Quantum algorithm for testing graph completeness
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm, which takes the number of nodes and the adjacency matrix as inp...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/129045 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/129045 |
| Access Level: | acceso abierto |
| Palabra clave: | 519.17 004.42 539.12 Quantum computing Quantum algorithms Szegedy quantum walk Quantum phase estimation Graphs Complete graphs Física (Física) Teoría de los quanta Informática (Informática) 2212 Física Teórica 1206.01 Construcción de Algoritmos 1203.17 Informática |
| Sumario: | Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm, which takes the number of nodes and the adjacency matrix as input, constructs a quantum walk operator and applies QPE to estimate its eigenvalues. These eigenvalues reveal the graph’s structural properties, enabling us to determine its completeness. We establish a relationship between the number of nodes in a complete graph and the number of marked nodes, optimizing the success probability and running time. The time complexity of our algorithm is (log2 ), where is the number of nodes of the graph. offering a clear quantum advantage over classical methods. This approach is useful in network structure analysis, evaluating classical routing algorithms, and assessing systems based on pairwise comparisons. |
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