Geometrical causality: casting Feynman integrals into quantum algorithms

TL;DR

This paper introduces a novel quantum algorithm approach for calculating complex Feynman integrals in quantum field theories by leveraging geometrical causality and the Loop-Tree Duality to potentially reduce computational complexity.

Contribution

It proposes a new method that uses geometrical causal rules to define a Hamiltonian, enabling quantum algorithms to efficiently compute Feynman integrals.

Findings

Hamiltonian based on geometrical causality is constructed.

Quantum algorithms can be applied to find the ground state related to Feynman integrals.

Potential for speed-up in quantum calculations of quantum field theory corrections.

Abstract

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 resources required to perform the calculation. With the purpose of overcoming these limitations, we discuss efficient strategies based on the Loop-Tree Duality, its manifestly causal representation and the underlying geometrical interpretation. In concrete, we exploit the geometrical causal selection rules to define a Hamiltonian whose ground-state is directly related to the terms contributing to the causal representation. In this way, the problem can be translated into a minimization one and implemented in a quantum computer to search for a potential speed-up.