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

Selomit Ramírez-Uribe1,2, Andrés E. Rentería-Olivo1, and Germán Rodrigo1

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Phys. Rev. D 114, 074038 – Published 15 October, 2026

DOI: https://doi.org/10.1103/b6jg-p8mr

Abstract

Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the 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 analyze the impact of traspilation and introduce an appropriate metric to assess the complexity of the algorithm, the quantum circuit area. We explicitly analyze 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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Phys. Rev. D 114, 074038– Published 15 October, 2026
  • Received 23 July 2025
  • Accepted 25 June 2026
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