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We present a computational study of phonon relaxation in face-centered cubic (fcc) nickel (Ni), focusing on ultra-fast magnetization dynamics. The phonons are excited beyond their thermal equilibrium population, and the relaxation behavior is analyzed as a function of both wave vector ($\vec{q}$) and phonon frequency ($\omega$). To efficiently investigate these excitations, we introduce a trajectory post-processing technique, the frozen-trajectory excitation, which facilitates the $(\vec{q},\omega)$-resolved analysis. Molecular dynamics simulations combined with the frozen-phonon multislice method predict relaxation signatures observable with time-resolved transmission electron microscopy (TEM) at 10 -- 20 fs resolution. Our findings indicate mode dependence in the relaxation processes, highlighting the importance of phonon-specific behavior consideration in ultrafast dynamics., Comment: 10 pages, 8 figures

Uniaxially strained Fe--Co disordered alloys have emerged as promising candidates for cost-effective rare-earth-free permanent magnets due to their high magnetocrystalline anisotropy energy (MAE). Using first-principles, fully relativistic calculations within the coherent potential approximation and PBE exchange-correlation potential, we explore the MAE of tetragonal Fe--Co alloys under uniaxial compression. Our results reveal a previously uncharted high-MAE region, distinct from known structures and accessible through uniaxial compression., Comment: 6 pages, 3 figures

We investigate the formation of self-bound states in a one-dimensional dipolar Bose gas under the influence of both strong short-range repulsive and strong non-local attractive interactions. While conventional methods like the Bogoliubov de-Gennes (BdG) method typically fail in regimes with strong interactions due to significant quantum depletion, we reveal a particular scenario where the interplay of these strong interactions significantly mitigates quantum depletion, thus restoring the applicability of the BdG method. Remarkably, this restoration occurs even though the system exhibits pronounced anti-bunching, a feature usually linked with strongly correlated systems. By comparing our BdG results with exact ab initio calculations, we confirm the accuracy of the BdG approach in predicting the ground-state energy and correlation functions under these conditions. Furthermore, we demonstrate that adjusting the polarization direction of the dipoles allows for a tunable transition between a strongly interacting regime and the novel balanced regime explored in this research.

Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators., Comment: 21+12 pages, 6+7 figures

Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. In this work, we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs., Comment: 12 pages, 5 figures

Classical machine learning has proven remarkably useful in post-processing quantum data, yet typical learning algorithms often require prior training to be effective. In this work, we employ a tensorial kernel support vector machine (TK-SVM) to analyze experimental data produced by trapped-ion quantum computers. This unsupervised method benefits from directly interpretable training parameters, allowing it to identify the non-trivial string-order characterizing symmetry-protected topological (SPT) phases. We apply our technique to two examples: a spin-1/2 model and a spin-1 model, featuring the cluster state and the AKLT state as paradigmatic instances of SPT order, respectively. Using matrix product states, we generate a family of quantum circuits that host a trivial phase and an SPT phase, with a sharp phase transition between them. For the spin-1 case, we implement these circuits on two distinct trapped-ion machines based on qubits and qutrits. Our results demonstrate that the TK-SVM method successfully distinguishes the two phases across all noisy experimental datasets, highlighting its robustness and effectiveness in quantum data interpretation., Comment: 16 pages, 11 figures

A formalism of systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for an associated Frobenius integrability condition on a Lie algebra. It is showed that this IVP has a formal solution and within the framewrok of two particular subalgebras of the hereditary Lie algebra the explicit forms of this formal solution are presented. Finally, this formalism is applied to Korteveg-de Vries, dispersive water waves and Ablowitz-Kaup-Newell-Segur soliton hierarchies., Comment: 25 pages

Schensted row insertion is a fundamental component of the Robinson-Schensted-Knuth (RSK) algorithm, a powerful tool in combinatorics and representation theory. This study examines the insertion of a deterministic number into a random tableau of a specified shape, focusing on the relationship between the value of the inserted number and the position of the new box created by the Schensted row insertion. Specifically, for a given tableau and a point on its boundary, we consider the threshold that separates values which, if inserted, would result in the new box being created above the point from those that would result in a new box below. We analyze a random tableau of fixed shape and study the corresponding random threshold value. Explicit combinatorial formulas for the cumulants of this random variable are provided, expressed in terms of Kerov's transition measure of the diagram. These combinatorial formulas involve summing over non-crossing alternating trees. As a first application of these results, we demonstrate that for random Young tableaux of prescribed large shape, the rightmost entry in the first row converges in distribution to an explicit Gaussian distribution., Comment: 39 pages, 16 figures. The first part of a series split from arXiv:2302.03762. It provides combinatorial tools related to alternating trees. The original paper will be replaced by the second part, which addresses the problem of inserting a deterministic number into a tableau

