Related papers: NMR implementations of Gauss sums

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…

This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice…

Gaussian mixtures are widely used for approximating density functions in various applications such as density estimation, belief propagation, and Bayesian filtering. These applications often utilize Gaussian mixtures as initial…

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a…

Quantum Mechanics/Molecular Mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and…

We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for…

An approach to constructing an upper bound for the Riemann-Farey sum is described.

We show that a Young's N slit interferometer can be used to factor the integer N. The device could factor four- or five-digit numbers in a practical fashion. This work shows how number theory may arise in physical problems, and may provide…

In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…

We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of the method for the solutions of nontrivial difference…

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of…

In this chapter we review the contributions of Nuclear Magnetic Resonance to the study of quantum correlations, including its capabilities to prepare initial states, generate unitary transformations, and characterize the final state. These…

We report a detailed analysis of the optical realization [1, 3, 2, 4] of the analogue algorithm described in the first paper of this series [5] for the simultaneous factorization of an exponential number of integers. Such an analogue…

The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…

Almost all public secure communication relies on the inability to factor large numbers. There is no known analytic or classical numeric method to rapidly factor large numbers. Shor[1] has shown that a quantum computer can factor numbers in…

While Nuclear Magnetic Resonance (NMR) techniques are unlikely to lead to a large scale quantum computer they are well suited to investigating basic phenomena and developing new techniques. Indeed it is likely that many existing NMR…

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…