Related papers: Transforming differential equations of multi-loop …
Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…
The first application of a quantum algorithm to Feynman loop integrals is reviewed. The connection between quantum computing and perturbative quantum field theory is feasible due to fact that the two on-shell states of a Feynman propagator…
In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version…
We consider the question of reducibility of the differential system to normalized Fuchsian form on the Riemann sphere. The differential equations for the multiloop integrals in $\epsilon$-form constitute a particular example of the…
We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of…
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…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with…
The calculation of higher-order corrections in Quantum Field Theories is a challenging task. In particular, dealing with multiloop and multileg Feynman amplitudes leads to severe bottlenecks and a very fast scaling of the computational…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations,…
In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
We present an efficient algorithm for calculating multiloop Feynman integrals perturbatively.
We present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a…
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…