This study addresses the critical challenge of detecting DeepFake tweets by leveraging advanced natural language processing (NLP) techniques to distinguish between genuine and AI-generated texts. Given the increasing prevalence of misinformation, our research utilizes the TweepFake dataset to train and evaluate various machine learning models. The objective is to identify effective strategies for recognizing DeepFake content, thereby enhancing the integrity of digital communications. By developing reliable methods for detecting AI-generated misinformation, this work contributes to a more trustworthy online information environment.

In previous experiments, thin films of L1$\mathrm{_0}$ FeNi with different surfaces, including (001), (110) and (111), were produced and studied. Each surface defines a different alignment of the crystallographic tetragonal axis with respect to the film's plane, resulting in different magnetic anisotropies. In this study, we use density functional theory calculations to examine three series of L1$\mathrm{_0}$ FeNi films with surfaces (001), (010), and (111), and with thicknesses ranging from 0.5 to 3 nm (from 4 to 16 atomic monolayers). Our results show that films (001) have perpendicular magnetic anisotropy, while (010) favor in-plane magnetization, with a clear preference for the tetragonal axis [001]. We propose calling this type of in-plane anisotropy fixed in plane. A film with surface (111) and a thickness of four atomic monolayers has the magnetization easy axis almost perpendicular to the plane of the film. As the thickness of the (111) film increases, the direction of magnetization rotates towards a tetragonal axis [001], positioned at an angle of about 45$^{o}$ to the plane of the film. Furthermore, the magnetic moment of ultrathin films increases by a maximum of 5%, and the most significant changes in spin and orbital magnetic moments occur at a depth of about three near-surface atomic monolayers. The presented results could be useful for experimental efforts to synthesize ultrathin L1$\mathrm{_0}$ FeNi films with different surfaces. Ultrathin L1$\mathrm{_0}$ FeNi films with varying magnetic anisotropies may find applications in spintronic devices.

Quantum error correction is a crucial tool for mitigating hardware errors in quantum computers by encoding logical information into multiple physical qubits. However, no single error-correcting code allows for an intrinsically fault-tolerant implementation of all the gates needed for universal quantum computing [1-3]. One way to tackle this problem is to switch between two suitable error-correcting codes, while preserving the encoded logical information, which in combination give access to a fault-tolerant universal gate set [4-6]. In this work, we present the first experimental implementation of fault-tolerant code switching between two codes. One is the seven-qubit color code [7], which features fault-tolerant CNOT and $H$ quantum gates, while the other one, the 10-qubit code [8], allows for a fault-tolerant $T$-gate implementation. Together they form a complementary universal gate set. Building on essential code switching building blocks, we construct logical circuits and prepare 12 different logical states which are not accessible natively in a fault-tolerant way within a single code. Finally, we use code switching to entangle two logical qubits employing the full universal gate set in a single logical quantum circuit. Our results experimentally open up a new route towards deterministic control over logical qubits with low auxiliary qubit overhead, not relying on the probabilistic preparation of resource states.

Noise is both ubiquitous and generally deleterious in settings where precision is required. This is especially true in the quantum technology sector where system utility typically decays rapidly under its influence. Understanding the noise in quantum devices is thus a prerequisite for efficient strategies to mitigate or even eliminate its harmful effects. However, this requires resources that are often prohibitive, such that the typically-used noise models rely on simplifications that sometimes depart from experimental reality. Here we derive a compact microscopic error model for single-qubit gates that only requires a single experimental input - the noise power spectral density. Our model goes beyond standard depolarizing or Pauli-twirled noise models, explicitly including non-Clifford and non-Markovian contributions to the dynamical error map. We gauge our predictions for experimentally relevant metrics against established characterization techniques run on a trapped-ion quantum computer. In particular, we find that experimental estimates of average gate errors measured through randomized benchmarking and reconstructed via quantum process tomography are tightly lower-bounded by our analytical estimates, while the depolarizing model overestimates the gate error. Our noise modeling including non-Markovian contributions can be readily applied to established frameworks such as dynamical decoupling and dynamically-corrected gates, or to provide more realistic thresholds for quantum error correction., Comment: 32 pages, 8 figures

