonstrate quantum simulations of strongly correlated nuclear many-body systems on the RIKEN-Quantinuum Reimei trapped-ion quantum computer, targeting ground states of oxygen, calcium, and nickel isotopes. By combining a hard-core-boson representation of the nuclear shell model with a pair-unitary coupled-cluster doubles ansatz, we achieve subpercent relative error in the ground-state energies compared to noise-free state vector simulations. Our approach leverages symmetry-aware state preparation and particle-number postselection to efficiently capture pairing correlations characteristic of systems with same-species nucleons. These findings highlight the viability of high-fidelity trapped-ion platforms for nuclear physics applications and provide a foundation for scaling to more complex nuclear systems.

Lagrangians can differ by a total derivative without altering the equations of motion, thus encoding the same physics. This is true both classically and quantum mechanically. We show, however, that in the context of open quantum systems, two Lagrangians that differ by a total derivative can lead to inequivalent reduced dynamics. While these Lagrangians are connected via unitary transformations at the level of the global system-plus-environment description, the equivalence breaks down after tracing out the environment. We argue that only those Lagrangians for which the canonical and mechanical momenta of the system coincide lead to operationally meaningful dynamics. Applying this insight to quantum electrodynamics (QED), we derive the master equation for bremsstrahlung due to an accelerated nonrelativistic electron upto second order in the interaction. The resulting reduced dynamics predicts decoherence in the position basis and closely matches the Caldeira-Leggett form, thus resolving previous discrepancies in the literature. Our findings have implications for both QED and gravitational decoherence, where similar ambiguities arise.

We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic structure, thereby unifying the axioms that traditionally distinguish the treatment of spacelike and timelike separations. Standard quantum evolution can be recovered from timelike correlators, defined by means of a quantum action operator, a quantum version of the action of classical mechanics. The corresponding map also provides an alternative perspective on the path integral formulation that, in the case of fermions, does not require the use of Grassmann variables. In addition, the formalism can be interpreted in terms of generalized quantum states, codifying both the conventional information of a quantum system at a given time and its evolution. We show that these states are solutions to a quantum principle of stationary action grounded in timelike correlations and pseudo-entropies.

We present a theoretical framework for a quantized memristive Leaky Integrate-and-Fire (LIF) neuron, uniting principles from neuromorphic engineering and open quantum systems. Starting from a classical memristive LIF circuit, we apply canonical quantization techniques to derive a quantum model grounded in circuit quantum electrodynamics. Numerical simulations demonstrate key dynamical features of the quantized memristor and LIF neuron in the weak-coupling and adiabatic regime, including memory effects and spiking behavior. Applications of this model to a sound localization benchmark show that it outperforms a phenomenological quantum LIF model as well as a classical LIF. This work establishes a foundational model for quantum neuromorphic computing, offering a pathway toward biologically inspired quantum spiking neural networks and paradigms in quantum machine learning.

We revisit the phenomenological Dzyaloshinskii framework, a central theoretical approach for describing magnetization processes in bulk chiral magnets, and demonstrate how magnetocrystalline cubic anisotropy reshapes the phase diagrams of states and provides the key mechanism stabilizing low-temperature skyrmion phases. We show that, for magnetic field directions along the easy anisotropy axes, the phase diagrams feature stable skyrmion pockets for both signs of the anisotropy constant. We further analyze the nature of the transitions at the critical field $H_{c1}$, associated with the reorientation of stable and metastable spirals along the field. We also examine the transition at $H_{c2}$, where the conical state closes into the homogeneous state accompanied by a deviation of the wave vector from the field direction. By mapping characteristic anisotropy-dependent parameters in the theoretical phase diagrams, we provide guidelines for connecting theory with experiment and for estimating the cubic anisotropy constant in ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ and MnSi. Our results indicate that samples ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ with small $x\sim 0.1$ possess sufficiently strong cubic anisotropy to stabilize a low-temperature skyrmion phase. Overall, these theoretical findings establish a quantitative framework for predicting and interpreting skyrmion stability in other cubic helimagnets as well.

