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These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…
Computational elements in thermodynamics have become increasingly important in contemporary chemical-engineering research and practice. However, traditional thermodynamics instruction provides little exposure to computational…
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and…
Twist fields are a powerful formal tool to compute R\'enyi entropies in quantum many-body systems, but their conventional formulation in tensor network states involves operations acting on virtual degrees of freedom, which are not directly…
Linear recurrent neural networks (LRNNs) provide a structured approach to sequence modeling that bridges classical linear dynamical systems and modern deep learning, offering both expressive power and theoretical guarantees on stability and…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
Transformers have shown a remarkable ability for in-context learning (ICL), making predictions based on contextual examples. However, while theoretical analyses have explored this prediction capability, the nature of the inferred context…
We construct an algorithm to simulate imaginary time evolution of translationally invariant spin systems with local interactions on an infinite, symmetric tree. We describe the state by symmetric iPEPS and use translation-invariant…
In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical systems of paramount relevance in Celestial Mechanics and other…
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…
Scorio.jl is a Julia package for evaluating and ranking systems from repeated responses to shared tasks. It provides a common tensor-based interface for direct score-based, pairwise, psychometric, voting, graph, and listwise methods, so the…
There are plenty of excellent plotting libraries. Each excels at a different use case: one is good for printed 2D publication figures, the other at interactive 3D graphics, a third has excellent L A TEX integration or is good for creating…
In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require…
MultiPrecisionArrays.jl is a Julia package. This package provides data structures and solvers for several variants of iterative refinement. It will become much more useful when half precision (aka Float16) is fully supported in LAPACK/BLAS.…
Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the…
Temporal information extraction (IE) aims to extract structured temporal information from unstructured text, thereby uncovering the implicit timelines within. This technique is applied across domains such as healthcare, newswire, and…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
We introduce the third major version of Metatheory.jl, a Julia library for general-purpose metaprogramming and symbolic computation. Metatheory.jl provides a flexible and performant implementation of e-graphs and Equality Saturation (EqSat)…