Lunar sulfides and oxides are a significant source of noble and base metals and will be vital for future human colonies' self-sustainability. Sulfide detection (pyrite and troilite) applies to many technological fields and use cases, for example, as a raw material source (available in situ on the Lunar surface) for new solar panel production methods. Ilmenite is the primary iron and titanium ore on the Moon and can provide helium-3 for nuclear fusion and oxygen for rocket fuel. The most important ore minerals have prominent absorption peaks in a narrow far-infrared (FIR) wavelength range of 20-40 $\mu$m, much stronger than the spectral features of other common minerals, including significant silicates, sulfates, and carbonates. Our simulations based on the linear mixing of pyrite with the silicates mentioned above indicated that areas containing at least 10-20% pyrite could be detected from the orbit in the FIR range. MIRORES, Multiplanetary far-IR ORE Spectrometer, proposed here, would operate with a resolution down to <5 m, enabling the detection of areas covered by 2-3 m$^2$ of pyrite (or ilmenite) on a surface of ~17 m$^2$ from an altitude of 50 km, creating possibilities for detecting large and local smaller orebodies along with their stockworks. The use of the Cassegrain optical system achieves this capability. MIRORES will measure radiation in eight narrow bands (0.3 $\mu$m in width) that can include up to five bands centered on the ore mineral absorption bands, for example, 24.3, 24.9, 27.6, 34.2, and 38.8 $\mu$m for pyrite, marcasite, chalcopyrite, ilmenite, and troilite, respectively. The instrument size is 32 $\times$ 32 $\times$ 42 cm, and the mass is <10 kg, which fits the standard microsatellite requirements., Comment: 41 pages, 14 figures

In this paper we systematically consider various ways of generating integrable and separable Hamiltonian systems in canonical and in non-canonical representations from algebraic curves on the plane. In particular, we consider St\"ackel transform between two pairs of St\"ackel systems, generated by 2n-parameter algebraic curves on the plane, as well as Miura maps between St\"ackel systems generated by (n+N)-parameter algebraic curves, leading to multi-Hamiltonian representation of these systems., Comment: Version accepted for publication in Special Issue 2 of Open Communications in Nonlinear Mathematical Physics. One reference added, some language issues fixed, additional explanations in Introduction

Encoding information redundantly using quantum error-correcting (QEC) codes allows one to overcome the inherent sensitivity to noise in quantum computers to ultimately achieve large-scale quantum computation. The Steane QEC method involves preparing an auxiliary logical qubit of the same QEC code used for the data register. The data and auxiliary registers are then coupled with a logical CNOT gate, enabling a measurement of the auxiliary register to reveal the error syndrome. This study presents the implementation of multiple rounds of fault-tolerant Steane QEC on a trapped-ion quantum computer. Various QEC codes are employed, and the results are compared to a previous experimental approach utilizing flag qubits. Our experimental findings show improved logical fidelities for Steane QEC. This establishes experimental Steane QEC as a competitive paradigm for fault-tolerant quantum computing., Comment: 16 pages, 13 figures

In this paper, we consider the problem of an adversary aiming to learn information about the network topology or the executed algorithm from some signals obtained during the algorithm's execution. The problem is defined in a very general form. However, it is mainly motivated by multi-hop ad hoc radio networks. In contrast to previous work concentrated on single-hop radio networks, this model is critically more complex due to the number of possible settings that need to be taken into account when considering different combinations of topologies and communication models. Moreover, the definition of the adversary is also ambiguous, and the adequate approach needs to depend on the adversary's aims and capabilities. This preliminary report presents a general theoretical background and some basic algorithms. We also propose some general taxonomy as a framework for future research.

