Related papers: Learning Feynman Diagrams with Tensor Trains
Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…
For a long time, the predictive limits of perturbative quantum field theory have been limited by our inability to carry out loop calculations to arbitrarily high order, which become increasingly complex as the order of perturbation theory…
We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single…
Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…
Solving the Schr\"{o}dinger equation for interacting many-body quantum systems faces computational challenges due to exponential scaling with system size. This complexity limits the study of important phenomena in materials science and…
Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…
The conductance of two Anderson impurity models, one with two-fold and another with four-fold degeneracy, representing two types of quantum dots, is calculated using a world-line quantum Monte Carlo (QMC) method. Extrapolation of the…
The tensor network algorithm, a family of prevalent numerical methods for quantum many-body problems, aptly captures the entanglement properties intrinsic to quantum systems, enabling precise representation of quantum states. However, its…
The quantum many-body problem lies at the center of the most important open challenges in condensed matter, quantum chemistry, atomic, nuclear, and high-energy physics. While quantum Monte Carlo, when applicable, remains the most powerful…
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body…
Many-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the…
We present a novel method for precise numerical solution of the irreducible two-body problem and apply it to excitons in solids. The approach is based on the Monte Carlo simulation of the two-body Green function specified by Feynman's…
High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the…
An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Green's function. Typically, the imaginary-time Green's function is generated by Monte Carlo methods. As the one-point fermionic…
We study a neural network framework for the numerical evaluation of Feynman loop integrals that are fundamental building blocks for perturbative computations of physical observables in gauge and gravity theories. We show that such a machine…
We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…