Cybernetics and Systems Analysis

, Volume 55, Issue 1, pp 10–21 | Cite as

Quantum Computing: Survey and Analysis

  • M. M. SavchukEmail author
  • A. V. Fesenko


The authors survey and analyze the main concepts and postulates of the quantum computing model, efficient quantum algorithms, and recent results, capabilities, and prospects in constructing a scalable quantum computer. A certain class of algebraic problems in the quantum computing model is considered for which there exists an efficient quantum solution algorithm. A detailed analysis of available quantum computer implementations was carried out, and it is shown that sufficient progress has not yet been made in constructing a scalable quantum computing device; nevertheless, most researchers expect that a full-fledged quantum computer will be created in the next 10–15 years.


quantum computing model quantum cryptography quantum computer efficient quantum algorithm postquantum cryptographic primitive 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Bennett and G. Brassard, “Quantum cryptography: Public-key distribution and coin tossing,” in: Proc. Intern. Conf. on Computers, Systems and Signal Processing (Bangalore, India) (1984), pp. 175–179.Google Scholar
  2. 2.
    Quantum Computer and Quantum Computing, Izhevsk Republican Printing House, Izhevsk (1999).Google Scholar
  3. 3.
    J. Preskill, Quantum Information and Computation [Russian translation], Volume 1, Research Center “Regular and chaotic dynamics;” Computer Research Institute, Moscow–Izhevsk (2008).Google Scholar
  4. 4.
    S. Aaronson, Quantum Computing since Democritus [Russian translation], Alpina Non-Fiction, Moscow (2018).zbMATHGoogle Scholar
  5. 5.
    M. N. Savchuk, “Works of the Kiev school of theoretical cryptography,” Cybernetics and Systems Analysis, Vol. 46, No. 3, 386–404 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000).zbMATHGoogle Scholar
  7. 7.
    A. Kitaev, “Quantum Computations: Algorithms and Error Correction,” Russian Mathematical Surveys, Vol. 52, No. 6, 53–112 (1997).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    A. Yao, “Quantum circuit complexity,” in: Proc. 34th Annual Symposium on Foundations of Computer Science (1993), pp. 352–361.Google Scholar
  9. 9.
    R. Boneh and R. Lipton, “Quantum cryptanalysis of hidden linear functions,” in: Proc. 15th Annual International Cryptology Conference (Santa Barbara, California, USA, August 27, 1995), Advances in Cryptology (Crypto’95); Lecture Notes in Computer Science, Vol. 31, 424–437 (1995).Google Scholar
  10. 10.
    D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. Royal Society of London, Series A, No. 439, 553–558 (1992).Google Scholar
  11. 11.
    P. W. Shor, “Algorithms for quantum computation: Discrete logs and factoring,” in: Proc. 35th Symposium on the Foundations of Computer Science (Santa Fe, NM, USA, Nov. 20–22, 1994) (1994), pp. 124-134.Google Scholar
  12. 12.
    P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Journal on Computing, Vol. 26, Iss. 5, 1484–1509 (1997).Google Scholar
  13. 13.
    W. Van Dam, S. Hallgren, and L. Ip, “Quantum algorithms for some hidden shift problems,” SIAM Journal on Computing, Vol. 36, No. 3, 763–778 (2006).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    A. V. Fesenko, “Vulnerability of cryptographic primitives based on power conjugacy search problem in quantum computing,” Cybernetics and Systems Analysis, Vol. 50, No. 5, 815–816 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Z. Bian, F. Chudak, W. Macready, L. Clark, and F. Gaitan, “Experimental determination of Ramsey numbers,” Physical Review Letters, Vol. 111, Iss. 13, p. 130505 (2013). DOI: URL:
  16. 16.
    A. Cho, “Quantum or not, controversial computer yields no speedup,” Science, Vol. 344, No. 6190, 1330–1331 (2014). DOI: Scholar
  17. 17.
    N. S. Dattani and N. Bryans, Quantum Factorization of 56153 with Only 4 Qubits, Quantum Physics Archive. arXiv:1411.6758 [quant-ph]. 2014. URL:

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”KyivUkraine

Personalised recommendations