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Monte Carlo simulations applied to the lattice formulation of quantum chromodynamics (QCD) enable a study of the theory from first principles, in a nonperturbative way. After over two decades of developments in the methodology for this…
With the advent of generalized unitarity and parametric integration techniques, the construction of a generic Next-to-Leading Order Monte Carlo becomes feasible. Such a generator will entail the treatment of QCD color in the amplitudes. We…
In this article we would like to consider some approaches to non-integer integro-differentiations and its implementation in computer algebra system Wolfram Mathematics.
The scalar isoscalar form factor of the nucleon is calculated in the limit of a large number of colours in the framework of the chiral quark-soliton model. The calculation is based on an approximation justified by arguments from the…
The lectures are a practical introduction to perturbative calculations in QED and QCD. I discuss methods of calculation of one- and two-loop diagrams in dimensional regularization, MSbar and on-shell renormalization schemes, decoupling of…
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…
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…
A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations…
The ALPHA algorithm to evaluate the exact, tree-level matrix elements is reviewed in the context of multi-parton processes in QCD. The algorithm is suited for the authomatic calculation of tree-level scattering amplitudes and allows for…
This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.
We introduce qprof, a new and extensible quantum program profiler able to generate profiling reports of various quantum circuits. We describe the internal structure and working of qprof and provide three practical examples on practical…
A formalism is discussed which simplifies the calculation of Feynman diagrams at finite temperature.
The inclusion of electromagnetic effects in unquenched QCD can be accomplished using ensembles generated in dynamical simulations with pure QCD provided the change in the quark determinant induced by a weak electromagnetic field can be…
This text reviews, hopefully in a pedagogical manner, a series of work on the automatic calculations of Feynman diagrams in the context of quantum nanoelectronics (Keldysh formalism) with an application to the Kondo effect in the…
The method of QCD sum rules has proven to be particularly useful in heavy quark physics, where a small distance scale is provided by the inverse heavy quark mass. We present two new examples for the application of this method to B-physics:…
Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…
By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…