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The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…

The reduction of Feynman integrals to a basis of linearly independent master integrals is a pivotal step in loop calculations, but also one of the main bottlenecks. In this paper, we assess the impact of using transverse integration…

High Energy Physics - Phenomenology · Physics 2025-06-17 Vsevolod Chestnov , Gaia Fontana , Tiziano Peraro

We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…

High Energy Physics - Phenomenology · Physics 2026-03-06 Pau Petit Rosàs

An algorithm for the reduction of massive Feynman integrals with any number of loops and external momenta to a minimal set of basic integrals is proposed. The method is based on the new algorithm for evaluating tensor integrals,…

High Energy Physics - Phenomenology · Physics 2011-03-17 O. V. Tarasov

In the computation of Feynman integrals which evaluate to multiple polylogarithms one encounters quite often square roots. To express the Feynman integral in terms of multiple polylogarithms, one seeks a transformation of variables, which…

High Energy Physics - Theory · Physics 2018-12-07 Marco Besier , Duco van Straten , Stefan Weinzierl

We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…

High Energy Physics - Theory · Physics 2023-09-19 Johannes Henn , Rourou Ma , Kai Yan , Yang Zhang

Standard integration-by-parts (IBP) reduction methods typically yield Feynman integral bases where the reduction of some integrals gives rise to coefficients singular as the dimensional regulator $\epsilon\rightarrow 0$. These singular…

High Energy Physics - Theory · Physics 2025-08-07 Stefano De Angelis , David A. Kosower , Rourou Ma , Zihao Wu , Yang Zhang

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…

Machine Learning · Statistics 2019-05-10 Ziyu Wang , Tongzheng Ren , Jun Zhu , Bo Zhang

FIRE7 is a major update to the FIRE program for integration-by-parts (IBP) reduction of Feynman integrals. A large part of improvements is related to the automatic reduction and reconstruction with the modular arithmetic approach, while the…

High Energy Physics - Phenomenology · Physics 2025-12-02 Alexander V. Smirnov , Mao Zeng

We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…

In this article, we present the package {\tt Blade} as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain…

High Energy Physics - Phenomenology · Physics 2025-02-07 Xin Guan , Xiao Liu , Yan-Qing Ma , Wen-Hao Wu

Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…

Computation · Statistics 2018-03-14 David J. Price , Nigel G. Bean , Joshua V. Ross , Jonathan Tuke

We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…

High Energy Physics - Phenomenology · Physics 2025-10-28 Yuanche Liu , Yingxuan Xu , Yang Zhang

We investigate the reduction of Feynman integrals to master integrals using Gr\"obner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of…

High Energy Physics - Phenomenology · Physics 2023-06-01 Mohamed Barakat , Robin Brüser , Claus Fieker , Tobias Huber , Jan Piclum

We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…

High Energy Physics - Phenomenology · Physics 2024-01-30 Germán Rodrigo

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically…

Machine Learning · Computer Science 2020-12-17 Silviu-Marian Udrescu , Andrew Tan , Jiahai Feng , Orisvaldo Neto , Tailin Wu , Max Tegmark

Negative dimensional integration method (NDIM) is revealing itself as a very useful technique for computing Feynman integrals, massless and/or massive, covariant and non-covariant alike. Up to now, however, the illustrative calculations…

High Energy Physics - Theory · Physics 2011-09-13 A. T. Suzuki , A. G. M. Schmidt

We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a…

High Energy Physics - Phenomenology · Physics 2008-11-26 A. V. Smirnov , V. A. Smirnov

This work investigates in detail the performance and advantages of a new quantum Monte Carlo integrator, dubbed Quantum Fourier Iterative Amplitude Estimation (QFIAE), to numerically evaluate for the first time loop Feynman integrals in a…

High Energy Physics - Phenomenology · Physics 2024-11-20 Jorge J. Martínez de Lejarza , Leandro Cieri , Michele Grossi , Sofia Vallecorsa , Germán Rodrigo

The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and…

Statistics Theory · Mathematics 2025-12-15 Piotr Bania , Anna Wójcik