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This paper introduces a novel architecture for Quantum Graph Neural Networks, which is significantly different from previous approaches found in the literature. The proposed approach produces similar outcomes with respect to previous models but with fewer parameters, resulting in an extremely interpretable architecture rooted in the underlying physics of the problem. The architectural novelties arise from three pivotal aspects. Firstly, we employ an embedding updating method that is analogous to classical Graph Neural Networks, therefore bridging the classical-quantum gap. Secondly, each layer is devoted to capturing interactions of distinct orders, aligning with the physical properties of the system. Lastly, we harness SWAP gates to emulate the problem's inherent symmetry, a novel strategy not found currently in the literature. The obtained results in the considered experiments are encouraging to lay the foundation for continued research in this field., Comment: 20 pages, 10 figures, 3 tables

Addressing the question of how to achieve optimal decision-making under risk and uncertainty is crucial for enhancing the capabilities of artificial agents that collaborate with or support humans. In this work, we address this question in the context of Public Goods Games. We study learning in a novel multi-objective version of the Public Goods Game where agents have different risk preferences, by means of multi-objective reinforcement learning. We introduce a parametric non-linear utility function to model risk preferences at the level of individual agents, over the collective and individual reward components of the game. We study the interplay between such preference modelling and environmental uncertainty on the incentive alignment level in the game. We demonstrate how different combinations of individual preferences and environmental uncertainties sustain the emergence of cooperative patterns in non-cooperative environments (i.e., where competitive strategies are dominant), while others sustain competitive patterns in cooperative environments (i.e., where cooperative strategies are dominant)., Comment: In press at ECAI 2024

Limited Voting (LV) is an approval-based method for multi-winner elections where all ballots are required to have a same fixed size. While it appears to be used as voting method in corporate governance and has some political applications, to the best of our knowledge, no formal analysis of the rule exists to date. We provide such an analysis here, prompted by a request for advice about this voting rule by a health insurance company in the Netherlands, which uses it to elect its work council. We study conditions under which LV would improve representation over standard approval voting and when it would not. We establish the extent of such an improvement, or lack thereof, both in terms of diversity and proportionality notions. These results help us understand if, and how, LV may be used as a low-effort fix of approval voting in order to enhance representation.

We prove the Bloch-Kato conjecture for critical values of Asai L-functions of p-ordinary Hilbert modular forms over quadratic fields (with p split); and one inclusion in the Iwasawa main conjecture for these L-functions (up to a power of p). Nous prouvons la conjecture de Bloch-Kato pour la fonction L Asai pour le formes modulaires Hilbert p-ordinaires associ\'ees \`a une extension r\'eelle quadratique dans laquelle p decompose. Egalement nous obtenons une inclusion de la Conjecture Principale d'Iwasawa., Comment: 13 pages

We discuss the emission of $\phi$ mesons with longitudinal and transverse polarization in ultra-relativistic heavy ion collisions. In the hadronic phase and in leading order in the kaon diluteness, $\phi$ emission is isotropic and driven by the flavor singlet and octet vector spectral functions. At next to leading order, the emissivities receive a non-isotropic correction from the flavor octet spectral function, and the non-equilibrium contributions originating from the shear and bulk viscosities. Implications for the $\phi$ meson alignment in heavy-ion collisions are discussed., Comment: 20 pages,5 figures

Compact groups (CGs) of galaxies are extreme environments for morphological transformations and the cessation of star formation. Our objective is to understand the dynamics of CGs and how their surrounding environment impacts galaxy properties. We selected a sample of 340 CGs in the Stripe 82 region, totaling 1083 galaxies, and a control sample of 2281 field galaxies. We find that at least 27\% of our sample of CGs are part of major structures, i.e. non-isolated CGs. We find a bimodality in the effective radius ($R_e$)-S\'ersic index ($n$) plane for all transition galaxies (those with $(u-r) > 2.3$ and $n<2.5$) in CGs. Additionally, transition galaxies in isolated CGs populate more densely the $R_e-n$ plane for $n < 1.75$. In contrast, transition galaxies in non-isolated CGs have smoothly increasing $n$ values, suggesting these galaxies have already suffered morphological transformation, and primarily contribute to the distribution of more compact galaxies in the $R_e-n$ plane for all transition galaxies in CGs. We also find significant differences in the specific star-formation rate (sSFR) distribution between the late-type galaxies (LTGs) ($(u-r)<2.3$ and $n< 2.5$) in non-isolated CGs and the same type of galaxies in the control sample, suggesting that the evolution of LTGs differs in non-isolated CGs. Early-type galaxies ($(u-r)>2.3$ and $n>2.5$) and transition galaxies in non-isolated CGs have lower sSFR values and a higher fraction of quenched galaxies, compared to those in isolated CGs. Based on our results, we propose an evolutionary scenario where the major structures in which the CGs are embedded accelerate the morphological transformations of their members. Our findings highlight the importance of considering the larger structures in which CGs may be located, when analysing the properties of their galaxy, as this can significantly affect the evolution of CGs and their galaxies., Comment: Submitted to A&A, 13 pages, 9 figures

