Abstract
The similarity measures for molecules play an important role for research in chemistry, biology and drug design. In order to obtain similarity measures for giant molecules such as muscle protein titin, the existing classical algorithms possess high computational complexity and many other disadvantages. An effective quantum algorithm, Quantum Method for Similarity Measures for Molecules (QMSM), is introduced to obtain similarity measure for molecules based on the quantum phase estimation algorithm. Moreover, we discuss the feasibility of simulating the quantum algorithm QMSM with quantum circuits. Finally, the performance evaluation and comparison of the QMSM algorithm are presented, where the QMSM can obtain exponential speedups compared to its classical counterparts.
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References
Rupp, M., Proschak, E., Schneider, G.: Kernel approach to molecular similarity based on iterative graph similarity. Chem. Inf. Model. 47(6), 2280–2286 (2007)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computation, pp 212–219. ACM, New York (1996)
Fröhlich, H., Wegner, J. K., Sieker, F., Zell, A.: Optimal Assignment Kernels for attributed molecular graphs. In: Proceedings of the 22nd International Conference on Machine Learning, Bonn (2005)
Daskin, A., Grama, A., Kais, S.: Multiple network alignment on quantum computers. Quantum Inf. Process. 13, 2653–2666 (2014)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)
Daskin, A.: Quatum IsoRank: efficient alignment of multiple PPI networks. arXiv:1506.05905v1 [cs.CE] (2015)
Keller, J.B.: Closest unitary, orthogonal and hermitian operators to a given operator. Math. Mag. 48(4), 192–196 (1975)
Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44 (4), 307–327 (2003)
Aharonov, D., Ta-Shma, A.: Adiabatic quantum state generation and statistical zero knowledge. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, STOC’03, pp 20–29. ACM, New York (2003), https://doi.org/10.1145/780542-780546
Acknowledgements
This work is supported by the Natural Science Foundation of Hubei Province of China under Grant No.2016CFB541 and the Applied Basic Research Program of Wuhan Science and Technology Bureau of China under Grant No.2016010101010003 and the Science and Technology Program of Shenzhen of China under Grant No. JCYJ20170307160458368 and No. JCYJ20170818160208570.
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Yang, LP., Lu, SF. & Li, L. Efficient Quantum Algorithm for Similarity Measures for Molecules. Int J Theor Phys 57, 2854–2862 (2018). https://doi.org/10.1007/s10773-018-3805-4
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DOI: https://doi.org/10.1007/s10773-018-3805-4