Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation.

Understanding the real-time evolution of many-electron quantum systems is essential for studying dynamical properties in condensed matter, quantum chemistry, and complex materials, yet it poses a significant theoretical and computational challenge. Our work introduces a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations by accurately capturing many-body correlations. We employ time-dependent Jastrow factors and backflow transformations, enhanced through neural networks parameterizations.

Variational benchmarks for quantum many-body problems.

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.

Network control by a constrained external agent as a continuous optimization problem.

Social science studies dealing with control in networks typically resort to heuristics or solely describing the control distribution. Optimal policies, however, require interventions that optimize control over a socioeconomic network subject to real-world constraints. We integrate optimisation tools from deep-learning with network science into a framework that is able to optimize such interventions in real-world networks.

Noise robustness of persistent homology on greyscale images, across filtrations and signatures.

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors.

Combined frequency-tagging EEG and eye-tracking measures provide no support for the "excess mouth/diminished eye attention" hypothesis in autism.

Background: Scanning faces is important for social interactions. Difficulty with the social use of eye contact constitutes one of the clinical symptoms of autism spectrum disorder (ASD). It has been suggested that individuals with ASD look less at the eyes and more at the mouth than typically developing (TD) individuals, possibly due to gaze aversion or gaze indifference.

Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries.

Although artificial neural networks have recently been proven to provide a promising new framework for constructing quantum many-body wave functions, the parametrization of a quantum wave function with non-abelian symmetries in terms of a Boltzmann machine inherently leads to biased results due to the basis dependence. We demonstrate that this problem can be overcome by sampling in the basis of irreducible representations instead of spins, for which the corresponding ansatz respects the non-abelian symmetries of the system. We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-1/2 and spin-1 degrees of freedom, and obtain a substantially higher accuracy than when using the s_{z} basis as an input to the neural network.