In this study, we consider a pulse-Doppler radar relying on a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) for scanning a given volume; the radar receiver is collocated with the STAR-RIS and aims to detect moving targets and estimate their radial velocity in the presence of clutter. To separate the echoes received from the transmissive and reflective half-spaces, the STAR-RIS superimposes a different slow-time modulation on the pulses redirected in each half-space, while the radar detector employs a decision rule based on a generalized information criterion (GIC). Two scanning policies are introduced, namely, simultaneous and sequential scanning, with different tradeoffs in terms of radial velocity estimation accuracy and complexity of the radar detector., Comment: Accepted at the 2024 European Signal Processing Conference, Lyon, France

In this work, we consider a backscatter communication system wherein multiple asynchronous sources (tags) exploit the reverberation generated by a nearby radar transmitter as an ambient carrier to deliver a message to a common destination (reader) through a number of available subchannels. We propose a new encoding strategy wherein each tag transmits both pilot and data symbols on each subchannel and repeats some of the data symbols on multiple subchannels. We then exploit this signal structure to derive two semi-blind iterative algorithms for joint estimation of the data symbols and the subchannel responses that are also able to handle some missing measurements. The proposed encoding/decoding strategies are scalable with the number of tags and their payload and can achieve different tradeoffs in terms of transmission and error rates. Some numerical examples are provided to illustrate the merits of the proposed solutions., Comment: Submitted to the IEEE Transactions on Wireless Communications

We study 51 jellyfish galaxy candidates in the Fornax, Antlia, and Hydra clusters. These candidates are identified using the JClass scheme based on the visual classification of wide-field, twelve-band optical images obtained from the Southern Photometric Local Universe Survey. A comprehensive astrophysical analysis of the jellyfish (JClass > 0), non-jellyfish (JClass = 0), and independently organized control samples is undertaken. We develop a semi-automated pipeline using self-supervised learning and similarity search to detect jellyfish galaxies. The proposed framework is designed to assist visual classifiers by providing more reliable JClasses for galaxies. We find that jellyfish candidates exhibit a lower Gini coefficient, higher entropy, and a lower 2D S\'ersic index as the jellyfish features in these galaxies become more pronounced. Jellyfish candidates show elevated star formation rates (including contributions from the main body and tails) by $\sim$1.75 dex, suggesting a significant increase in the SFR caused by the ram-pressure stripping phenomenon. Galaxies in the Antlia and Fornax clusters preferentially fall towards the cluster's centre, whereas only a mild preference is observed for Hydra galaxies. Our self-supervised pipeline, applied in visually challenging cases, offers two main advantages: it reduces human visual biases and scales effectively for large datasets. This versatile framework promises substantial enhancements in morphology studies for future galaxy image surveys., Comment: 25 pages, 22 figures, accepted for publication in MNRAS

