相关论文: Fast and accurate evaluation of Wigner 3j, 6j, and…
In the paper an explicit formula for an arbitrary $6j$-symbol for finite-dimensional irreducible representations of the algebra $\mathfrak{gl}_3$ is derived. A $6j$-symbol is written as a result of substitution of $\pm 1$ into a series of…
There are two types of asymptotic formulas for the $12j$ symbol with one small and 11 large angular momenta. We have derived the first type of formula previously in [L. Yu, Phys. Rev. A84 022101 (2011)]. We will derive the second type in…
Quantum algorithms are at the heart of the ongoing efforts to use quantum mechanics to solve computational problems unsolvable on ordinary classical computers. Their common feature is the use of genuine quantum properties such as…
An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincar\'e letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
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…
We present a method of representing an element of $\mathbb{F}_3^n$ as an element of $\mathbb{F}_n^2 \times \mathbb{F}_n^2$ which in practice will be a pair of unsigned integers. We show how to do addition, subtraction and pointwise…
In each of the 10 cases with propagators of unit or zero mass, the finite part of the scalar 3-loop tetrahedral vacuum diagram is reduced to 4-letter words in the 7-letter alphabet of the 1-forms $\Omega:=dz/z$ and $\omega_p:=dz/…
In the context of spinfoam models for quantum gravity, we investigate the asymptotical behavior of the 6j-symbol at next-to-leading order. We compute it analytically and check our results against numerical calculations. The 6j-symbol is the…
The asymptotic behavior of quantum $6j$-symbols is closely related to the volume of truncated hyperideal tetrahedra\,\cite{C}, and plays a central role in understanding the asymptotics of the Turaev-Viro invariants of $3$-manifolds. In this…
We show how a simple and elegant graphical notation can be used to derive the Biedenharn-Elliot identity for the 6j-symbol and we demonstrate how the same technique can be applied to obtain new identities for the 6j. We then employ the same…
The expressions of the coupling coefficients (3j-symbols) for the most degenerate (symmetric) representations of the orthogonal groups SO(n) in a canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical or tree bases…
We present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern-Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix…
The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution…
We present a compact quantum circuit for factoring a large class of integers, including some whose classical hardness is expected to be equivalent to RSA (but not including RSA integers themselves). Most notably, we factor $n$-bit integers…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
We discuss the calculation of two-point three-loop functions with an arbitrary number of massive propagators and one large external momentum. The relevant subdiagrams are generated automatically. The resulting massless two-point integrals…
Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not…
Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that…