Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs
arxiv(2024)
摘要
Quantum algorithms are a promising framework for a proper treatment of
Feynman loop integrals due to the existence of a manifestly causal
representation scenario. Particularly, unfolding causal configurations of
multiloop Feynman diagrams is understood as querying directed acyclic
graph (DAG) configurations of undirected graphs in graph theory. In this paper
we present a quantum algorithm for querying causality of multiloop Feynman
diagrams using an ingenious change in the logic of the design of the oracle
operator. The construction of the quantum oracle is surprisingly based
exclusively on multicontrolled Toffoli gates and XNOT gates. The efficiency of
the algorithm is evaluated performing a comparison with a quantum algorithm
based on binary clauses. Additionally, we explicitly analise several three-,
four- and five-eloop topologies, which have not been previously explored due to
their higher complexity.
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