Related papers: Lecture Notes on Normalizing Flows for Lattice Qua…

Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed,…

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to…

The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from…

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…

These lectures about lattice field theory were written for, and given at, TASI 2019, ``The many dimensions of quantum field theory.'' The students at this TASI were mostly interested in formal things, and so these are slightly unusual…

Quantum computers, with parallel computing and entanglement effects, excel in cryptography analysis and big data processing. However, they are not fully developed yet, and their performance needs further evaluation. Traditional computer…

This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…

A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new effect is an underlying lattice which is…

The last decade has seen an explosive growth of interest in exploiting developments in machine learning to accelerate lattice QCD calculations. On the sampling side, generative models are a promising approach to mitigating critical slowing…

We review the recent literature on lattice simulations for few- and many-body systems. We focus on methods and results that combine the framework of effective field theory with computational lattice methods. Lattice effective field theory…

After discussing the problem of defining the hydrodynamic limit from microscopic scales, we give an introduction to ideal hydrodynamics in the Lagrange picture, and show that it can be viewed as a field theory, which can be quantized using…

In this paper, the key ideas of characterizing universality classes of dissipation-free (incompressible) quantum Hall fluids by mathematical objects called quantum Hall lattices are reviewed. Many general theorems about the classification…

An old and apparently persistent problem in numerical lattice QCD is that the simulations tend to get trapped in a sector of fixed topological charge when the lattice spacing is taken to zero. The effect sets in very rapidly and may…

We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian approach to the problem of bound states on the Light Front and the limiting transition from formulating a theory in Lorentzian coordinates…

Lecture notes with a brief introduction to Quantum field theory and the Standard Model are presented. The lectures were given at the 2017 European School of High-Energy Physics. The main features, the present status, and problems of the…

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…

There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process,…

The lattice Boltzmann method has become a standard technique for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular…

The lecture note consists of four parts. In the first part, we review a 2+1 dimensional lattice model which realizes emergent supersymmetry at a quantum critical point. The second part is devoted to a phenomenon called fractionalization…