Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs

• URL: http://arxiv.org/abs/2404.03544v2
• Date: Thu, 24 Jul 2025 11:15:59 GMT
• Title: Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs
• Authors: Selomit Ramírez-Uribe, Andrés E. Rentería-Olivo, Germán Rodrigo,
• Abstract summary: We present a quantum algorithm for querying in both types of applications.<n>The efficiency of the algorithm is evaluated by comparison with a quantum algorithm based on binary clauses.<n>We explicitly analyse three-, four- and five-eloop topologies, which have not previously been explored.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph theory. In this paper, we present a quantum algorithm for querying in both types of applications, using a systematic and sparing logic in the design of an oracle operator. The construction of the quantum oracle is based exclusively on multicontrolled Toffoli (MCX) gates and quantum NOT (Pauli-$X$) gates. The efficiency of the algorithm is evaluated by comparison with a quantum algorithm based on binary clauses. Furthermore, we analyse the impact of traspilation and introduce an appropriate metric to assess the complexity of the algorithm, the \emph{quantum circuit area}. We explicitly analyse three-, four- and five-eloop topologies, which have not previously been explored due to their higher complexity and the current limitations of quantum simulators.

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