Quantum algorithm for Feynman loop integrals

TL;DR

This paper introduces a quantum algorithm leveraging Grover's search to efficiently identify causal configurations in Feynman loop integrals, demonstrating potential speed-ups over classical methods and applications in graph theory.

Contribution

The paper presents a novel quantum algorithm for analyzing Feynman loop integrals, utilizing Grover's algorithm for quadratic speed-up in identifying causal states.

Findings

Successfully implemented on IBM Quantum and QUTE simulators.

Demonstrated quadratic speed-up over classical algorithms for specific configurations.

Potential applications in graph theory and directed acyclic graph problems.

Abstract

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.