Related papers: Algorithmic transformation of multi-loop Feynman i…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…
We present an efficient algorithm for calculating multiloop Feynman integrals perturbatively.
In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
We present $\text{Fuchsia}$ $-$ an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients $\partial_x\,\mathbf{f}(x,\epsilon) =…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly…
We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…
In modern quantum field theory, one of the most important tasks is the calculation of loop integrals. Loop integrals appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. Even though…
Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a…
We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can…
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…
In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop…
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the…
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…