We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $[[7,1,3]]$ color code on Quantinuum H2-2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant (FT) techniques for the Clifford+$R_{Z}$ (arbitrary-angle single-qubit rotation) gate set, and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits' performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (mid-circuit measurements), and $\sim$3900 ($\sim$760) total operations are applied on average. The energy $E$ is experimentally estimated to within $E - E_{\mathrm{FCI}} = 0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols towards higher memory noise protection is the most promising avenue to improve our experimental results.

We report the details of the growth of ultra-clean single crystals for RuO2, a candidate material for altermagnetism. By using a crystal-growth tube with a necking structure and precisely controlling the conditions of the sublimation transport method, it is possible to control the morphology of the crystals. We obtained crystals in mainly three kinds of morphology: thick plate-like crystals typically 5 x 3 x 2mm3 and up to 10 x 5 x 2mm3 with a large (101) facet, rhombohedral columnar crystals elongating along the [001] direction, and fiber and needle crystals of length up to 8 mm and the width of 0.1-0.4 mm. These crystals show residual resistivity of about 30 nOhmcm and a residual resistivity ratio (RRR) up to 1200. The crystals do not exhibit any signs of magnetic ordering down to low temperatures.

Reduced basis methods provide an efficient way of mapping out phase diagrams of strongly correlated many-body quantum systems. The method relies on using the exact solutions at select parameter values to construct a low-dimensional basis, from which observables can be efficiently and reliably computed throughout the parameter space. Here we show that this method can be generalized to driven-dissipative Markovian systems allowing efficient calculations of observables in the transient and steady states. A subsequent distillation of the reduced basis vectors according to their explained variances allows for an unbiased exploration of the most pronounced parameter dependencies indicative of phase boundaries in the thermodynamic limit.

The field equations of pre-geometric theories of gravity are derived and analysed, both without and with matter. After the spontaneous symmetry breaking that reduces the gauge symmetry of these theories à la Yang-Mills, a metric structure for spacetime emerges and the field equations recover both the Einstein and the Cartan field equations for gravity. A first exact solution of the pre-geometric field equations is also presented. This solution can be considered as a pre-geometric de Sitter universe and provides a possible resolution for the problem of the Big Bang singularity.

The Einstein-Cartan theory of gravity can arise from a mechanism of spontaneous symmetry breaking within the context of pre-geometric gauge theories. In this work, we develop the Hamiltonian analysis of such theories. By making contact with the ADM formalism, we show that all the results of canonical General Relativity are correctly recovered in the IR limit of the spontaneously broken phase. We then apply Dirac's algorithm to study the algebra of constraints and determine the number of degrees of freedom in the UV limit of the unbroken phase. We also discuss possible pathways toward a UV completion of General Relativity, including a pre-geometric generalisation of the Wheeler-DeWitt equation and an extended BF formulation of the pre-geometric theory.

In type IIB superstring compactifications, incorporating log-loop corrections and higher-derivative ${(α^\prime)}^3$-corrections can stabilize the overall volume of the compact internal space at exponentially large values. This mechanism forms the basis of the perturbative Large Volume Scenario (LVS). In this report, we briefly review two inflationary models realized within the perturbative LVS framework. The first one is the volume modulus inflation (also known as inflection point inflation) and the second one is popularly known as fibre inflation. Using an explict Calabi-Yau orientifold, some concrete global embeddings of both models are also discussed.

Let $F$ be an entire function of exponential type represented by the Taylor series \[ F(z) = \sum_{n\ge 0} ω_n \frac{z^n}{n!} \] with unimodular coefficients $|ω_n|=1$. We show that either the counting function $n_F(r)$ of zeroes of $F$ grows linearly at infinity, or $F$ is an exponential function. The same conclusion holds if only a positive asymptotic proportion of the coefficients $ω_n$ is unimodular. This significantly extends a classical result of Carlson (1915). The second result requires less from the coefficient sequence $ω$, but more from the counting function of zeroes $n_F$. Assuming that $0<c\le |ω_n| \le C <\infty$, $n\in\mathbb Z_+$, we show that $n_F(r) = o(\sqrt{r})$ as $r\to\infty$, implies that $F$ is an exponential function. The same conclusion holds if, for some $α<1/2$, $n_F(r_j)=O(r_j^α)$ only along a sequence $r_j\to\infty$. Furthermore, this conclusion ceases to hold if $n_F(r)=O(\sqrt r)$ as $r\to\infty$.

