Related papers: A simple and efficient algorithm for computing the…
We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier…
By establishing an interesting connection between ordinary Bell polynomials and rational convolution powers, some composition and inverse relations of Bell polynomials as well as explicit expressions for convolution roots of sequences are…
We introduce an algebra qCCS of pure quantum processes in which no classical data is involved, communications by moving quantum states physically are allowed, and computations is modeled by super-operators. An operational semantics of qCCS…
Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
We present economical iterative algorithms built on the Biconjugate $A$-Orthonormalization Procedure for real unsymmetric and complex non-Hermitian systems. The principal characteristics of the developed solvers is that they are fast…
In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming…
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm…
We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature…
We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability…
Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a…
This work presents a new approach for simulating the HHL linear systems of equations solver algorithm with tensor networks. First, a novel HHL in the qudits formalism, the generalization of qubits, is developed, and then its operations are…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
Numerical investigations are an important research tool in quantum information theory. There already exists a wide range of computational tools for quantum information theory implemented in various programming languages. However, there is…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear…
Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…
We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
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 present an efficient algorithm for computing the leading monomials of a minimal Groebner basis of a generic sequence of homogeneous polynomials. Our approach bypasses costly polynomial reductions by exploiting structural properties…