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Online event via MS Teams, ISSN: 0148-7191, e-ISSN: 2688-3627; International audience

We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We encounter two phase transitions with increasing projection rate: The first is the volume-to-area law transition observed in quantum circuits with projective measurements; The second separates the pure Poisson level statistics phase at large projective measurement rates from a regime of residual level repulsion in the entanglement spectrum within the area-law phase, characterized by non-universal level spacing statistics that interpolates between the Wigner-Dyson and Poisson distributions. By applying a tensor network contraction algorithm introduced in Ref. [1] to the circuit spacetime, we identify this second projective-measurement-driven transition as a percolation transition of entangled bonds. The same behavior is observed in both circuits of random two-qubit unitaries and circuits of universal gate sets, including the set implemented by Google in its Sycamore circuits., 7 pages, 7 figures

An amendment to this paper has been published and can be accessed via the original article.

Quantum many-body systems (QMBs) are some of the most challenging physical systems to simulate numerically. Methods involving approximations for tensor network (TN) contractions have proven to be viable alternatives to algorithms such as quantum Monte Carlo or simulated annealing. However, these methods are cumbersome, difficult to implement, and often have significant limitations in their accuracy and efficiency when considering systems in more than one dimension. In this paper, we explore the exact computation of TN contractions on two-dimensional geometries and present a heuristic improvement of TN contraction that reduces the computing time, the amount of memory, and the communication time. We run our algorithm for the Ising model using memory optimized x1.32x large instances on Amazon Web Services (AWS) Elastic Compute Cloud (EC2). Our results show that cloud computing is a viable alternative to supercomputers for this class of scientific applications., 25 pages, 11 figures

International audience

International audience; Improvement of vibroacoustic models prediction capabilities requires an adapted indicator to compare experimental measurements with the results of the computational model. When dealing with highly uncertain objects such as series production cars, a probabilistic approach is mandatory to be able to describe the dispersion of experimental results. Moreover, a probabilistic non-parametric model also account for modeling uncertainties and simplifications that are part of any engineering process. The proposed approach deals with Frequency Response Functions since FRFs are the common way to handle vibroacoustic models. When considering multiple input and outputpoints configuration, FRFs are frequency dependent complex matrices. Since the probabilistic modeling is available in current vibroacoustic software, collections of random realizations of the FRF matrix can be computed from the existing FE model. The model’s likelihood naturally appears as the probability of a measured quantity to be part of its model. It is a single number that can advantageously be used as an indicator of the model‘s relevance regarding measurements. A novel complex FRF matrix statistical reduction is proposed, allowing the model’s likelihood computation. This reduction relies on the separation of statistically independent components such that the probability of the whole is the product of the probability of the components. The reduction is performed by a two stage Independent Component Analysis, first along the frequencies and second on frequency independent complex matrices. For each of the components, the joint probability density function of the complex coefficient is constructed from the various realization of the considered FRF matrix. The projection of any experimental or computed matrix on the components basis provides the complex coefficients which probabilities are known. The product of the componentprobabilities is the model’s likelihood. The proposed approach is applied to a mid-size vehicle body.

National audience; Dans un contexte probabiliste, l’amélioration des capacités de prédiction des modèles vibroacoustiques nécessite un indicateur adapté pour comparer les mesures avec les prédictions. La comparaison est faite en utilisant la vraisemblance, dès qu’elle peut être estimée pour un résultat donné. L’analyse repose principalement sur des fonctions de réponse en fréquence complexes à valeurs matricielles qui peuvent être mesurées et calculées. Une réduction statistique est proposée. Cette réduction statistique présente en plus de la réduction des données, une analyse du comportement physique du système étudié.

International audience; Improvement of vibroacoustic models prediction capabilities in a probabilistic context requires a adapted metric to compare experimental results with stochasitic computations. The likelihood appears as the natural tool to compare experiments with probabilistic computations as soon as the probability of a given result may be computed. Since vibroacoustic analysis mainly rely on complex Frequency Response Functions ([FRF] = {ω → [FRF(ω)]}) matrices that can be easily measured and computed, the likelihood of such complex and frequency dependent matrices is investigated. A two stage statistical reduction, based on Indepen-dant Components Analysis, is proposed in order to separate statisticaly independent components with complex amplitudes which probability may be computed independently one from each others. Bi-dimensional probability density fonctions of the complex components amplitudes are deduced from a Monte-Carlo simulation of a non-parametric stochastic model, using MSC/NASTRAN. The proposed statistical reduction presents many interesting properties regarding the physical understanding of FRF matrices as well as a numerical aspects.