For a simple graph $Γ$, a (bipartite)tree-line graph and a tree-graph of $Γ$ can be defined. With a (bipartite)tree-line graph constructed by the function $(b)\ell$, we study the continuous quantum walk on $(b)\ell ^n Γ$. An equitable partition of a bipartite tree-line graph is obtained by its corresponding derived tree graph. This paper also examines quantum walks on derived graphs, whose vertices represent their basis state.

We investigate the dipolar-exchange spin wave spectrum in thin ferromagnetic bilayers with inplane magnetization, incorporating interlayer exchange coupling and intra- and interlayer dipolar interactions. In the continuum approximation we analyze the nonreciprocity of propagating magnetic stray fields emitted by spin waves as a function of the relative orientation of the layer magnetizations that are observable by magnetometry of synthetic antiferromagnets or weakly coupled type-A van der Waals antiferromagnetic bilayers as a function of an applied magnetic field.

It has been observed that the hint about dynamical dark energy in the DESI BAO observation might point to non-minimally coupled gravity. We report the first $3σ$ evidence for non-minimal coupling in a model-agnostic effective field theory (EFT) approach. In a non-parametric reconstruction approach, we detect a clear departure from the General Relativity expectation of non-minimal coupling based on a combined analysis of DESI DR2 BAO together with CMB and Type Ia supernova data. Also, it is found that current data can constrain up to the quadratic order $(n=2)$ if the EFT function representing non-minimal coupling is Taylor expanded as a general function of the dark energy fraction $Ω_{\rm DE}$, i.e. $Ω^{\rm EFT}(a)=\sum_{i=0}^{n} c^{\rm EFT}_i Ω^i_{\rm DE}(a)$. Our findings constitute a detection of modified-gravity effects and call for a more flexible parametrization of the EFT functions than commonly used ones in literature.

Encryption is crucial for securing sensitive data during transmission over networks. Various encryption techniques exist, such as AES, DES, and RC4, with AES being the most renowned algorithm. We proposed methodology that enables users to encrypt text messages for secure transmission over cellular networks. This approach utilizes the AES algorithm following the proposed protocols for encryption and decryption, ensuring fast and reliable data protection. This approach ensures secure text encryption and enables users to enter messages that are encrypted using a key at the sender's end and decrypted at the recipient's end, which is compatible with any Android device. SMS are encrypted with the AES algorithm, making them resistant to brute-force attempts. As SMS has become a popular form of communication, protecting personal data, email alerts, banking details, and transactions information. It addresses security concerns by encrypting messages using AES and cryptographic techniques, providing an effective solution for protecting sensitive data during SMS exchanges.

Let $X$ be the special fiber of a unitary Shimura variety of hyperspecial level at a prime $p$ inert in the totally real field $F$. Let $Y\to X$ be the associated flag space. For every $L$-dominant weight $λ$, let $\mathcal{L}_Y(λ)$ denote the corresponding automorphic line bundle. We give an explicit necessary and sufficient criterion, in terms of the signature data and the coordinates of $λ$, for the ampleness of $\mathcal{L}_Y(λ)$. %, which effectively detects the coherent cohomology of automorphic vector bundles on $X$. The criterion generalizes the known ample cone for Hilbert modular and $U(2)$-Shimura varieties. The proof develops the machinery of the description of certain Ekedahl--Oort strata, a geometric Jacquet--Langlands correspondence between strata of unitary Shimura varieties with different signatures, and the construction of stratum Hasse invariants, and introduced a way to systematically deal with combinatorical data in the higher rank case.

We study the action of the absolute Galois group on the fundamental groups.

We derive analytical expressions for the spin wave frequencies and precession amplitudes in monolayer and antiferromagnetically coupled bilayer CrSBr under in-plane external magnetic fields. The analysis covers the antiferromagnetic, ferromagnetic, and canted phases, demonstrating that the spin wave frequencies in all phases are tunable by the applied magnetic field. We discuss the roles of intra- and interlayer exchange interactions, triaxial anisotropy, and intralayer dynamic dipolar fields in controlling the magnetization dynamics.

