Related papers: Collier: a fortran-based Complex One-Loop LIbrary …
In this talk we review the GOLEM approach to one-loop calculations and present an automated implementation of this technique. This method is based on Feynman diagrams and an advanced reduction of one-loop tensor integrals which avoids…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
We compute the one-loop corrections to \tth up to order $\mathcal{O}(\epsilon^2)$ in the dimensional regularization parameter. We apply the projector method to compute polarized amplitudes, which generalize massless helicity amplitudes to…
We review progress in calculating one-loop scattering amplitudes required for next-to-leading-order corrections to QCD processes. The underlying technical developments include the spinor helicity formalism, color decompositions,…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on a matrix exponential version of Euler's formula…
In this short paper we present a linear constraint solver for the UniCalc system, an environment for reliable solution of mathematical modeling problems.
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Progress in the realisation of reliable large-scale quantum computers has motivated research into the design of quantum machine learning models. We present Quixer: a novel quantum transformer model which utilises the Linear Combination of…
We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source…
We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically…
We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the…
We develop a simple recursive approach to treat reversible condensation polymerization with cyclization. Based upon a minimum set of balance equations, the law of mass action, Gaussian chain statistics, and the assumption of independent…
Detailed notes on the functions included in the DMRjulia library are included here. This discussion of how to program functions for a tensor network library are intended to be a supplement to the other documentation dedicated to explaining…
We present a package 'MixedMultiplicity' for computing mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over a field. This enables us to find mixed volumes of convex lattice polytopes…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
In this article, we study the triple-collinear limit of scattering amplitudes, focusing the discussion in processes which include at least one photon. To deal with infrared divergences we applied dimensional regularization (DREG) and we…
The use of Lagrange multipliers in the context of quintessence/phantom scalar fields allows to constrain the behavior of the scalar field, which provides a powerful tool, not only for the reconstruction of cosmological solutions but also…
The success and popularity of deep learning is on the rise, partially due to powerful deep learning frameworks such as TensorFlow and PyTorch that make it easier to develop deep learning models. However, these libraries also come with steep…