Searcharxiv⌕ Search

arXiv subjects

Germán Rodrigo

Publications and source records attributed to Germán Rodrigo.

At least 37 records · Page 2Linked to original sources
arXiv2024

Loop Feynman integration on a quantum computer

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 near-term quantum computer and a quantum simulator. In order to achieve a quadratic speedup, QFIAE introduces a Quantum Neural Network (QNN) that efficiently decomposes the multidimensional integrand into its Fourier series. For a one-loop tadpole Feynman diagram, we have successfully implemented the quantum algorithm on a real quantum computer and obtained a reasonable agreement with the analytical values. One-loop Feynman diagrams with more external legs have been analyzed in a quantum simulator. These results thoroughly illustrate how our quantum algorithm effectively estimates loop Feynman integrals and the method employed could also find applications in other fields such as finance, artificial intelligence, or other physical sciences.

hep-ph↗
arXiv2024

Quantum algorithms in particle physics

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 clustering algorithms, such as anti-kT , and show how quantum algorithms efficiently identify causal configurations of multiloop Feynman diagrams. We also present a quantum integration algorithm, called QFIAE, which is successfully applied to the evaluation of one-loop Feynman integrals in a quantum simulator or in a real quantum device.

hep-ph↗
arXiv2023

Triple-collinear splittings with massive particles

We analyze in detail the most singular behaviour of processes involving triple-collinear splittings with massive particles in the quasi-collinear limit, and present compact expressions for the splitting amplitudes and the corresponding splitting kernels at the squared-amplitude level. Our expressions fully agree with well-known triple-collinear splittings in the massless limit, which are used as a guide to achieve the final expressions. These results are important to quantify dominant mass effects in many observables, and constitute an essential ingredient of current high-precision computational frameworks for collider phenomenology.

hep-ph↗
arXiv2023

Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs

We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams in the Loop-Tree Duality (LTD) or, equivalently, the selection of acyclic configurations in directed graphs. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations. The algorithm has been adapted to select multiple degenerated minima and thus achieves higher detection rates. A performance comparison with a Grover's based algorithm is discussed in detail. The VQE approach requires, in general, fewer qubits and shorter circuits for its implementation, albeit with lesser success rates.

hep-ph↗
arXiv2023

Towards higher-order collinear splittings with massive partons

The singularities associated with QCD factorization in the collinear limit are key ingredients for high-precision theoretical predictions in particle physics. They govern the collinear behaviour of scattering amplitudes, as well as the perturbative energy evolution of parton densities (PDFs) and fragmentation functions (FFs). In this talk, we present the computation of multiple collinear and higher-order QCD splittings with massive partons. Our results are highly-relevant for the consistent introduction of mass effects in the subtraction formalism and PDF/FF evolution.

hep-ph↗
arXiv2023

Quantum Fourier Iterative Amplitude Estimation

Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several quantum algorithms have been proposed to achieve this goal. In this paper, we present an application of Quantum Machine Learning (QML) and Grover's amplification algorithm to build a new tool for estimating Monte Carlo integrals. Our method, which we call Quantum Fourier Iterative Amplitude Estimation (QFIAE), decomposes the target function into its Fourier series using a Parametrized Quantum Circuit (PQC), specifically a Quantum Neural Network (QNN), and then integrates each trigonometric component using Iterative Quantum Amplitude Estimation (IQAE). This approach builds on Fourier Quantum Monte Carlo Integration (FQMCI) method, which also decomposes the target function into its Fourier series, but QFIAE avoids the need for numerical integration of Fourier coefficients. This approach reduces the computational load while maintaining the quadratic speedup achieved by IQAE. To evaluate the performance of QFIAE, we apply it to a test function that corresponds with a particle physics scattering process and compare its accuracy with other quantum integration methods and the analytic result. Our results show that QFIAE achieves comparable accuracy while being suitable for execution on real hardware. We also demonstrate how the accuracy of QFIAE improves by increasing the number of terms in the Fourier series. In conclusion, QFIAE is a promising end-to-end quantum algorithm for Monte Carlo integrals that combines the power of PQC with Fourier analysis and IQAE to offer a new approach for efficiently approximating integrals with high accuracy.

quant-ph↗
arXiv2022

From five-loop scattering amplitudes to open trees with the Loop-Tree Duality

Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group them according to their topological properties. Then, we identify a kernel generator, the so-called N$^7$MLT universal topology, that allow us to describe any scattering amplitude of up to five loops. Furthermore, we provide factorization and recursion relations that enable us to write these multiloop topologies in terms of simpler subtopologies, including several subsets of Feynman diagrams with an arbitrary number of loops. Our approach takes advantage of many symmetries present in the graphical description of the original fundamental five-loop topologies. The results obtained in this article might shed light into a more efficient determination of higher-order corrections to the running couplings, which are crucial in the current and future precision physics program.

hep-ph↗
arXiv2022

Quantum jet clustering with LHC simulated data

We study the case where quantum computing could improve jet clustering by considering two new quantum algorithms that might speed up classical jet clustering algorithms. The first one is a quantum subroutine to compute a Minkowski-based distance between two data points, while the second one consists of a quantum circuit to track the rough maximum into a list of unsorted data. When one or both algorithms are implemented in classical versions of well-known clustering algorithms (K-means, Affinity Propagation and $k_T$-jet) we obtain efficiencies comparable to those of their classical counterparts. Furthermore, in the first two algorithms, an exponential speed up in dimensionality and data length can be achieved when applying the distance or the maximum search algorithm. In the $k_T$ algorithm, a quantum version of the same order as FastJet is achieved.

