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

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