Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs

• DOI: 10.48550/arxiv.2210.13240
• Publication Date: 2022-01-01
• Authors: Giuseppe Clemente; Arianna Crippa; Karl Jansen; Selomit Ramírez-U...; Andrés E. Renterí...; Germán Rodrigo; Germán F. R. Sbor...; Luiz Vale Silva
• Keywords: Hamiltonian (control theory); Precomputation; Adjacency list; Adjacency matrix

We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of causal representation multiloop Feynman diagrams in Loop-Tree Duality (LTD) or, equivalently, selection acyclic configurations directed graphs. A loop Hamiltonian based on adjacency matrix describing topology, and whose different energy levels correspond to number cycles, is minimized by VQE identify or configurations. The has been adapted select multiple degenerated minima thus achieves higher detection rates. performance comparison with Grover's discussed detail. approach requires, general, fewer qubits shorter circuits its implementation, albeit lesser success