Related papers: Computer Algebra in Particle Physics
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
Symmetry lies at the heart of todays theoretical study of particle physics. Our manuscript is a tutorial introducing foundational mathematics for understanding physical symmetries. We start from basic group theory and representation theory.…
Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…
Information algebra is algebraic structure for local computation and inference. Given an initial universe set and a parameter set, we show that a soft set system over them is an information algebra. Moreover, in a soft set system, the…
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by…
Excellent computer simulations are done for a purpose. The most valid purposes are to explore uncharted territory, to resolve a well-posed scientific or technical question, or to make a design choice. Stand-alone modeling can serve the…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
This review gives a survey of numerical algorithms and software to simulate quantum computers.It covers the basic concepts of quantum computation and quantum algorithms and includes a few examples that illustrate the use of simulation…
This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the…
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…
We introduce a newly designed undergraduate-level interdisciplinary course in scientific computing that aims to prepare students as the next generation of research-oriented computational scientists and engineers. The course offers students…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
A large multitude of scientific computing tools is available today. This article gives an overview of available tools and explains the main application fields. In addition basic principles of number representations in computing and the…
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied…