Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918102868951040 |
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| author | Ramírez-Uribe, Selomit Rentería-Olivo, Andrés E. Rodrigo, Germán |
| author_facet | Ramírez-Uribe, Selomit Rentería-Olivo, Andrés E. Rodrigo, Germán |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs Ramírez-Uribe, Selomit Rentería-Olivo, Andrés E. Rodrigo, Germán Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Quantum querying based on multicontrolled Toffoli gates for causal Feynman loop configurations and directed acyclic graphs |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.03544 |