Quantum generative modeling is among the promising candidates for achieving a practical advantage in data analysis. Nevertheless, one key challenge is to generate large-size images comparable to those generated by their classical counterparts. In this work, we take an initial step in this direction and introduce the Latent Style-based Quantum GAN (LaSt-QGAN), which employs a hybrid classical-quantum approach in training Generative Adversarial Networks (GANs) for arbitrary complex data generation. This novel approach relies on powerful classical auto-encoders to map a high-dimensional original image dataset into a latent representation. The hybrid classical-quantum GAN operates in this latent space to generate an arbitrary number of fake features, which are then passed back to the auto-encoder to reconstruct the original data. Our LaSt-QGAN can be successfully trained on realistic computer vision datasets beyond the standard MNIST, namely Fashion MNIST (fashion products) and SAT4 (Earth Observation images) with 10 qubits, resulting in a comparable performance (and even better in some metrics) with the classical GANs. Moreover, we analyze the barren plateau phenomena within this context of the continuous quantum generative model using a polynomial depth circuit and propose a method to mitigate the detrimental effect during the training of deep-depth networks. Through empirical experiments and theoretical analysis, we demonstrate the potential of LaSt-QGAN for the practical usage in the context of image generation and open the possibility of applying it to a larger dataset in the future., Comment: 28 pages, 22 figures

Databases are an essential component of modern computing infrastructures and allow efficient access to data stored persistently. Their structure depends on the type and relationships of the stored data elements and on the access pattern. Extending the concept of databases to the quantum domain is expected to increase both the storage efficiency and the access parallelism through quantum superposition. In addition, quantum databases may be seen as the result of a prior state preparation ready to be used by quantum algorithms when needed. On the other hand, limiting factors exist and include entanglement creation, the impossibility of perfect copying due to the no-cloning theorem, and the impossibility of coherently erasing a quantum state. In this work, we introduce quantum databases within the broader context of data structures using classical and quantum data and indexing. In particular, we are interested in quantum databases practical implementation and usability, focusing on the definition of the basic operations needed to create and manipulate data stored in a superposition state. Specifically, we address the case of quantum indexing in combination with classical data. For this scenario, we define the operations for database preparation, extension, removal of indices, writing, and read-out of data, as well as index permutation. We present their algorithmic implementation and highlight their advantages and limitations. Finally, we introduce steps toward defining the same operations in the more general context of quantum indexing and quantum data., Comment: 26 pages, 4 figures

Graphlets of order $k$ in a graph $G$ are connected subgraphs induced by $k$ nodes (called $k$-graphlets) or by $k$ edges (called edge $k$-graphlets). They are among the interesting subgraphs in network analysis to get insights on both the local and global structure of a network. While several algorithms exist for discovering and enumerating graphlets, the cost per solution of such algorithms typically depends on the size of the graph $G$, or its maximum degree. In real networks, even the latter can be in the order of millions, whereas $k$ is typically required to be a small value. In this paper we provide the first algorithm to list all graphlets of order $k$ in a graph $G=(V,E)$ with an amortized cost per solution depending \emph{solely} on the order $k$, contrarily to previous approaches where the cost depends \emph{also} on the size of $G$ or its maximum degree. Specifically, we show that it is possible to list $k$-graphlets in $O(k^2)$ time per solution, and to list edge $k$-graphlets in $O(k)$ time per solution. Furthermore we show that, if the input graph has bounded degree, then the cost per solution for listing $k$-graphlets is reduced to $O(k)$. Whenever $k = O(1)$, as it is often the case in practical settings, these algorithms are the first to achieve constant time per solution.

We give a lattice-theoretic classification of non-symplectic automorphisms of prime order of irreducible holomorphic symplectic manifolds of OG10 type. We determine which automorphisms are induced by a non-symplectic automorphism of prime order of a cubic fourfold on the associated LSV manifolds, giving a geometric and lattice-theoretic description of the algebraic and transcendental lattices of the cubic fourfold. As an application we discuss the rationality conjecture for a general cubic fourfold with a non-symplectic automorphism of prime order., Comment: Minor improvements, comments are very welcome!

We have studied the spin polarization of $\Lambda$ hyperons in heavy ion collisions at center-of-mass energies $\sqrt{s_{NN}} = 200$ GeV and $\sqrt{s_{NN}} = 5.02$ TeV carried out at RHIC and LHC colliders. We have calculated the mean spin vector at local thermodynamic equilibrium, including all known first-order terms in the gradients of the thermo-hydrodynamic fields, assuming that the hadronization hypersurface has a uniform temperature. We have also included the feed-down contributions to the polarization of $\Lambda$ stemming from the decays of polarized $\Sigma^*$ and $\Sigma^0$ hyperons. The obtained results are in good agreement with the data. In general, the component of the spin vector along the global angular momentum, orthogonal to the reaction plane, shows strong sensitivity to the initial longitudinal flow velocity. Furthermore, the longitudinal component of the spin vector turns out to be very sensitive to the bulk viscosity of the plasma at the highest LHC energy. Therefore, the azimuthal dependence of spin polarization can effectively constrain the initial hydrodynamic conditions and the transport coefficients of the Quark Gluon Plasma., Comment: 15 pages, 10 figures. V4: Modified Glissando IS. Polarization computed in more centralities