Recommender systems are central to digital platforms, yet they face a fundamental trade-off between accuracy and explainability. Black-box models achieve strong performance but lack interpretability needed for trust and adoption. Existing explainable AI approaches either treat explanations as post-hoc or at the cost of accuracy. We challenge this view, proposing that explanations, when designed as an integral component of a system and aligned with prediction outcomes, can improve both interpretability and performance. We introduce RecPIE (Recommendation with Prediction-Informed Explanations), a framework that jointly optimizes recommendation predictions and natural-language explanations generated by LLMs. RecPIE embeds explanation generation into the learning loop: predictions guide explanation generation (prediction-informed explanations), which are fed back to refine subsequent predictions (explanation-informed predictions) via alternating training. The LLM is fine-tuned using LoRA and reinforcement learning with a customized reward derived from recommendation accuracy. Drawing on multi-environment statistical learning theory, we formally ground why explanation generation and prediction can be mutually reinforcing. We evaluate RecPIE on large-scale point-of-interest recommendation data from Google Maps, where user preferences span diverse place categories. RecPIE improves predictive accuracy by 3-4% over state-of-the-art baselines and matches the best performing model using only 12% of the training data. In human evaluations with 566 participants, RecPIE explanations are preferred 61.5% of the time (versus 16.6% for the best baseline) and rated closer to human-generated explanations. These results reframe explainability not as a constraint on performance but as a design lever for improving AI systems, with implications for trust, data efficiency, and marketplace deployment.

With the proliferation of data-driven services, the volume of data that needs to be processed by satellite networks has significantly increased. Federated learning (FL) is well-suited for big data processing in distributed, resource-constrained satellite environments. However, ensuring its convergence performance while minimizing processing time and energy consumption remains a challenge. To this end, we propose a hierarchical clustered federated learning framework, FedHC. This framework employs a satellite-clustered parameter server (PS) selection algorithm at the cluster aggregation stage, grouping nearby satellites into distinct clusters and designating a cluster center as the PS to accelerate model aggregation. Several communicable cluster PS satellites are then selected through ground stations to aggregate global parameters, facilitating the FL process. Moreover, a meta-learning-driven satellite re-clustering algorithm is introduced to enhance adaptability to dynamic satellite cluster changes. The extensive experiments on satellite networks testbed demonstrate that FedHC can significantly reduce processing time (up to 3x) and energy consumption (up to 2x) compared to other comparative methods while maintaining model accuracy.

A global fit for $α_s(m_Z)$ is performed on available $e^+e^-$ data for the heavy jet mass distribution. The state-of-the-art theory prediction includes $\mathcal{O}(α_s^3)$ fixed-order results, N$^3$LL$^\prime$ dijet resummation, N$^2$LL Sudakov shoulder resummation, and a first-principles treatment of power corrections in the dijet region. Theoretical correlations are incorporated through a flat random-scan covariance matrix. The global fit results in $0.1148^{+ 0.0015}_{-0.0022}$, compatible with similar determinations from thrust and $C$-parameter. Dijet resummation is essential for a robust fit, as it engenders insensitivity to the fit-range lower cutoff; without resummation the fit-range sensitivity is overwhelming. In addition, we find evidence for a negative power correction in the trijet region if and only if Sudakov shoulder resummation is included.

Lipid membranes and membrane deformations are a long-standing area of research in soft matter and biophysics. Computer simulations have complemented analytical and experimental approaches as one of the pillars in the field. However, setting up and using membrane simulations can come with barriers due to the multidisciplinary effort involved and the vast choice of existing simulations models. In this review, we introduce the non-expert reader to coarse-grained membrane simulations (CGMS) at the mesoscale. Firstly, we give a concise overview of the modelling approaches to study fluid membranes, together with guidance to more specialized references. Secondly, we provide a conceptual guide on how to develop CGMS. Lastly, we construct a hands-on tutorial on how to apply CGMS, by providing a pedagogical examination of tether pulling, tubulation and fluctuations with three different membrane models, and discussing them in terms of their scope and how resource-intensive they are. To ease the reader's venture into the field, we provide a repository with ready-to-run tutorials.

Recently, the fundamental lemma by Willems et al. has been extended towards stochastic LTI systems subject to process disturbances. Using this lemma requires previously recorded data of inputs, outputs, and disturbances. In this paper, we exploit causality concepts of stochastic control to propose a variant of the stochastic fundamental lemma that does not require past disturbance data in the Hankel matrices. Our developments rely on polynomial chaos expansions and on the knowledge of the disturbance distribution. Similar to our previous results, the proposed variant of the fundamental lemma allows to predict future input-output trajectories of stochastic LTI systems. We draw upon a numerical example to illustrate the proposed variant in data-driven control context.

