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Algorithms for triangle-finding, the smallest nontrivial instance of the k-clique problem, have been proposed for quantum computers.
1903
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A. M. Childs, E. Farhi, J. Goldstone, and S. Gutmann, “Finding cliques by quantum adiabatic evolution,” arXiv preprint quant-ph/0012104 , 2000
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J.-M. Bourjolly, G. Laporte, and G. Pesant, “Heuristics for finding k-clubs in an undirected graph,” Computers & Operations Research , vol. 27, no. 6, pp. 559–569, 2000
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M. Pelillo, “Encyclopedia of optimization, chapter heuristics for maximum clique and independent set,” 2001
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J. L. Castellanos, S. Gómez, and V. Guerra, “The triangle method for finding the corner of the l-curve,” Applied Numerical Mathematics , vol. 43, no. 4, pp. 359–373, 2002
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X. Hu, R. de Sousa, and S. D. Sarma, “Decoherence and dephasing in spin-based solid state quantum computers,” in Foundations Of Quantum Mechanics In The Light Of New Technology: ISQM—Tokyo’01 . World Scientific, 2002, pp. 3–11
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A. M. Childs and J. M. Eisenberg, “Quantum algorithms for subset finding,” arXiv preprint quant-ph/0311038 , 2003
2003
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N. Rhodes, P. Willett, A. Calvet, J. B. Dunbar, and C. Humblet, “Clip: similarity searching of 3d databases using clique detection,” Journal of chemical information and computer sciences , vol. 43, no. 2, pp. 443–448, 2003
2003
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V. Vassilevska Williams, J. R. Wang, R. Williams, and H. Yu, “Finding four-node subgraphs in triangle time,” in Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms . SIAM, 2014, pp. 1671–1680
2014
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F. Le Gall, “Improved quantum algorithm for triangle finding via combinatorial arguments,” in 2014 IEEE 55th Annual Symposium on Foundations of Computer Science . IEEE, 2014, pp. 216–225
2014
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B. Rossman, “The monotone complexity of k-clique on random graphs,” SIAM Journal on Computing , vol. 43, no. 1, pp. 256–279, 2014
2014
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D. Lin, X. Wang, and M. Yung, Information security and cryptology: 11th International Conference, Inscrypt 2015, Beijing, China, November 1-3, 2015, revised selected papers . Springer, 2016
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V. Spirin and L. A. Mirny, “Protein complexes and functional modules in molecular networks,” Proceedings of the national Academy of sciences , vol. 100, no. 21, pp. 12 123–12 128, 2003
2003
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F. Magniez, M. Santha, and M. Szegedy, “Quantum algorithms for the triangle problem,” SIAM Journal on Computing , vol. 37, no. 2, pp. 413–424, 2007
2007
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S. K. Özdemir, J. Shimamura, and N. Imoto, “A necessary and sufficient condition to play games in quantum mechanical settings,” New Journal of Physics , vol. 9, no. 2, p. 43–43, Feb 2007. [Online]. Available: http://dx.doi.org/10.1088/1367-2630/9/2/043
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M. Regneri, “Finding all cliques of an undirected graph,” in Seminar current trends in IE WS jun , 2007
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V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum random access memory,” Physical review letters , vol. 100, no. 16, p. 160501, 2008
2008
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R. Prevedel, G. Cronenberg, M. S. Tame, M. Paternostro, P. Walther, M. S. Kim, and A. Zeilinger, “Experimental realization of dicke states of up to six qubits for multiparty quantum networking,” Physical Review Letters , vol. 103, no. 2, Jul 2009. [Online]. Available: http://dx.doi.org/10.1103/PhysRevLett.103.020503
2009
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V. Vassilevska, “Efficient algorithms for clique problems,” Information Processing Letters , vol. 109, no. 4, pp. 254–257, 2009
2009
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G. Tóth, “Multipartite entanglement and high-precision metrology,” Physical Review A , vol. 85, no. 2, Feb 2012. [Online]. Available: http://dx.doi.org/10.1103/PhysRevA.85.022322
2012
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M. Y. Siraichi, V. F. d. Santos, S. Collange, and F. M. Q. Pereira, “Qubit allocation,” in Proceedings of the 2018 International Symposium on Code Generation and Optimization , ser. CGO 2018. New York, NY, USA: ACM, 2018, pp. 113–125. [Online]. Available: http://doi.acm.org/10.1145/3168822
2018
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G. Aleksandrowicz, T. Alexander, P. Barkoutsos, L. Bello, Y. Ben-Haim, D. Bucher, F. Cabrera-Hernández, J. Carballo-Franquis, A. Chen, C. Chen et al. , “Qiskit: An open-source framework for quantum computing,” Accessed on: Mar , vol. 16, 2019
2019
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A. Bärtschi and S. Eidenbenz, “Deterministic preparation of dicke states,” in International Symposium on Fundamentals of Computation Theory . Springer, 2019, pp. 126–139
2019
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D. Cruz, R. Fournier, F. Gremion, A. Jeannerot, K. Komagata, T. Tosic, J. Thiesbrummel, C. L. Chan, N. Macris, M.-A. Dupertuis et al. , “Efficient quantum algorithms for ghz and w states, and implementation on the ibm quantum computer,” Advanced Quantum Technologies , vol. 2, no. 5-6, p. 1900015, 2019
2019
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2019
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P. Andrés-Martínez and C. Heunen, “Automated distribution of quantum circuits via hypergraph partitioning,” Physical Review A , vol. 100, no. 3, p. 032308, 2019
2019
Later among the works it cites.
A. W. Cross, L. S. Bishop, S. Sheldon, P. D. Nation, and J. M. Gambetta, “Validating quantum computers using randomized model circuits,” Physical Review A , vol. 100, no. 3, p. 032328, 2019
2019
Later among the works it cites.
2019
Later among the works it cites.
B. Nash, V. Gheorghiu, and M. Mosca, “Quantum circuit optimizations for NISQ architectures,” Quantum Science and Technology , vol. 5, no. 2, p. 025010, mar 2020. [Online]. Available: https://doi.org/10.1088/2F2058-9565/2Fab79b1
2020
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