1 research outputs found
Variational quantum eigensolver for causal loop Feynman diagrams and acyclic directed graphs
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.Comment: 32 pages, 7 figures. Improved discussion and success rates of
multi-run VQ