We establish sufficient mild conditions for a sequence of multitype Bienaymé-Galton-Watson trees, conditioned in some sense to be large, to converge to a limiting compact metric space which we call a \emph{multitype Lévy tree}. More precisely, we condition on the size of the maximal subtree of vertices of the same type joined by the root to be large. While we employ a different conditioning, our result can be seen as a generalization to the multitype setting of the continuum random trees defined by Aldous, Duquesne and Le Gall in [Ald91a,Ald91b,Ald93,DLG02]. Our main result is an invariance principle for the convergence of such trees, by gluing single-type Lévy trees together in a method determined by the limiting spectrally positive additive Lévy field, as constructed by Chaumont and Marolleau [CM21]. Our approach is an improvement of a result about the convergence in the Gromov-Hausdorff-Prohorov topology, of compact marked metric spaces equipped with vector-valued measures, which are then glued via an iterative operation. To analyze the gluing operation, we extend the techniques developed by Sénizergues [Sen19,Sen22] to the multitype setting. While the single-type case exhibits a more homogeneous structure with simpler dependency patterns, the multitype case introduces interactions between different types, leading to a more intricate dependency structure where functionals must account for type-specific behaviors and inter-type relationships.

We broaden the application of the $l^{2}$-decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the $\mathbb{T}^d$ setting. We establish space-time bilinear estimates, and hence the unconditional uniqueness of solutions to the $\mathbb{R}^d$ and $\mathbb{T}^d$ Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff, adopting a unified hierarchy scheme originally developed for the nonlinear Schrödinger equation.

In this paper, we show how to use the approach of the strongly order-preserving semiflow with respect to high-rank cones to solve the open dense conjecture on eventually slow oscillations of the differential equation with delayed negative feedback.

Sequential search models provide a powerful framework for studying consumer search using rich data that records the sequence of consumer actions taken during the search process. In existing empirical applications, their implementation often builds on optimal policies, in which later decisions depend on outcomes from earlier actions that are often fully observed by researchers. Therefore, implementation is largely restricted by computation burden and limited model flexibility. This paper establishes a theoretical equivalence showing that, under common and mild assumptions of Independence and Invariance, a sequential search process is optimal if and only if a corresponding ranking over all feasible actions throughout the process holds, thereby introducing a ranking representation of optimal sequential search. This representation enables a novel, simple, and unified empirical strategy for implementing sequential search models. For the classic \cite{weitzman1979optimal} model, the proposed approach reduces simulation requirements while improving accuracy, computational efficiency, and ease of implementation. We further show that the same strategy extends to a broad class of sequential search settings, including partially observed action sequences and multi-stage information acquisition, such as discovery. Overall, the results enhance both the tractability and the empirical applicability of sequential search models.

For discrete-time nonautonomous linear dynamics and a large class of discrete growth rates $μ$, we show that the notion of $μ$ dichotomy (with respect to a sequence of norms) can be completely characterized in terms of ordinary and exponential dichotomy (with respect to a sequence of norms) by employing a suitable rescaling of time. Previously, such a result was known only in the particular case of polynomial dichotomies. As a nontrivial application of our results, we study the structure of a generalized Sacker-Sell spectrum and obtain a series of nonautonomous topological and smooth linearization results.

Complex materials with internal microstructure such as suspensions and emulsions exhibit time-dependent rheology characterized by viscoelasticity and thixotropy. In many large-scale applications such as turbulent pipe flow, the elastic response occurs on a much shorter timescale than the thixotropy, hence these flows are purely thixotropic. The fundamental dynamics of thixotropic turbulence is poorly understood, particularly the interplay between microstructural state, rheology, and turbulence structure. To address this gap, we conduct direct numerical simulations (DNS) of fully developed turbulent pipe flow of a model thixotropic (Moore) fluid over a range of thixoviscous numbers $Λ$ from slow ($Λ\ll 1$) to fast ($Λ\gg 1$) thixotropic kinetics relative to the eddy turnover time. Analysis of DNS results in the Lagrangian frame shows that, as expected, in the limits of slow and fast kinetics, these time-dependent flows behave as time-independent purely viscous (generalized Newtonian) analogues. For intermediate kinetics ($Λ\sim 1$), the rheology is governed by a \emph{path integral} of the thixotropic fading memory kernel over the distribution of Lagrangian shear history, the latter of which is modelled via a simple stochastic model for the radially non-stationary pipe flow. DNS computations based on this effective viscosity closure exhibit excellent agreement (within 2.4\% error) with the fully thixotropic model for $Λ=1$, indicating that the purely viscous (generalized Newtonian) analogue persists for arbitrary values of $Λ\in[0,\infty^+)$ and across nonlinear rheology models. These results uncover the feedback mechanisms between microstructure, rheology, and turbulence and offer fundamental insights into the structure of thixotropic turbulence.

