Related papers: A Monomial-Oriented GVW for Computing Gr\"obner Ba…
We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr\"obner bases. If successful, a push forward Gaussian…
Inspired by the decomposition in the hybrid quantum-classical optimization algorithm we introduced in arXiv:1902.04215, we propose here a new (fully classical) approach to solving certain non-convex integer programs using Graver bases. This…
We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and…
The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford's formalism…
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…
The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…
Questions at the intersection of the AdS/CFT correspondence and quantum information theory motivate the study of projectors in sequences of subalgebras of finite-dimensional commutative associative semisimple algebras $\mathcal{A}$,…
Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits…
I present a simple dynamic programming algorithm for the evaluation of operators in a wide range of superconformal algebras. Special care is taken to describe the computation of the Gram matrix. A Mathematica package, Weaver.m, is provided…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
In this paper, we explore the application of variational quantum algorithms designed for classical optimization to the problem of matched filtering in the detection of gravitational waves. Matched filtering for detecting gravitational wave…
The $(1+(\lambda,\lambda))$ genetic algorithm is a recently proposed single-objective evolutionary algorithm with several interesting properties. We show that its main working principle, mutation with a high rate and crossover as repair…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
We generalize the Brouwer-Zimmermann algorithm, which is the most efficient general algorithm for computing the minimum distance of a random linear code, to the case of generalized Hamming weights. We also adapt this algorithm to compute…
We consider three modifications of our involutive algorithm for computing Janet bases. These modifications are related to degree compatible monomial orders and specify selection strategies for non-multiplicative prolongations. By using the…
The theory of Groebner Bases originated in the work of Buchberger and is now considered to be one of the most important and useful areas of symbolic computation. A great deal of effort has been put into improving Buchberger's algorithm for…
The Grover algorithm is a crucial solution for addressing unstructured search problems and has emerged as an essential quantum subroutine in various complex algorithms. By using a different approach with previous studies, this research…
Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gr\"{o}bner bases of vanishing ideals of finite points, which has been implemented in Maple$^\circledR$ as a build-in command. In this paper, we present a two-dimensional…
Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Grobner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Grobner bases based…
The Chow group of zero cycles in the moduli space of stable pointed curves of genus zero is isomorphic to the integer additive group. Let $M$ be monomial in this Chow group. If no two factors of $M$ fulfill a particular quadratic relation,…