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

• URL: http://arxiv.org/abs/2210.13240v3
• Date: Tue, 14 Nov 2023 16:13:31 GMT
• Title: Variational quantum eigensolver for causal loop Feynman diagrams and directed acyclic graphs
• Authors: Giuseppe Clemente, Arianna Crippa, Karl Jansen, Selomit Ram\'irez-Uribe, Andr\'es E. Renter\'ia-Olivo, Germ\'an Rodrigo, German F. R. Sborlini, Luiz Vale Silva
• Abstract summary: We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a variational quantum eigensolver (VQE) algorithm for the efficient bootstrapping of the causal representation of multiloop Feynman diagrams in the Loop-Tree Duality (LTD) or, equivalently, the selection of acyclic configurations in directed graphs. A loop Hamiltonian based on the adjacency matrix describing a multiloop topology, and whose different energy levels correspond to the number of cycles, is minimized by VQE to identify the causal or acyclic configurations. The algorithm has been adapted to select multiple degenerated minima and thus achieves higher detection rates. A performance comparison with a Grover's based algorithm is discussed in detail. The VQE approach requires, in general, fewer qubits and shorter circuits for its implementation, albeit with lesser success rates.

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