Let C be a locally Cohen-Macaulay curve in complex projective 3-space. The maximum genus problem predicts the largest possible arithmetic genus g(d,s) that C can achieve assuming that it has degree d and does not lie on surfaces of degree less than s. In this paper, we prove that this prediction is correct when d=s or d is at least 2s-1. We obtain this result by proving another conjecture, by Beorchia, Lella, and the second author, about initial ideals associated to certain homogeneous forms in a non-standard graded polynomial ring.

Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the $\mathbb{Z}_2^{\mathcal{C}}\times\mathbb{Z}_2^{\mathcal{R}}\times\mathbb{Z}_2^{\mathcal{T}}$ for scalar bosons. In fact, the CRT symmetry for fermions can be extended by internal symmetries such as fermion parity, thereby forming a group extension of the $\mathbb{Z}_2$ direct product. Conventionally, a Majorana fermion is defined by one Dirac fermion with trivial charge conjugation. However, when the spacetime dimension $d+1=5,6,7\bmod8$, the real dimension of Majorana fermion (dim$_{\mathbb{R}}χ_{\mathcal{C}\ell(d,0)}$) aligns with the real dimension of Dirac fermion (dim$_{\mathbb{R}}ψ_{\mathcal{C}\ell(d)}$), rather than being half, which necessitates the introduction of a symplectic Majorana fermion, defined by two Dirac fermions with trivial charge conjugation. To include these two types of Majorana fermions, we embed the theory in $n_{\mathbb{R}}$ and define the Majorana fermion field as a representation of the real Clifford algebra with 8-fold periodicity. Within the Hamiltonian formalism, we identify the 8-fold CRT-internal symmetry groups across general dimensions. Similarly, Dirac fermion field is defined as a representation of the complex Clifford algebra with 2-fold periodicity. Interestingly, we discover that the CRT-internal symmetry groups exhibit an 8-fold periodicity that is distinct from that of the complex Clifford algebra. In certain dimensions where distinct mass terms can span a mass manifold, the CRT-internal symmetries can act non-trivially upon this mass manifold. Employing domain wall reduction method, we are able to elucidate the relationships between symmetries across different dimensions.

Large Language Models (LLMs) are increasingly being applied across various domains, including code-related tasks such as code translation. Previous studies have explored using LLMs for translating code between different programming languages. Since LLMs are more effective with natural language, using natural language as an intermediate representation in code translation tasks is an intuitively appealing approach. However, whether this benefit is general or highly context-dependent remains unclear. In this work, we investigate using NL-specification as an intermediate representation for code translation. We evaluate our method using three datasets, five popular programming languages, and 29 language pair permutations. Our results show that using NL-specification alone does not lead to performance improvements. However, when combined with source code, it provides gains in certain language pairs (notably with Python and C++ as source languages), while offering no consistent improvement overall. Besides analyzing the performance of code translation, we also investigate the quality of the translated code and provide insights into the issues present in the translated code.

Quantitative description of finite-temperature properties of displacive ferroelectrics, and in particular the critical behavior, is of fundamental importance to both theory and device design, going beyond the Landau-Ginzburg approach, which requires known knowledge of critical behaviors and temperature-dependent parameter fitting. Here within quantum statistic description of polarization fluctuations, we develop a self-consistent, microscopically based computationalframework for finite-temperature thermodynamics and phase transitions in displacive ferroelectrics. It enables one to use only the ground-state properties to predict the finite-temperature properties and in particular, the criticality of phase transitions of various displacive ferroelectrics. Its applications to the classical ferroelectric PbTiO$_3$, quantum paraelectrics SrTiO$_3$ and KTaO$_3$, and recently fabricated ferroelectric strained SrTiO$_3$, demonstrate remarkable quantitative agreements with the experimentally measured dielectric/ferroelectric properties throughout the entire temperature ranges of the phases, including the critical behaviors of phase transitions. The proposed computational framework offers a tractable quantitative basis for bridging microscopic ground-state modeling and macroscopic device-level design in a broad range of ferroelectric systems under diverse thermodynamic and external conditions.

Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity performance. If such codes exist, decoders with linear runtime in the code length are also desired. In this paper, we present erasure capacity-achieving quantum codes under maximum-likelihood decoding (MLD), though MLD requires cubic runtime in the code length. For QEC, using an accurate decoder with the shortest possible runtime will minimize the degradation of quantum information while awaiting the decoder's decision. To address this, we propose belief propagation (BP) decoders that run in linear time and exploit error degeneracy in stabilizer codes, achieving capacity or near-capacity performance for a broad class of codes, including bicycle codes, product codes, and topological codes. We furthermore explore the potential of our BP decoders to handle mixed erasure and depolarizing errors, and also local deletion errors via concatenation with permutation invariant codes.