Related papers: Gauss sum factorization with cold atoms

A majority of ultracold atom experiments utilize resonant absorption imaging techniques to obtain the atomic density. To make well-controlled quantitative measurements, the optical intensity of the probe beam must be precisely calibrated in…

We give a geometric approach to integer factorization. This approach is based on special approximations of segments of the curve that is represented by $y=n/x$, where $n$ is the integer whose factorization we need.

We construct an analog computer based on light interference to encode the hyperbolic function f({\zeta}) = 1/{\zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the…

In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…

We investigate Rabi oscillation of an atom ensemble in Gaussian spatial distribution. By using the ultrafast laser interaction with the cold atomic rubidium vapor spatially confined in a magneto-optical trap, the oscillatory behavior of the…

We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…

A Ramsey-type interferometer is suggested, employing a cold trapped ion and two time-delayed off-resonant femtosecond laser pulses. The laser light couples to the molecular polarization anisotropy, inducing rotational wavepacket dynamics.…

We offer interferometry models for thermal ensembles with one-body losses and the phenomenological inclusion of perturbations covering most of the thermal atom experiments. A possible extension to the many-body case is briefly discussed.…

We consider probe-based quantum thermometry and show that machine classification can provide model-independent estimation with quantifiable error assessment. Our approach is based on the k-nearest-neighbor algorithm. The machine is trained…

Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…

We propose and demonstrate a new scheme for atom interferometry, using light pulses inside an optical cavity as matter wave beamsplitters. The cavity provides power enhancement, spatial filtering, and a precise beam geometry, enabling new…

We demonstrate nuclear magnetic resonance of optically trapped ground-state ultracold 87Sr atoms. Using a scheme in which a cloud of ultracold 87Rb is co-trapped nearby, we improve the determination of the nuclear g factor, gI , of atomic…

We present efficient algorithms to calculate the color factors for the $SU(N)$ gauge group and to evaluate $\gamma$ traces. The aim of these notes is to give a self-contained, proved account of the basic results with particular emphasis on…

We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set of any affine semigroup, (ii) an improved method of…

We demonstrate a dual-axis accelerometer and gyroscope atom interferometer, which forms the building blocks of a six-axis inertial measurement unit. By recapturing the atoms after the interferometer sequence, we maintain a large atom number…

We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…

Gaussian blur is a commonly-used method to filter image data. This paper introduces the collapsing sum, a new operator on matrices that provides a combinatorial interpretation of Gaussian blur. We study the combinatorial properties of this…

Ramsey interferometers have wide applications in science and engineering. Compared with the traditional interferometer based on internal states, the interferometer with external quantum states has advantages in some applications for quantum…

In this paper, we introduce a novel quantum algorithm for the factorization of composite odd numbers. This work makes two significant contributions. First, we present a new improvement to the classical Fermat method, fourfold reducing the…

We propose a Ramsey interferometry experiment using an entangled state of N atoms to reach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation,…