We generalize previous studies on constraining operators of the Standard Model Effective Field Theory using Drell-Yan (DY) measurements to include at the same time all relevant operators and uncertainties. It has been shown that fully differential measurements (triple differential for neutral and double differential for charged) are more sensitive to EFT effects. Nevertheless, due to the finite statistics, the fully differential measurements sacrifice some statistical power on the shape (less invariant mass or transverse momentum bins) in favour of more kinematic variables. We show that when the observables are particularly sensitive to the shape of the distributions, such as the invariant mass of the two leptons in neutral DY, the single differential measurement with more bins, may be as sensitive as the fully differential one, at least for specific EFT operators. This suggests to always supplement fully differential analyses with projections into the relevant distributions evaluated with finer bins., Comment: 11 pages, 2 figures, 3 tables

The non-trivial complete totally geodesic submanifolds of the complex hyperbolic plane $\mathbb H_{\mathbb C}^2$ are the complex geodesics and the real planes. We present two new proofs for this fact. One is a short proof based on an algebraic formula for the Riemann curvature tensor due to S. Anan'in and C. Grossi and resembles the traditional proof using Lie theory. The other is purely elementary and geometric, relying on the structures in $\mathbb H_{\mathbb C}^2$ instead of general theories. In this second approach, we prove a slightly stronger result: the only non-trivial complete totally geodesic subsets of $\mathbb H_{\mathbb C}^2$ are the complex geodesics and the real planes without assuming that the subsets are submanifolds a priori. This second proof is also intriguing for only making use of elementary geometric constructions.

Generalizing work of Markushevich--Tikhomirov and Arbarello--Sacc\`a--Ferretti, we use relative Prym varieties to construct Lagrangian fibered symplectic varieties in infinitely many dimensions. We then give criteria for when the construction yields primitive symplectic varieties, respectively, irreducible symplectic varieties. The starting point of the construction is a K3 surface endowed with an anti-symplectic involution and an effective linear system on the quotient surface. We give sufficient conditions on the linear system to ensure that the relative Prym varieties satisfy the criteria above. As a consequence, we produce infinite series of irreducible symplectic varieties., Comment: 41 pages, 2 figures, comments welcome!

Probabilistic electricity price forecasting (PEPF) is subject of increasing interest, following the demand for proper quantification of prediction uncertainty, to support the operation in complex power markets with increasing share of renewable generation. Distributional neural networks ensembles have been recently shown to outperform state of the art PEPF benchmarks. Still, they require critical reliability enhancements, as fail to pass the coverage tests at various steps on the prediction horizon. In this work, we propose a novel approach to PEPF, extending the state of the art neural networks ensembles based methods through conformal inference based techniques, deployed within an on-line recalibration procedure. Experiments have been conducted on multiple market regions, achieving day-ahead forecasts with improved hourly coverage and stable probabilistic scores., Comment: 48 pages