hep-ph↗
arXiv2022

Quantum clustering and jet reconstruction at the LHC

Clustering is one of the most frequent problems in many domains, in particular, in particle physics where jet reconstruction is central in experimental analyses. Jet clustering at the CERN's Large Hadron Collider (LHC) is computationally expensive and the difficulty of this task will increase with the upcoming High-Luminosity LHC (HL-LHC). In this paper, we study the case in which quantum computing algorithms might improve jet clustering by considering two novel quantum algorithms which may speed up the classical jet clustering algorithms. The first one is a quantum subroutine to compute a Minkowski-based distance between two data points, whereas the second one consists of a quantum circuit to track the maximum into a list of unsorted data. The latter algorithm could be of value beyond particle physics, for instance in statistics. When one or both of these algorithms are implemented into the classical versions of well-known clustering algorithms (K-means, Affinity Propagation and $k_T$-jet) we obtain efficiencies comparable to those of their classical counterparts. Even more, exponential speed-up could be achieved, in the first two algorithms, in data dimensionality and data length when the distance algorithm or the maximum searching algorithm are applied.

hep-ph↗
arXiv2022

Quantum algorithm for Feynman loop integrals

We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. To identify such configurations, we exploit Grover's algorithm for querying multiple solutions over unstructured datasets, which presents a quadratic speed-up over classical algorithms when the number of solutions is much smaller than the number of possible configurations. A suitable modification is introduced to deal with topologies in which the number of causal states to be identified is nearly half of the total number of states. The output of the quantum algorithm in \emph{IBM Quantum} and \emph{QUTE Testbed} simulators is used to bootstrap the causal representation in the loop-tree duality of representative multiloop topologies. The algorithm may also find application and interest in graph theory to solve problems involving directed acyclic graphs.

hep-ph↗
arXiv2022

$m_b$ at $m_H$: the running bottom quark mass and the Higgs boson

We present a new measurement of the bottom quark mass in the $\bar{MS}$ scheme at the renormalization scale of the Higgs boson mass from measurements of Higgs boson decay rates at the LHC: $m_b(m_H)= 2.60^{+0.36}_{-0.31}$ GeV. The measurement has a negligible theory uncertainty and excellent prospects to improve at the HL-LHC and a future Higgs factory. Confronting this result, and $m_b(m_b)$ from low-energy measurements and $m_b(m_Z)$ from $Z-$pole data, with the prediction of the scale evolution of the renormalization group equations, we find strong evidence for the "running" of the bottom quark mass.

hep-ph↗
arXiv2021

Four-loop scattering amplitudes journey into the forest

We present an overview of the analysis of the multiloop topologies that appear for the first time at four loops and the assembly of them in a general expression, the N$^4$MLT universal topology. Based on the fact that the Loop-Tree Duality enables to open any scattering amplitude in terms of convolutions of known subtopologies, we go through the dual representation of the universal N$^4$MLT topology and the manifestly causal representation. Additionally, we expose the application of a quantum algorithm as an alternative methodology to identify the causal singular configurations of multiloop Feynman diagrams.

hep-ph↗
arXiv2021

A stroll through the loop-tree duality

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over an Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.

hep-ph↗
arXiv2020

Asymptotic expansions through the loop-tree duality

First results towards a general method for asymptotic expansions of Feynman amplitudes in the loop-tree duality (LTD) formalism are presented. The asymptotic expansion takes place at integrand-level in the Euclidean space of the loop three-momentum, where the hierarchies among internal and external scales are well-defined. Additionally, the UV behaviour of the individual contributions to the asymptotic expansion emerges only in the first terms of the expansion and is renormalized locally in four space-time dimensions. These two properties represent an advantage over the method of Expansion by Regions (EbR). We explore different approaches in different kinematical limits, and derive general guidelines with several benchmark examples.

hep-ph↗
arXiv2019

Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders

We present the first comprehensive analysis of the unitarity thresholds and anomalous thresholds of scattering amplitudes at two loops and beyond based on the loop-tree duality, and show how non-causal unphysical thresholds are locally cancelled in an efficient way when the forest of all the dual on-shell cuts is considered as one. We also prove that soft and collinear singularities at two loops and beyond are restricted to a compact region of the loop three-momenta, which is a necessary condition for implementing a local cancellation of loop infrared singularities with the ones appearing in real emission; without relying on a subtraction formalism.

hep-ph↗
arXiv2019

Standard Model radiative corrections in the pion form factor measurements do not explain the $a_μ$ anomaly

In this letter, we address the question of whether the almost four standard deviations difference between theory and experiment for the muon anomalous magnetic moment $a_μ$ can be explained as a higher-order Standard Model perturbation effect in the pion form factor measurements. This question has, until now, remained open, obscuring the source of discrepancies between the measurements. We calculate the last radiative corrections for the extraction of the pion form factor, which were believed to be potentially substantial enough to explain the data within the Standard Model. We find that the corrections are too small to diminish existing discrepancies in the determination of the pion form factor for different kinematical configurations of low-energy BABAR, BESS-III and KLOE experiments. Consequently, they cannot noticeably change the previous predictions for $a_μ$ and decrease the deviations between theory and direct measurements. To solve the above issues, new data and better understanding of low-energy experimental setups are needed, especially as new direct $a_μ$ measurements at Fermilab and J-PARC will provide new insights and substantially shrink the experimental error.

hep-ph↗
arXiv2017

QED and QCD self-energy corrections through the loop-tree duality

The loop-tree duality (LTD) theorem establishes that loop contributions to scattering amplitudes can be computed through dual integrals, which are build from single cuts of the virtual diagrams. In order to build a complete LTD representation of a cross section and to achieve a local cancellation of singularities, it is crucial to include the renormalized self-energy corrections in an unintegrated form. In this document, we calculate the scalar functions related to the self-energy corrections in QED and QCD in the LTD formalism and extract explicitly their UV behaviour.

hep-ph↗