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 encoding Feynman propagators as qubits, a challenging task closely analogous to querying directed acyclic graphs in graph theory. In this paper, we introduce the Minimum Clique-optimised quantum Algorithm (MCA), an automated quantum algorithm designed to efficiently query the causal structures within the Loop-Tree Duality, wherein manifestly causal integrand representations of multiloop Feynman diagrams play a central role. The MCA quantum algorithm is optimised by exploiting graph theory techniques, specifically, by analogy with the Minimum Clique Partition problem. The performance of the MCA quantum algorithm across diverse multiloop topologies is assessed by analysing the transpiled quantum circuit depth and quantum circuit area, showing a significant reduction in the quantum resources needed for implementation. Quantum algorithms hold promise for addressing complex problems in high-energy physics, such as deciphering the causal configurations of multiloop Feynman diagrams. Here, the authors introduce the Minimum Clique-optimised quantum Algorithm (MCA), which leverages graph theory techniques to significantly reduce quantum resource requirements, enhancing efficiency in querying causal structures within Loop-Tree Duality.