The Fornax galaxy cluster is the richest nearby (D ~ 20 Mpc) galaxy association in the southern sky. As such, it provides a wealth of oportunities to elucidate on the processes where environment holds a key role in transforming galaxies. Although it has been the focus of many studies, Fornax has never been explored with contiguous homogeneous wide-field imaging in 12 photometric narrow- and broad-bands like those provided by the Southern Photometric Local Universe Survey (S-PLUS). In this paper we present the S-PLUS Fornax Project (S+FP) that aims to comprehensively analyse the galaxy content of the Fornax cluster using S-PLUS. Our data set consists of 106 S-PLUS wide-field frames (FoV ~ 1.4 x 1.4 deg$^2$) observed in five SDSS-like ugriz broad-bands and seven narrow-bands covering specific spectroscopic features like [OII], CaII H+K, H$\delta$, G-band, Mg b triplet, H$\alpha$, and the CaII triplet. Based on S-PLUS specific automated photometry, aimed at correctly detecting Fornax galaxies and globular clusters in S-PLUS images, our dataset provides the community with catalogues containing homogeneous 12-band photometry for ~ 3 x 10$^6$ resolved and unresolved objects within a region extending over ~ 208 deg$^2$ (~ 5 Rvir in RA) around Fornax' central galaxy, NGC 1399. We further explore the EAGLE and IllustrisTNG cosmological simulations to identify 45 Fornax-like clusters and generate mock images on all 12 S-PLUS bands of these structures down to galaxies with M$\star \geq 10^8$ M$\odot$. The S+FP dataset we put forward in this first paper of a series will enable a variety of studies some of which are briefly presented., Comment: 25 pages, 30 figures, accepted for publication in MNRAS

The optimal operation of transportation networks is often susceptible to unexpected disruptions, such as traffic incidents and social events. Many established control strategies rely on mathematical models that struggle to cope with real-world uncertainties, leading to a significant decline in effectiveness when faced with substantial disruptions. While previous research works have dedicated efforts to improving the robustness or resilience of transportation systems against disruptions, this paper applies the cutting-edge concept of antifragility to better design a traffic control strategy for urban road networks. Antifragility sets itself apart from robustness and resilience as it represents a system's ability to not only withstand stressors, shocks, and volatility but also thrive and enhance performance in the presence of such adversarial events. Hence, modern transportation systems call for solutions that are antifragile. In this work, we propose a model-free deep Reinforcement Learning (RL) scheme to control a two-region urban traffic perimeter network. The system exploits the learning capability of RL under disruptions to achieve antifragility. By monitoring the change rate and curvature of the traffic state with the RL framework, the proposed algorithm anticipates imminent disruptions. An additional term is also integrated into the RL algorithm as redundancy to improve the performance under disruption scenarios. When compared to a state-of-the-art model predictive control approach and a state-of-the-art RL algorithm, our proposed method demonstrates two antifragility-related properties: (a) gradual performance improvement under disruptions of constant magnitude; and (b) increasingly superior performance under growing disruptions., Comment: 32 pages, 13 figures

In this manuscript, we explore the intersection of QML and TN in the context of the one-dimensional ANNNI model with a transverse field. The study aims to concretely connect QML and TN by combining them in various stages of algorithm construction, focusing on phase diagram reconstruction for the ANNNI model, with supervised and unsupervised techniques. The model's significance lies in its representation of quantum fluctuations and frustrated exchange interactions, making it a paradigm for studying magnetic ordering, frustration, and the presence of a floating phase. It concludes with discussions of the results, including insights from increased system sizes and considerations for future work, such as addressing limitations in QCNN and exploring more realistic implementations of QC., Comment: 15 pages, 15 figures

Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several universality properties have been proven. However, in the case of quantum generative modelling, much less is known, especially when the task is to model distributions over continuous variables. In this work, we elucidate expectation value sampling-based models. Such models output the expectation values of a set of fixed observables from a quantum circuit into which classical random data has been uploaded. We prove the universality of such variational quantum algorithms for the generation of multivariate distributions. We explore various architectures which allow universality and prove tight bounds connecting the minimal required qubit number, and the minimal required number of measurements needed. Our results may help guide the design of future quantum circuits in generative modelling tasks.

Quantum machine learning provides a fundamentally novel and promising approach to analyzing data. However, many data sets are too complex for currently available quantum computers. Consequently, quantum machine learning applications conventionally resort to dimensionality reduction algorithms, e.g., auto-encoders, before passing data through the quantum models. We show that using a classical auto-encoder as an independent preprocessing step can significantly decrease the classification performance of a quantum machine learning algorithm. To ameliorate this issue, we design an architecture that unifies the preprocessing and quantum classification algorithms into a single trainable model: the guided quantum compression model. The utility of this model is demonstrated by using it to identify the Higgs boson in proton-proton collisions at the LHC, where the conventional approach proves ineffective. Conversely, the guided quantum compression model excels at solving this classification problem, achieving a good accuracy. Additionally, the model developed herein shows better performance compared to the classical benchmark when using only low-level kinematic features., Comment: 9 pages, 3 figures