Time delay is ubiquitous in many experimental and real-world situations. However, from measurable data it is often unclear whether time delay plays a significant role in the dynamics, and if it does, how long the time lag really is. This would be invaluable knowledge when analyzing and modeling such systems. Hitherto, no universal method is available by which the time delay can be inferred. To address this problem, we propose and demonstrate two different methods to infer time delay in overdamped Langevin systems with delayed feedback. In the first part, we focus on the power spectral density based on the positional data and use a characteristic signature of the time delay to infer the delay time. In limiting cases, we establish a direct relation between the observations made for nonlinear time-delayed feedback forces and analytical results obtained for the linear system. In other situations, despite the absence of this direct relation, the characteristic signature remains and can be exploited by a semiautomatic method to infer the delay time. Furthermore, it may not always desirable or possible to observe a system for a long time to infer dependencies and parameters. Thus, in the second part, we propose a probing method combined with a neural network to infer the delay time, which requires only short observation time series. These proposed methods for inferring time delays in stochastic systems can be valuable tools for gaining deeper insight into the role of delay across a wide range of applications—from the behavior of individual colloidal particles under feedback control to emergent collective phenomena such as flocking and swarming.

Quantum computing promises to revolutionize many-body simulations for quantum chemistry, but its potential is constrained by limited qubits and noise in current devices. In this work, we introduce the lossy quantum-selected configuration interaction   (Lossy-QSCI) framework, which combines a lossy subspace Hamiltonian preparation pipeline with a generic QSCI selection process. This framework integrates a chemistry-inspired lossy random linear encoder (Chemical-RLE) with a neural network assisted fermionic expectation decoder (NN-FED). The RLE leverages fermionic number conservation to compress quantum states, reducing qubit requirements to $O\left(N{log}_{2}M\right)$ for $M$ spin orbitals and $N$ electrons while preserving crucial ground-state information and enabling self-consistent configuration recovery. NN-FED, powered by a neural network trained with minimal data, efficiently decodes these compressed states, overcoming the measurement challenges common in the approaches of the traditional QSCI and its variants. Through iterative quantum sampling and classical postprocessing, our hybrid method refines ground-state estimates with high efficiency. This framework offers a resource-efficient pathway for ground-state simulations on near-term noisy hardware and could inspire resource-efficient extensions to future devices by minimizing qubit overhead.

Logical consistency with free local operations is compatible with nontrivial classical communications, where all parties can be both in each other’s past and future—a phenomenon known as noncausality. Noncausal processes, such as the “Lugano process,” violate causal inequalities, yet their physical realizability remains an open question. In contrast, the quantum switch—a physically realizable process with indefinite causal order—can only generate causal correlations. Building on a recently established correspondence [Kunjwal and Baumeler, Phys. Rev. Lett. 131, 120201 (2023)] between the SHIFT measurement, which exhibits nonlocality without entanglement, and the Lugano process, we demonstrate that the SHIFT measurement can be implemented using a quantum switch of classical communications in a scenario with quantum inputs. This shows that the structure of the Lugano process can be simulated by a quantum switch and that successful SHIFT discrimination witnesses causal nonseparability rather than noncausality. Finally, we identify a broad class of “superposition of classical communications” derived from classical processes without global past capable of realizing similar causally indefinite measurements. We examine these results in relation to the ongoing debate on implementations of indefinite causal orders.

We present benchmark theoretical values of the fine-structure splittings in the ground ${}^3{P}^e$ and low-lying excited ${}^3{P}^e$ and ${}^3{D}^e$ states of the ${}^{12}\mathrm{C}$, ${}^{13}\mathrm{C}$, and ${}^{14}\mathrm{C}$ isotopes of the neutral carbon atom. We handle the correlations in the dynamics of all particles (six electrons and a nucleus) in all considered states in the practically exact manner by employing very large expansions of the wave functions in terms of all-particle explicitly correlated Gaussian basis sets, whose nonlinear parameters were extensively optimized. The resulting wave functions were used to compute the fine-structure splittings for the three isotopes by including the leading-order spin-orbit and electron spin-spin corrections $(\propto {\alpha }^2)$, contribution from the electron anomalous magnetic moment $(\propto {\alpha }^3)$, and by taking into account the most significant couplings between the targeted and neighboring electronic states $(\propto {\alpha }^4)$. Our results show a notable improvement in accuracy compared to any previous theoretical calculations, are in good agreement with the best available experimental data, and demonstrate that the calculations of six-electron systems are now sufficiently advanced for precision measurement applications.