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A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…

We present a new interface called FeynHelpers that connects FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and calculations in quantum field theory (QFT) to Package-X and FIRE. The former provides…

Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate…

We present a Mathematica package AmpRed for the semi-automatic calculations of multi-loop Feynman amplitudes with high efficiency and precision. AmpRed implements the methods of integration by parts and differential equations in the…

With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the…

I discuss algorithms for the evaluation of Feynman integrals. These algorithms are based on Hopf algebras and evaluate the Feynman integral to (multiple) polylogarithms.

Catalytic carbon fixation to formic acid is important for studying the reduction of carbon footprint and the emergence of life. Can discrete quantum exhaustive search merged with other methods help reduce the carbon footprint? We suggest…

It is well-known that molecular dynamics integrators, which are used for lattice quantum chromodynamics (QCD), suffer from instabilities and possess a rather low order of the accuracy. Hence, it is highly desirable to construct a new class…

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…

Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…

In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…

The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…

This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum…

FeynMaster is a multi-tasking software for particle physics studies. By making use of already existing programs (FeynRules, QGRAF, FeynCalc), FeynMaster automatically generates Feynman rules, generates and draws Feynman diagrams, generates…

This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…

This paper focuses on providing the computation methods for the backward time tempered fractional Feynman-Kac equation, being one of the models recently proposed in [Wu, Deng, and Barkai, Phys. Rev. E, 84 (2016) 032151]. The discretization…

One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena like: high temperature superconductivity, solid-state…

We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…

We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values. In order to perform these simplifications, we view the series as…

I present an introduction to the field of Quantum Chromodynamics (QCD) with emphasis on nucleon spin structure and perturbative methods. After a somewhat comprehensive overview of perturbative QCD, including the systematics of…