Quantum invariants for the graph isomorphism problem
| dc.contributor.author | Cruz Calvo, Hernán Indíbil de la | |
| dc.contributor.author | Pelayo, Fernando L. | |
| dc.contributor.author | Pascual, Vicente | |
| dc.contributor.author | Paulet González, Jose Javier | |
| dc.contributor.author | Cuartero Gómez, Fernando | |
| dc.contributor.author | Llana Díaz, Luis Fernando | |
| dc.contributor.author | Mezzini, Mauro | |
| dc.date.accessioned | 2023-06-22T12:29:45Z | |
| dc.date.available | 2023-06-22T12:29:45Z | |
| dc.date.issued | 2022-10-07 | |
| dc.description.abstract | Graph Isomorphism is such an important problem in computer science, that it has been widely studied over the last decades. It is well known that it belongs to NP class, but is not NP-complete. It is thought to be of comparable difficulty to integer factorisation. The best known proved algorithm to solve this problem in general, was proposed by László Babai and Eugene Luks in 1983. Recently, there has been some research in the topic by using quantum computing, that also leads the present piece of research. In fact, we present a quantum computing algorithm that defines an invariant over Graph Isomorphism characterisation. This quantum algorithm is able to distinguish more non-isomorphic graphs than most of the known invariants so far. The proof of correctness and some hints illustrating the extent and reason of the improvement are also included in this paper. | |
| dc.description.department | Sección Deptal. de Sistemas Informáticos y Computación | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO)/FEDER | |
| dc.description.sponsorship | Comunidad de Madrid/FEDER | |
| dc.description.status | unpub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/75648 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/72679 | |
| dc.language.iso | eng | |
| dc.relation.projectID | AwESOMe (PID2021- 122215NB-C31) | |
| dc.relation.projectID | FORTE-CM (S2018/TCS-4314) | |
| dc.relation.projectID | (220426UCTR) | |
| dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/es/ | |
| dc.subject.cdu | 510.52 | |
| dc.subject.ucm | Cibernética matemática | |
| dc.subject.unesco | 1207.03 Cibernética | |
| dc.title | Quantum invariants for the graph isomorphism problem | |
| dc.type | journal article | |
| dcterms.references | [1] R. C. Read and D. G. Corneil, The graph isomorphism disease, Journal of Graph Theory 1, 339 (1977). [2] L. Babai and E. M. Luks, Canonical labeling of graphs, in Proc. of the ACM STOC Conference (IOS Press Amsterdam, 1983) pp. 171–183. [3] L. Babai, D. Y. Grigoryev, and D. M. Mount, Isomorphism of graphs with bounded eigenvalue multiplicity, in Proc. of the 14th Annual ACM Symposium on Theory of Computing (1984) pp. 310–324. [4] B. D. McKay, Practical graph isomorphism, in 10th. Manitoba Conference on Numerical Mathematics and Computing (1981) pp. 45–87. [5] P. Darga, K. Sakallah, and I. Markov, Faster symmetry discovery using sparsity of symmetries, in Proc. of the 45th Design Automation Conference (2004) pp. 149–154. [6] T. Junttila and P. Kaski, Engineering an efficient canonical labeling tool for large and sparse graphs, in Proc. of the 9th Workshop on Algorithm Engineering and Experiments (2007) pp. 135–149. [7] J. López-Presa and A. Fernández Anta, Fast algorithm for graph isomorphism testing, in Proc. of the 8th International Symposium on Experimental Algorithms (2009) pp. 221–232. [8] L. Babai, Graph isomorphism in quasipolynomial time [extended abstract], in Proc. of the 48th Annual Symposium on Theory of Computing (2016). [9] D. Conte, P. Foggia, C. Sansone, and M. Vento, Thirty years of graph matching in pattern recognition, Intl. Journal of Pattern Recognition and AI 18, 265 (2004). [10] S. Hallgren, A. Russell, and A. Ta-Shma, The hidden subgroup problem and quantum computation using group representations, SIAM Journal on Computing 32, 916 (2003). [11] F. Gaitan and L. Clark, Graph isomorphism and adiabatic quantum computing, Phys. Rev. A 89, 022342 (2014). [12] M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. V. d. Nest, and H. Briegel, Entanglement in graph states and its applications, in 2006 International School of Physics “Enrico Fermi”, Vol. 162 (IOS Press Amsterdam, 2006) pp. 115–218. [13] M. Hein, J. Eisert, and H. J. Briegel, Multiparty entanglement in graph states, Phys. Rev. A 69, 062311 (2004). [14] L. Zhao, C. A. Pérez-Delgado, and J. F. Fitzsimons, Fast graph operations in quantum computation, Phys. Rev. A 93, 032314 (2016). [15] P. W. Mills, R. P. Rundle, J. H. Samson, S. J. Devitt, T. Tilma, V. M. Dwyer, and M. J. Everitt, Quantum invariants and the graph isomorphism problem, Phys. Rev. A 100, 052317 (2019). [16] R. P. Rundle, P. W. Mills, T. Tilma, J. H. Samson, and M. J. Everitt, Simple procedure for phase-space measurement and entanglement validation, Phys. Rev. A 96, 022117 (2017). [17] A. Y. Kitaev, Quantum measurements and the abelian stabilizer problem, arXiv 10.48550/ARXIV.QUANT-PH/9511026 (1995). [18] P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Review 41, 303 (1999). [19] G. Tóth, W. Wieczorek, D. Gross, R. Krischek, C. Schwemmer, and H. Weinfurter, Permutationally invariant quantum tomography, Phys. Rev. Lett. 105, 250403 (2010). [20] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000). [21] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969). [22] C. Gidney, Quirk Quantum Simulator (https://github.com/Strilanc/Quirk, cited October 2021). [23] N. Biggs, Algebraic Graph Theory (Cambridge University Press, 1974). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 680f556a-4f1b-4eda-9add-da2c9b24796a | |
| relation.isAuthorOfPublication.latestForDiscovery | 680f556a-4f1b-4eda-9add-da2c9b24796a |
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