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We present a new ab-initio approach to study molecules containing heavy atoms strongly interacting with quantum fields in optical devices. The relativistic quantum electrodynamics (QED) theory has been rewritten with a formalism close to relativistic quantum chemistry. This general framework represents the ideal starting point to extend the main quantum chemistry methods to relativistic QED. The Polaritonic Dirac Hartree Fock (Pol-DHF) approach is the first method we propose based on this theory. Pol-DHF allows for the simulation of field induced effects on the ground and excited state properties of heavy transition metals molecular complexes. The method is able to include not only the effects of the photons but can be easily extended also to include explicit interactions with positrons. Application of Pol-DHF to three metal hydrides revealed the importance of including radiative QED corrections to the treatment in strong coupling conditions. Due to an accurate description of spin-orbit coupling, the method is able to reproduce polaritonic effects happening at the crossing between singlet and triplet potential energy surfaces., Comment: 17 pages, 8 figures

Variational Quantum Imaginary Time Evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that requiring the imaginary-time evolution to be correct only when projected onto a chosen set of operators allows to achieve a twofold reduction in circuit depth by bypassing fidelity estimations, and reduces measurement complexity from quadratic to linear in the number of parameters. We demonstrate by a simulation of the transverse-field Ising model that our algorithm achieves a several orders of magnitude improvement in the number of measurements required for the same accuracy.

In recent years, significant advancements have been made in computational methods for analyzing masonry structures. Within the Finite Element Method, two primary approaches have gained traction: Micro and Macro Scale modeling, and their subsequent integration via Multi-scale methods based on homogenization theory and the representative volume element concept. While Micro and Multi-scale approaches offer high fidelity, they often come with a substantial computational burden. On the other hand, calibrating homogenized material parameters in Macro-scale approaches presents challenges for practical engineering problems. Machine learning techniques have emerged as powerful tools for training models using vast datasets from various domains. In this context, we propose leveraging Machine Learning methods to develop a novel homogenization strategy for the in-plane analysis of masonry structures. This strategy involves automatically calibrating a continuum nonlinear damage constitutive law and an appropriate yield criteria using relevant data derived from Micro-scale analysis. The optimization process not only enhances material parameters but also refines yield criteria and damage evolution laws to better align with existing data. To achieve this, a virtual laboratory is created to conduct micro-model simulations that account for the individual behaviors of constituent materials. Subsequently, a data isotropization process is employed to reconcile the results with typical isotropic constitutive models. Next, an optimization algorithm that minimizes the difference of internal dissipated work between the micro and macro scales is executed. We apply this technique to the in-plane homogenization of a Flemish bond masonry wall. Evaluation examples, including simulations of shear and compression tests, demonstrate the method's accuracy compared to micro modeling of the entire structure., Comment: Submitted to Computers and Structures

While automated vehicle (AV) research has grown steadily in recent years, the impact of automated lane changing behavior on transportation systems remains a largely understudied topic. The present work aims to explore the effects of automated lane changing behavior on urban network efficiency as the penetration rate of AVs increases. To the best of the authors knowledge, this represents the first attempt to do so by isolating the effects of the lane changing behavior; this was obtained by considering AVs with automated lateral control, yet retaining the same longitudinal control characteristics of conventional vehicles (CV). An urban road network located in Hannover, Germany, was modeled with the microsimulation software SUMO, and several scenarios were analyzed, starting from a baseline with only CVs and then progressively increasing the AV penetration rate with 10% increments. Results highlight a modest, but statistically significant, decrease in system performance, with travel times increasing, and average speed and network capacity decreasing, as penetration rates increase. This was likely caused by a more prudent behavior of AVs, which accepted larger gaps than CVs when performing lane changing maneuvers., Comment: Accepted article version of paper presented at the 2023 8th International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS)

Shared spaces aim to reduce the dominance of motor vehicles by promoting pedestrian and cyclist activity and minimizing segregation between road users. Despite the intended scope to improve the safety of vulnerable road users, only few works in the literature focused on before after safety evaluations, mainly analyzing changes in users trajectories and speeds, traffic volumes, and conflict counts, which, while useful, cannot univocally quantify road safety. Here, we propose a more advanced methodology, based on surrogate measures of safety and Extreme Value Theory, to assess road safety before and after the implementation of a shared space. The aim is to produce a crash risk estimation in different scenarios, obtaining a quantitative and comprehensive indicator, useful to practitioners for evaluating the safety of urban design solutions. A real world case study illustrates the proposed procedure. Video data were collected on two separate days, before and after a shared space implementation, and were semiautomatically processed to extract road users trajectories. Analysis of traffic volumes, trajectories, speeds and yield ratios allowed to understand the spatial behavior of road users in the two scenarios. Traffic conflicts, identified with an innovative surrogate measure of safety called time to avoided collision point, TTAC, were then used to estimate a Lomax distribution, and therefore to model the probabilistic relationship between conflicts and crashes, eventually retrieving a crash risk estimate. Results show that the analyzed shared space was able to significantly reduce the risk of crashes, and these findings are consistent with the observed changes in users speed and spatial behavior. The analyzed case study and its limitations were useful in highlighting the methodology main features and suggesting practical prescriptions for practitioners., Comment: This is the Accepted Manuscript version. The version of record of this manuscript has been published and is available on Case Studies on Transport Policy, Volume 13, 101021