Iron-based layered systems are of great interest because of their ability to tune effective material parameters such as magnetic anisotropy energy (MAE). The influence of the crystallographic structure of Fe, its thickness, and the presence of other layers above and below the Fe layer on magnetic parameters, such as the MAE of the studied system, is an intriguing and important topic from an application point of view. Here, we present a density functional theory (DFT) study of the magnetic anisotropy of nine-monolayer Fe, FeCo, and FeCo films with B, C, and N dopants placed in octahedral interstitial positions. The theoretical study is based on calculations using the full-potential local-orbital code FPLO and the generalized gradient approximation. The chemical disorder in the FeCo layers was modeled using the virtual crystal approximation. The structures of the layers were subjected to optimization of the geometry of the interlayer spacings and the neighborhood of the dopant sites. We determined the local magnetic moments and the excess charge at each layer position. We also identified the influence of dopant atoms on the magnetic properties of FeCo layers, such as magnetization and magnetic anisotropy., Comment: 7 pages, 5 figures

As evidenced by recent survey results, majority of asteroids are slow rotators (P>12 h), but lack spin and shape models due to selection bias. This bias is skewing our overall understanding of the spins, shapes, and sizes of asteroids, as well as of their other properties. Also, diameter determinations for large (>60km) and medium-sized asteroids (between 30 and 60 km) often vary by over 30% for multiple reasons. Our long-term project is focused on a few tens of slow rotators with periods of up to 60 hours. We aim to obtain their full light curves and reconstruct their spins and shapes. We also precisely scale the models, typically with an accuracy of a few percent. We used wide sets of dense light curves for spin and shape reconstructions via light-curve inversion. Precisely scaling them with thermal data was not possible here because of poor infrared data: large bodies are too bright for WISE mission. Therefore, we recently launched a campaign among stellar occultation observers, to scale these models and to verify the shape solutions, often allowing us to break the mirror pole ambiguity. The presented scheme resulted in shape models for 16 slow rotators, most of them for the first time. Fitting them to stellar occultations resolved previous inconsistencies in size determinations. For around half of the targets, this fitting also allowed us to identify a clearly preferred pole solution, thus removing the ambiguity inherent to light-curve inversion. We also address the influence of the uncertainty of the shape models on the derived diameters. Overall, our project has already provided reliable models for around 50 slow rotators. Such well-determined and scaled asteroid shapes will, e.g. constitute a solid basis for density determinations when coupled with mass information. Spin and shape models continue to fill the gaps caused by various biases., Comment: Accepted to Astronomy & Astrophysics. 12 pages + appendices

Second generation quantum technologies aim to outperform classical alternatives by utilizing engineered quantum systems. Maintaining the coherence required to enable any quantum advantage requires detailed knowledge and control over the noise the hosting system is subjected to. Characterizing noise processes via their power spectral density is routinely done throughout science and technology and can be a demanding task. Determining the phase noise power spectrum in leading quantum technology platforms, for example, can be either outside the reach of many phase noise analyzers, or be prohibitively expensive. In this work, we present and characterize a cost-effective optical phase noise analyzer for quantum technology applications. Using this setup we compare two $\approx1\ \rm{Hz}$ linewidth ultra-stable oscillators near $729\ \rm{nm}$, using them as references to determine and discuss the noise floor achieved in this measurement apparatus with a focus on limitations and their tradeoffs. The achieved noise floor in this implementation of a low-cost, all-stock component, low-complexity phase noise analyzer compares favourably to commercial offerings. This setup can find application in particular without a more stable reference or operational quantum system as sensor as would be the case for many component manufacturers., Comment: 9 pages, 6 figures

This work aims at constraining the size, shape, and geometric albedo of the dwarf planet candidate 2002 MS4 through the analysis of nine stellar occultation events. Using multichord detection, we also studied the object's topography by analyzing the obtained limb and the residuals between observed chords and the best-fitted ellipse. We predicted and organized the observational campaigns of nine stellar occultations by 2002 MS4 between 2019 and 2022, resulting in two single-chord events, four double-chord detections, and three events with three to up to sixty-one positive chords. Using 13 selected chords from the 8 August 2020 event, we determined the global elliptical limb of 2002 MS4. The best-fitted ellipse, combined with the object's rotational information from the literature, constrains the object's size, shape, and albedo. Additionally, we developed a new method to characterize topography features on the object's limb. The global limb has a semi-major axis of 412 $\pm$ 10 km, a semi-minor axis of 385 $\pm$ 17 km, and the position angle of the minor axis is 121 $^\circ$ $\pm$ 16$^\circ$. From this instantaneous limb, we obtained 2002 MS4's geometric albedo and the projected area-equivalent diameter. Significant deviations from the fitted ellipse in the northernmost limb are detected from multiple sites highlighting three distinct topographic features: one 11 km depth depression followed by a 25$^{+4}_{-5}$ km height elevation next to a crater-like depression with an extension of 322 $\pm$ 39 km and 45.1 $\pm$ 1.5 km deep. Our results present an object that is $\approx$138 km smaller in diameter than derived from thermal data, possibly indicating the presence of a so-far unknown satellite. However, within the error bars, the geometric albedo in the V-band agrees with the results published in the literature, even with the radiometric-derived albedo.

