International Journal of Theoretical Physics

, Volume 57, Issue 9, pp 2854–2862 | Cite as

Efficient Quantum Algorithm for Similarity Measures for Molecules

  • Li-Ping Yang
  • Song-Feng LuEmail author
  • Li Li


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.


Quantum algorithms Phase estimation algorithm Molecular similarity Molecular graphs Quantum bioinformatics 



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.


  1. 1.
    Rupp, M., Proschak, E., Schneider, G.: Kernel approach to molecular similarity based on iterative graph similarity. Chem. Inf. Model. 47(6), 2280–2286 (2007)CrossRefGoogle Scholar
  2. 2.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Daskin, A., Grama, A., Kais, S.: Multiple network alignment on quantum computers. Quantum Inf. Process. 13, 2653–2666 (2014)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)CrossRefzbMATHGoogle Scholar
  7. 7.
    Daskin, A.: Quatum IsoRank: efficient alignment of multiple PPI networks. arXiv:1506.05905v1 [cs.CE] (2015)
  8. 8.
    Keller, J.B.: Closest unitary, orthogonal and hermitian operators to a given operator. Math. Mag. 48(4), 192–196 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44 (4), 307–327 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    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),

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyHuazhong University of Science and TechnologyWuhanChina
  2. 2.Shenzhen Research InstituteHuazhong University of Science and TechnologyShenzhenChina
  3. 3.College of Mathematics and StatisticsShenzhen UniversityShenzhenChina

Personalised recommendations