Related papers: Factorizing numbers with classical interference: s…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
We consider the most general form of soft and collinear factorization for hard-scattering amplitudes to all orders in perturbative Quantum Chromodynamics. Specifically, we present the generalization of collinear factorization to…
Many modern asymmetric encryption methods rely on prime numbers, as they have distinctive properties. For instance, the security of RSA cryptosystem relies on the computational difficulty of factoring a large composite number in its prime…
Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
For a composite $n$ and an odd $c$ with $c$ not dividing $n$, the number of solutions to the equation $n+a\equiv b\mod c$ with $a,b$ quadratic residues modulus $c$ is calculated. We establish a direct relation with those modular solutions…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\times n$ matrix with $m\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The…
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
Sum of powers 1^p+...+n^p, with n and p being natural numbers and n>=1, can be expressed as a polynomial function of n of degree p+1. Such representations are often called Faulhaber formulae. A simple recursive algorithm for computing…
Consider the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with complex refractive index. We show that an approximate factorization method can be applied to reconstruct the support of the complex…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
An extension to the factorisation principle as suggested by Fermat is presented.We start from a symmetry of natural numbers and obtain the factorisation principle therefrom.Later it is extended further to test the primality of any natural…
A beam splitter is one of the most important devices in an optics laboratory because of its handiness and versatility; equivalent devices are found in various quantum systems to couple two subsystems or to interfere them. While it is normal…
In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.
We present conditions for the efficient simulation of a broad class of optical quantum circuits on a classical machine: this class includes unitary transformations, amplification, noise, and measurements. Various proposed schemes for…
In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulae in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with…