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create and sample from random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. By exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states -- in single instances and on average -- and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage., Comment: 11+16 pages. Comments welcome. v2: improved presentation

This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent on dynamically changing population structures, appear in a variety of applications such as crowd dynamics, tissue regeneration, cancer development, and coagulation-fragmentation processes. The current body of literature regarding mathematical modeling presents common challenges to mathematicians due to the multiscale nature of the structures that underlie self-organisation and control within complex, heterogeneous systems. In various applications, similar, abstract mathematical concepts arise through problem formulation and the assimilation of mathematical depictions into the language of measure evolution on a multi-faceted state space. In view of the above observations, we propose an overarching mathematical framework for nonlinear structured population models on abstract metric spaces, which are only assumed to be separable and complete. To achieve this, we exploit the structure of the space of non-negative Radon measures under the dual bounded Lipschitz distance (flat metric), a generalization of the Wasserstein distance that is capable of addressing non-conservative problems. The formulation of models on generic metric spaces facilitates the study on infinite-dimensional state spaces or graphs with a combination of discrete and continuous structures. This opens up exciting possibilities for modeling single cell data, crowd dynamics or coagulation-fragmentation processes., Comment: corrected introduction

Fe-Co alloys with induced tetragonal strain are promising materials for rare-earth-free permanent magnets. However, as ultrathin-film studies have shown, tetragonal Fe-Co structures tend to a rapid relaxation toward a cubic structure as the thickness of the deposited film increases. One of the main methods of inducing the stable strain in the bulk material is interstitial doping with small atoms, like B, C, or N. In this work, we present a full configuration space analysis in density functional theory approach for (Fe$_{1-x}$Co$_x$)$_{16}$C supercells with a single C impurity in one of the octahedral interstitial positions and for the full range of Co concentrations $x$. We discuss all assumptions and considerations leading to calculated lattice parameters, mixing enthalpies, magnetic moments, and averaged magnetocrystalline anisotropy energies (MAE). We present a comprehensive qualitative analysis of the structural and magnetic properties' dependence on short- and long-range ordering parameters. We analyzed all unique Fe/Co atoms occupancies at all stoichiometric concentrations possible in 2x2x2 supercell based on 2-atom tetragonal representation. We rely on the thermodynamic averaging method and large sample count to obtain accurate MAE values. We reevaluate several chemical disorder approximation methods, including effective medium methods (virtual crystal approximation and coherent potential approximation) and special quasirandom structures method applied to Fe-Co-based alloys. We observe a structural phase transition from the body-centered tetragonal structure above 70% Co concentration and confirm the structural stability of Fe-Co-C alloys in the tetragonal range. We show the presence of a broad MAE maximum of around 50% Co concentration and notably high MAE values for Co content $x$ as low as 25%. In addition, we show a positive correlation between MAE and mixing enthalpy.

We introduce the concept of Miura maps between parameter-dependent algebraic curves of hyperelliptic type. These Miura maps induce Miura maps between St\"{a}ckel systems defined (on the extended phase space) by the considered algebraic curves. This construction yields a new way of generating multi-Hamiltonian representations for St\"{a}ckel systems.

We investigate the effect of a quench from a one-dimensional gas with strong and repulsive local interactions to a strongly attractive one, known as the super-Tonks-Girardeau effect. By incorporating both an optical lattice and non-local interactions (specifically nearest-neighbor), we discover a previously unexplored phenomenon: the disruption of the state during the quench, but within a specific range of interactions. Our study employs the extended Bose-Hubbard model across various system sizes, starting with analytical results for two atoms and progressing to few-body systems using exact diagonalization, DMRG and TDVP methods. Finally, we use a numerical implementation of the local density approximation for a macroscopic number of atoms. Consistently, our findings unveil a region where the initially self-bound structure expands due to the super-Tonks-Girardeau quench. The fast evaporation provides a tool to characterize the phase diagram in state-of-art experiments exploring the physics of the extended Bose-Hubbard model., Comment: Comments welcome!