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A quantum simulator is a device engineered to reproduce the properties of an ideal quantum model. It allows the study of quantum systems that cannot be efficiently simulated on classical computers. While a universal quantum computer is also…
We present a new Monte Carlo tool that computes full tree-level matrix elements in high-energy physics. The program accepts user-defined models and has no restrictions on the process multiplicity. To achieve acceptable performance, CAMORRA…
General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
We present some theorems and algorithms for calculating perpendicular categories and locally semi-simple decompositions. We implemented a computer program {\sc TETIVA} based on these algorithms and we offer this program for everybody's use.
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
This paper explores the application of geometric algebra to Galilean spacetime and its physical implications. We introduce the Galilean Spacetime Algebra (GSTA), a five-dimensional conformal geometric algebra (CGA) generated by a specific…
We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package Excalc. Subsequently we list some…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
Computationally efficient classification system architecture is proposed. It utilizes fast tensor-vector multiplication algorithm to apply linear operators upon input signals . The approach is applicable to wide variety of recognition…
The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way…
The equations of General Relativity are recast in the form of a wave equation for the Weyl tensor. This allows to reformulate gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse…
Transformer-based models have demonstrated superior performance in various fields, including natural language processing and computer vision. However, their enormous model size and high demands in computation, memory, and communication…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…