The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational quantum time evolution is a promising candidate for these tasks, as the required circuit model can be tailored to trade off available device capabilities and approximation accuracy. However, even if the circuits can be reliably executed, variational quantum time evolution algorithms quickly become infeasible for relevant system sizes due to the calculation of the Quantum Geometric Tensor (QGT). In this work, we propose a solution to this scaling problem by leveraging a dual formulation that circumvents the explicit evaluation of the QGT. We demonstrate our algorithm for the time evolution of the Heisenberg Hamiltonian and show that it accurately reproduces the system dynamics at a fraction of the cost of standard variational quantum time evolution algorithms. As an application of quantum imaginary-time evolution, we calculate a thermodynamic observable, the energy per site, of the Heisenberg model.

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by using kernel methods. Our scheme is an approximate realization of the power method, where supervised learning is used to learn the next step of the power iteration. We show that the ground state properties of arbitrary gapped quantum hamiltonians can be reached with polynomial resources under the assumption that the supervised learning is efficient. Using kernel ridge regression, we provide numerical evidence that the learning assumption is verified by applying our scheme to find the ground states of several prototypical interacting many-body quantum systems, both in one and two dimensions, showing the flexibility of our approach.

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible., Comment: 27 pages, 6 figures

We investigate the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations allowing for the computation of spectral properties in the infinite-size limit and, crucially, with arbitrary momentum resolution. We show that three distinct regimes are found as a function of doping and interaction strength, corresponding to a weakly correlated metal with properties close to those of the non-interacting system, a correlated metal with strong interaction effects including a reshaping of the Fermi surface, and a pseudogap regime at low doping in which quasiparticle excitations are selectively destroyed near the antinodal regions of momentum space. We study the physical mechanism leading to the pseudogap and show that it forms both at weak coupling when the magnetic correlation length is large and at strong coupling when it is shorter. In both cases, we show that spin-fluctuation theory can be modified in order to account for the behavior of the non-local component of the self-energy. We discuss the fate of the pseudogap as temperature goes to zero and show that, remarkably, this regime extrapolates precisely to the ordered stripe phase found by ground-state methods. This handshake between finite temperature and ground-state results significantly advances the elaboration of a comprehensive picture of the physics of the doped Hubbard model.

We introduce the Gram-Hadamard Density Operator (GHDO), a new deep neural-network architecture that can encode positive semi-definite density operators of exponential rank with polynomial resources. We then show how to embed an autoregressive structure in the GHDO to allow direct sampling of the probability distribution. These properties are especially important when representing and variationally optimizing the mixed quantum state of a system interacting with an environment. Finally, we benchmark this architecture by simulating the steady state of the dissipative transverse-field Ising model. Estimating local observables and the R\'enyi entropy, we show significant improvements over previous state-of-the-art variational approaches., Comment: 9 pages, 4 figures, 63 references

We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports perfect sampling and wave function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension., Comment: 14 pages, 10 figures

The evolution of High-Performance Computing (HPC) platforms enables the design and execution of progressively larger and more complex workflow applications in these systems. The complexity comes not only from the number of elements that compose the workflows but also from the type of computations they perform. While traditional HPC workflows target simulations and modelling of physical phenomena, current needs require in addition data analytics (DA) and artificial intelligence (AI) tasks. However, the development of these workflows is hampered by the lack of proper programming models and environments that support the integration of HPC, DA, and AI, as well as the lack of tools to easily deploy and execute the workflows in HPC systems. To progress in this direction, this paper presents use cases where complex workflows are required and investigates the main issues to be addressed for the HPC/DA/AI convergence. Based on this study, the paper identifies the challenges of a new workflow platform to manage complex workflows. Finally, it proposes a development approach for such a workflow platform addressing these challenges in two directions: first, by defining a software stack that provides the functionalities to manage these complex workflows; and second, by proposing the HPC Workflow as a Service (HPCWaaS) paradigm, which leverages the software stack to facilitate the reusability of complex workflows in federated HPC infrastructures. Proposals presented in this work are subject to study and development as part of the EuroHPC eFlows4HPC project.

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature and interaction strength. Through these quantities, we identify a weak-coupling regime, a strong-coupling regime with short-range correlations and an intermediate-coupling regime with long magnetic correlation lengths. In the spin channel, we observe an additional crossover from commensurate to incommensurate correlations. In contrast, we find charge correlations to be only short ranged for all studied temperatures, which suggests that the spin and charge responses are decoupled. These findings were obtained by a novel connected determinant diagrammatic Monte Carlo algorithm for the computation of double expansions, which we introduce in this paper. This permits us to obtain numerically exact results at unprecedentedly low temperatures $T\geq 0.067$ for interactions up to $U\leq 8$, while working on arbitrarily large lattices. Our method also allows us to gain physical insights from investigating the analytic structure of perturbative series. We connect to previous work by studying smaller lattice geometries and report substantial finite-size effects.

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good approximations to such distributions, but suffer from either intrinsic bias or high variance. In this Letter, we propose a way to make this approximation unbiased and with low variance. Our method uses physical symmetries and variable-size cluster updates which utilize the structure of autoregressive factorization. We test our method for first- and second-order phase transitions of classical spin systems, showing its viability for critical systems and in the presence of metastable states., Comment: 12 pages, 9 figures

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming a magnetic insulator at strong coupling. In this multimethod study, we combine a finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo and cellular dynamical mean-field theory, to establish several aspects of this model. We elucidate the evolution from the metallic to the insulating regime from the complementary perspectives brought by these different methods. We compute the full thermodynamics of the model on a width-four cylinder using METTS in the intermediate to strong coupling regime. We find that the insulating state hosts a large entropy at intermediate temperatures, which increases with the strength of the coupling. Correspondingly, and consistently with a thermodynamic Maxwell relation, the double occupancy has a minimum as a function of temperature which is the manifestation of the Pomeranchuk effect of increased localization upon heating. The intermediate coupling regime is found to exhibit both pronounced chiral as well as stripy antiferromagnetic spin correlations. We propose a scenario in which time-reversal symmetry-broken states compete with stripy-spin states at lowest temperatures., Comment: (23 pages, 18 figures)

We propose a minimal generalization of the celebrated Markov-Chain Monte Carlo algorithm which allows for an arbitrary number of configurations to be visited at every Monte Carlo step. This is advantageous when a parallel computing machine is available, or when many biased configurations can be evaluated at little additional computational cost. As an example of the former case, we report a significant reduction of the thermalization time for the paradigmatic Sherrington-Kirkpatrick spin-glass model. For the latter case, we show that, by leveraging on the exponential number of biased configurations automatically computed by Diagrammatic Monte Carlo, we can speed up computations in the Fermi-Hubbard model by two orders of magnitude., Comment: 10 pages, 8 figures

We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase approximation in either the particle-hole or particle-particle channels. The algorithm's efficiency is achieved by the summation over contributions of all symmetrized Feynman diagram topologies using determinants, and by integrating out analytically the two-body long-range interactions in order to yield an effective zero-range interaction. Notably, the exponential scaling of the algorithm as a function of perturbation order leads to a polynomial scaling of the approximation error with computational time for a convergent series. To assess the performance of our approach, we apply it to the non-perturbative regime of the square-lattice fermionic Hubbard model away from half-filling and report, as compared to the bare interaction expansion algorithm, significant improvements of the Monte Carlo variance as well as the convergence properties of the resulting perturbative series., Comment: 12 pages, 10 figures

We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We show that this formulation compares advantageously to the currently standard techniques due to its high efficiency, simplicity, and broad range of applicability. Our formalism permits to easily complement perturbation theory with non-perturbative information, which we illustrate by implementing expansions renormalized by the addition of a gap or the inclusion of Dynamical Mean-Field Theory. As a result, we present numerically-exact results for the square-lattice Fermi-Hubbard model in the low temperature non-Fermi-liquid regime and show the momentum-dependent suppression of fermionic excitations in the antinodal region., Comment: 6 pages, 5 figures

The use of neural networks to predict airport passenger activity choices inside the terminal is presented in this paper. Three network architectures are proposed: Feedforward Neural Networks (FNN), Long Short-Term Memory (LSTM) networks, and a combination of the two. Inputs to these models are both static (passenger and trip characteristics) and dynamic (real-time passenger tracking). A real-world case study exemplifies the application of these models, using anonymous WiFi traces collected at Bologna Airport to train the networks. The performance of the models were evaluated according to the misclassification rate of passenger activity choices. In the LSTM approach, two different multi-step forecasting strategies are tested. According to our findings, the direct LSTM approach provides better results than the FNN, especially when the prediction horizon is relatively short (20 minutes or less)., Comment: Post-print of paper presented at the 2019 6th International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS)

We demonstrate that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of non-relativistic fermions in three-dimensional continuous space. Diagrams are built from partially-dressed or fully-dressed propagators of single particles and pairs. The series is resummed by a conformal-Borel transformation that incorporates the large-order behavior and the analytic structure in the Borel plane, which are found by the instanton approach. We report highly accurate numerical results for the equation of state in the normal unpolarized regime, and reconcile experimental data with the theoretically conjectured fourth virial coefficient.