9 research outputs found
From a causal representation of multiloop scattering amplitudes to quantum computing in the Loop-Tree Duality
La teoría cúantica de campos con enfoque perturbativo ha logrado de manera exitosa proporcionar predicciones teóricas increíblemente precisas en física de altas energías. A pesar del desarrollo de diversas técnicas con el objetivo de incrementar la eficiencia de estos cálculos, algunos ingredientes continuan siendo un verdadero reto. Este es el caso de las amplitudes de dispersión con lazos múltiples, las cuales describen las fluctuaciones cuánticas en los procesos de dispersión a altas energías.
La Dualidad Lazo-Árbol (LTD) es un método innovador, propuesto con el objetivo de afrontar estas dificultades abriendo las amplitudes de lazo a amplitudes conectadas de tipo árbol. En esta tesis presentamos tres logros fundamentales: la reformulación de la Dualidad Lazo-Árbol a todos los órdenes en la expansión perturbativa, una metodología general para obtener expresiones LTD con un comportamiento manifiestamente causal, y la primera aplicación de un algoritmo cuántico a integrales de lazo de Feynman. El cambio de estrategia propuesto para implementar la metodología LTD, consiste en la aplicación iterada del teorema del residuo de Cauchy a un conjunto de topologías con lazos m\'ultiples y configuraciones internas arbitrarias. La representación LTD que se obtiene, sigue una estructura factorizada en términos de subtopologías más simples, caracterizada por un comportamiento causal bien conocido. Además, a través de un proceso avanzado desarrollamos representaciones duales analíticas explícitamente libres de singularidades no causales. Estas propiedades permiten escribir cualquier amplitud de dispersión, hasta cinco lazos, de forma factorizada con una mejor estabilidad numérica en comparación con otras representaciones, debido a la ausencia de singularidades no causales.
Por último, establecemos la conexión entre las integrales de lazo de Feynman y la computación cuántica, mediante la asociación de los dos estados sobre la capa de masas de un propagador de Feynman con los dos estados de un qubit. Proponemos una modificación del algoritmo cuántico de Grover para encontrar las configuraciones singulares causales de los diagramas de Feynman con lazos múltiples. Estas configuraciones son requeridas para establecer la representación causal de topologías con lazos múltiples.The perturbative approach to Quantum Field Theories has successfully provided incredibly accurate theoretical predictions in high-energy physics. Despite the development of several techniques to boost the efficiency of these calculations, some ingredients remain a hard bottleneck. This is the case of multiloop scattering amplitudes, describing the quantum fluctuations at high-energy scattering processes.
The Loop-Tree Duality (LTD) is a novel method aimed to overcome these difficulties by opening the loop amplitudes into connected tree-level diagrams. In this thesis we present three core achievements: the reformulation of the Loop-Tree Duality to all orders in the perturbative expansion, a general methodology to obtain LTD expressions which are manifestly causal, and the first flagship application of a quantum algorithm to Feynman loop integrals.
The proposed strategy to implement the LTD framework consists in the iterated application of the Cauchy's residue theorem to a series of mutiloop topologies with arbitrary internal configurations. We derive a LTD representation exhibiting a factorized cascade form in terms of simpler subtopologies characterized by a well-known causal behaviour. Moreover, through a clever approach we extract analytic dual representations that are explicitly free of noncausal singularities. These properties enable to open any scattering amplitude of up to five loops in a factorized form, with a better numerical stability than in other representations due to the absence of noncausal singularities. Last but not least, we establish the connection between Feynman loop integrals and quantum computing by encoding the two on-shell states of a Feynman propagator through the two states of a qubit. We propose a modified Grover's quantum algorithm to unfold the causal singular configurations of multiloop Feynman diagrams used to bootstrap the causal LTD representation of multiloop topologies
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 NMLT
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.Comment: 14 pages, 6 figures, 2 table
Variational quantum eigensolver for causal loop Feynman diagrams and acyclic directed 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.Comment: 32 pages, 7 figures. Improved discussion and success rates of
multi-run VQ
Modelo estadístico para datos sobre años de extinción, experimentando por medio de simulación
El propósito de esta tesina es entender de manera más profunda el proceso de registro de años de "extinción", y por supuesto la variabilidad que dicho proceso pueda causar a los datos. Para ésto, primero se identifican factores que pudieran estar causando fuerte variabilidad en los datos. Después se propone un modelo estadístico que incorpora dichos factores, y que pretende representar de manera adecuada el proceso de recopilación de datos. Además, también se desea proponer alguna metodología razonable para identificar el estado de la extinción, con el objetivo de que las aseveraciones que se hagan con respecto a la evolución de las extinciones sean válidas y pertinentes
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 N7MLT universal topology, that allows 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
Quantum algorithm for Feynman loop integrals
We present the first flagship 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. Since the number of causal states to be identified is nearly half of the total number of states in most cases, an efficient modification of Grover’s algorithm is introduced, requiring only (1) iterations. The output of the quantum algorithm in the IBM quantum simulator 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
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 a 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