Major cities worldwide experience problems with the performance of their road transportation systems, and the continuous increase in traffic demand presents a substantial challenge to the optimal operation of urban road networks and the efficiency of traffic control strategies. The operation of transportation systems is widely considered to display fragile property, i.e., the loss in performance increases exponentially with the linearly increasing magnitude of disruptions. Meanwhile, the risk engineering community is embracing the novel concept of antifragility, enabling systems to learn from historical disruptions and exhibit improved performance under black swan events. In this study, based on established traffic models, namely fundamental diagrams and macroscopic fundamental diagrams, we first conducted a rigorous mathematical analysis to prove the fragile nature of the systems theoretically. Subsequently, we propose a skewness-based indicator that can be readily applied to cross-compare the degree of fragility for different networks solely dependent on the MFD-related parameters. At last, by taking real-world stochasticity into account, we implemented a numerical simulation with realistic network data to bridge the gap between the theoretical proof and the real-world operations, to reflect the potential impact of uncertainty on the fragility of the systems. This work aims to demonstrate the fragile nature of road transportation systems and help researchers better comprehend the necessity to consider explicitly antifragile design for future traffic control strategies., Comment: 44 pages, 15 figures

This white paper outlines a long-term scientific vision for the development of digital-democracy technology. We contend that if digital democracy is to meet the ambition of enabling a participatory renewal in our societies, then a comprehensive multi-methods research effort is required that could, over the years, support its development in a democratically principled, empirically and computationally informed way. The paper is co-authored by an international and interdisciplinary team of researchers and arose from the Lorentz Center Workshop on ``Algorithmic Technology for Democracy'' (Leiden, October 2022).

Terminalizations of symplectic quotients are sources of new deformation types of irreducible symplectic varieties. We classify all terminalizations of quotients of Hilbert schemes of K3 surfaces or of generalized Kummer varieties, by finite groups of symplectic automorphisms induced from the underlying K3 or abelian surface. We determine their second Betti number and the fundamental group of their regular locus. In the Kummer case, we prove that the terminalizations have quotient singularities, and determine the singularities of their universal quasi-\'etale cover. In particular, we obtain at least nine new deformation types of irreducible symplectic varieties of dimension four. Finally, we compare our deformation types with those in [FM21; Men22]. The smooth terminalizations are only three and of K$3^{[n]}$-type, and surprisingly they all appeared in different places in the literature [Fuj83; Kaw09; Flo22]., Comment: 47 pages, 11 tables, 5 pictures. Comments are welcome!

Hamiltonian moments in Fourier space - expectation values of the unitary evolution operator under a Hamiltonian at different times - provide a convenient framework to understand quantum systems. They offer insights into the energy distribution, higher-order dynamics, response functions, correlation information and physical properties. This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. These techniques, combined with purification and error suppression methods, effectively address quantum hardware decoherence. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude. Moreover, quantum circuits involving up to 266 CNOT gates over five qubits demonstrate high accuracy under these methodologies when run on IBM superconducting quantum devices., Comment: 12 pages, 7 pages appendix, comments are welcome

Understanding the emergence of cooperation in systems of computational agents is crucial for the development of effective cooperative AI. Interaction among individuals in real-world settings are often sparse and occur within a broad spectrum of incentives, which often are only partially known. In this work, we explore how cooperation can arise among reinforcement learning agents in scenarios characterised by infrequent encounters, and where agents face uncertainty about the alignment of their incentives with those of others. To do so, we train the agents under a wide spectrum of environments ranging from fully competitive, to fully cooperative, to mixed-motives. Under this type of uncertainty we study the effects of mechanisms, such as reputation and intrinsic rewards, that have been proposed in the literature to foster cooperation in mixed-motives environments. Our findings show that uncertainty substantially lowers the agents' ability to engage in cooperative behaviour, when that would be the best course of action. In this scenario, the use of effective reputation mechanisms and intrinsic rewards boosts the agents' capability to act nearly-optimally in cooperative environments, while greatly enhancing cooperation in mixed-motive environments as well.

