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

TL;DR

This paper introduces MCA, a quantum algorithm inspired by graph theory, optimized for efficiently analyzing causal structures in high-energy physics Feynman diagrams, leveraging the analogy with the Minimum Clique Partition problem.

Contribution

The paper presents MCA, a novel automated quantum algorithm that uses graph theory techniques to efficiently query causal configurations in multiloop Feynman diagrams.

Findings

MCA optimizes quantum circuit depth and area.

The algorithm effectively identifies causal structures in Loop-Tree Duality.

Graph theory techniques enhance quantum algorithm efficiency.

Abstract

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.