arXiv subjects

Selomit Ramírez-Uribe

Publications and source records attributed to Selomit Ramírez-Uribe.

14 recordsLinked to original sources

arXiv2026

Graph theory-based automated quantum algorithm for efficient querying of acyclic and multiloop causal configurations

Quantum algorithms provide a promising framework in high-energy physics, in particular, for unraveling the causal configurations of multiloop Feynman diagrams by identifying Feynman propagators with qubits, a challenge analogous to querying directed acyclic graphs in graph theory. In this paper, we present the Minimum Clique-optimised quantum Algorithm (MCA), an automated quantum algorithm designed to efficiently query the causal structures within the Loop-Tree Duality. The MCA quantum algorithm is optimised by exploiting graph theory techniques, specifically, by analogy with the Minimum Clique Partition problem. The evaluation of the MCA quantum algorithm is exhibited by analysing the transpiled quantum circuit depth and quantum circuit area.

quant-ph↗

arXiv2026

A Systematic Approach to Finite Multiloop Feynman Integrals

Finite Feynman integrals have been advocated as the optimal components for constructing a basis of master integrals in multiloop calculations, due to their improved analytic and numerical properties. In this paper, we show how the Loop-Tree Duality (LTD) is particularly well suited for systematically identifying finite integrals, as it makes the origin of infrared and threshold singularities fully transparent at the integrand level. This clear separation of singular and non-singular contributions enables a more efficient strategy for isolating and promoting finite integrals, thereby streamlining both reduction and numerical evaluation. We present a new strategy based on numerator and raised propagator Ansätze that provides results similar to other methods, although in a clearer and compact way. While this construction and other approaches establish a robust foundation, they often produce integrands that exhibit a rapid growth in the ultraviolet (UV) regime. To mitigate this bad UV behaviour, we introduce a generalized set of integrands fully defined within LTD. This new set is inherently infrared-finite and frequently free of threshold singularities, offering a more versatile framework for high-order calculations.

hep-ph↗

arXiv2025

Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs

Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph theory. In this paper, we present a quantum algorithm for querying in both types of applications, using a systematic and sparing logic in the design of an oracle operator. The construction of the quantum oracle is based exclusively on multicontrolled Toffoli (MCX) gates and quantum NOT (Pauli-$X$) gates. The efficiency of the algorithm is evaluated by comparison with a quantum algorithm based on binary clauses. Furthermore, we analyse the impact of traspilation and introduce an appropriate metric to assess the complexity of the algorithm, the \emph{quantum circuit area}. We explicitly analyse three-, four- and five-eloop topologies, which have not previously been explored due to their higher complexity and the current limitations of quantum simulators.

quant-ph↗

arXiv2024

Vacuum amplitudes and time-like causal unitary in the loop-tree duality

We present the first proof-of-concept application to decay processes at higher perturbative orders of LTD causal unitary, a novel methodology that exploits the causal properties of vacuum amplitudes in the loop-tree duality (LTD) and is directly well-defined in the four physical dimensions of the space-time. The generation of loop- and tree-level contributions to the differential decay rates from a kernel multiloop vacuum amplitude is shown in detail, and explicit expressions are presented for selected processes that are suitable for a lightweight understanding of the method. Specifically, we provide a clear physical interpretation of the local cancellation of soft, collinear and threshold singularities, and of the local renormalisation of ultraviolet singularities. The presentation is illustrated with numerical results that showcase the advantages of the method.

hep-ph↗

arXiv2024

Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes

We propose multiloop vacuum amplitudes as the optimal building blocks for efficiently assembling theoretical predictions at high-energy colliders. This hypothesis is strongly supported by the manifestly causal properties of the loop-tree duality (LTD) representation of a vacuum amplitude. The vacuum amplitude, acting as a kernel, encodes all the final states contributing to a given scattering or decay process through residues in the on-shell energies of the internal propagators. It also naturally implements gauge invariance and the wave function renormalisation of the external legs. This methodological approach, dubbed LTD causal unitary, leads to a novel representation of differential cross sections and decay rates that is locally free of ultraviolet and infrared singularities at all orders in perturbation theory. Threshold singularities also match between different phase-space residues. Most notably, it allows us to conjecture for the first time the local functional form of initial-state collinear singularities. The fulfillment of all these properties provides a theoretical description of differential observables at colliders that is well defined in the four physical dimensions of the space-time.

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↗

arXiv2022

Quantum Algorithm for Querying Causality of Multiloop Scattering Amplitudes

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 are naturally encoded in a qubit. The particular problem to be addressed is the identification of the causal singular configurations of multiloop Feynman diagrams. The identification of such configurations is carried out through the implementation of a modified Grover's quantum algorithm for querying multiple solutions over unstructured datasets.

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 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

From Causal Representation of Multiloop Scattering Amplitudes to Quantum Computing

An overview of a quantum algorithm application for the identification of causal singular configurations of multiloop Feynman diagrams is presented. The quantum algorithm is implemented in two different quantum simulators, the output obtained is directly translated to causal thresholds needed for the causal representation in the loop-tree duality.

hep-ph↗

arXiv2021

Four-loop scattering amplitudes through the loop-tree duality

A general outlook is presented on the study of multiloop topologies appearing for the first time at four loops. A unified description and representation of this family is provided, the so-called N$^4$MLT universal topology. Based on the Loop-Tree Duality framework, we discuss the dual opening of this family and expose the relevance of a causal representation. We explore an alternative procedure for the search of causal singular configurations of selected N$^4$MLT Feynman diagrams through the application of a modified Grover's quantum algorithm.

hep-th↗

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↗

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↗