Geometric quantum machine learning based on equivariant quantum neural networks (EQNN) recently appeared as a promising direction in quantum machine learning. Despite the encouraging progress, the studies are still limited to theory, and the role of hardware noise in EQNN training has never been explored. This work studies the behavior of EQNN models in the presence of noise. We show that certain EQNN models can preserve equivariance under Pauli channels, while this is not possible under the amplitude damping channel. We claim that the symmetry breaking grows linearly in the number of layers and noise strength. We support our claims with numerical data from simulations as well as hardware up to 64 qubits. Furthermore, we provide strategies to enhance the symmetry protection of EQNN models in the presence of noise., Comment: 12 pages, 10 figures. supplementary material 7 pages, 6 figures

This Letter investigates in detail the performance and advantages of a new quantum Monte Carlo integrator, dubbed Quantum Fourier Iterative Amplitude Estimation (QFIAE), to numerically evaluate for the first time loop Feynman integrals in a near-term quantum computer and a quantum simulator. In order to achieve a quadratic speedup, QFIAE introduces a Quantum Neural Network (QNN) that efficiently decomposes the multidimensional integrand into its Fourier series. For a one-loop tadpole Feynman diagram, we have successfully implemented the quantum algorithm on a real quantum computer and obtained a reasonable agreement with the analytical values. Oneloop Feynman diagrams with more external legs have been analyzed in a quantum simulator. These results thoroughly illustrate how our quantum algorithm effectively estimates loop Feynman integrals and the method employed could also find applications in other fields such as finance, artificial intelligence, or other physical sciences., Comment: 9 pages (7+2), 7 figures, 3 tables

In many causal studies, outcomes are censored by death, in the sense that they are neither observed nor defined for units who die. In such studies, the focus is usually on the stratum of always survivors up to a single fixed time s. Building on a recent strand of the literature, we propose an extended framework for the analysis of longitudinal studies, where units can die at different time points, and the main endpoints are observed and well defined only up to the death time. We develop a Bayesian longitudinal principal stratification framework, where units are cross classified according to the longitudinal death status. Under this framework, the focus is on causal effects for the principal strata of units that would be alive up to a time point s irrespective of their treatment assignment, where these strata may vary as a function of s. We can get precious insights into the effects of treatment by inspecting the distribution of baseline characteristics within each longitudinal principal stratum, and by investigating the time trend of both principal stratum membership and survivor-average causal effects. We illustrate our approach for the analysis of a longitudinal observational study aimed to assess, under the assumption of strong ignorability of treatment assignment, the causal effects of a policy promoting start ups on firms survival and hiring policy, where firms hiring status is censored by death.

Heavy quarks (i.e. charm and beauty) in heavy-ion collisions are initially produced out of kinetic equilibrium via hard partonic scattering processes. However, recent measurements of anisotropic flow of charmed hadrons pose the question regarding the thermalization of heavy quarks in the quark-gluon plasma (QGP). Exploiting a mapping between transport theory and fluid dynamics, we develop a fluid-dynamic description for charm quarks and show results for charm-hadron momentum distributions. Inspired by recent Lattice-QCD (LQCD) calculations, we show that a late hydrodynamization within the lifetime of the QGP is possible also for beauty quarks., Comment: 4 pages, 2 figures, Contribution to Quark Matter 2023. arXiv admin note: substantial text overlap with arXiv:2307.15580

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions., Comment: 60 pages, 14 figures; comments welcome

Let $E/\mathbb{Q}$ be an elliptic curve and $p$ an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for the $p$-adic Tate module of $E$ derived from Heegner points on $E$ over ring class fields of an imaginary quadratic field $K$ is non-trivial. In this paper we prove Kolyvagin's conjecture in the cases where $p$ is a prime of good ordinary reduction for $E$ that splits in $K$ and a $p$-adic anticyclotomic Iwasawa Main Conjecture for $E/K$ holds. In particular, our results cover many cases where $p$ is an Eisenstein prime, complementing W. Zhang's progress towards the conjecture. Our methods also yield a proof of a refinement of Kolyvagin's conjecture expressing the divisibility index of the $p$-adic Heegner point Kolyvagin system in terms of the Tamagawa numbers of $E$, as conjectured by W. Zhang in 2014, as well as proofs of analogous results for the Kolyvagin systems obtained from the cyclotomic Euler system of Beilinson--Kato elements., Comment: 30 pages, comments are welcome!