Skip to main content
Log in

Testing the shift-equivalence of polynomials using quantum machines

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. E. Bernstein and U. Vazirani, “Quantum complexity theory”, In:Proc. STOC, ACM (1993), pp. 11–20.

  2. T. Beth,Verfahren der schnellen Fourier-transformation, Teubner, Stuttgart (1984).

    Google Scholar 

  3. A. Chistov, private communication, 1995.

  4. A. Chistov, D. Grigoriev,Solving algebraic systems in subexponential time. I, II, preprints LOMI E-9-83, E-10-83, Leningrad, 1983.

  5. D. Coppersmith,An approximate Fourier transform useful in quantum factoring, research report 19642, IBM, 1994.

  6. D. Grigoriev and M. Karpinski, “An approximate algorithm for the number of zeroes of arbitrary polynomials overGF[q],” In:Proc. FOCS, IEEE (1991), pp. 662–669.

  7. D. Grigoriev and M. Karpinski, “A zero-test and an interpolation algorithm for the shifted sparse polynomials,” In:Proc. AEECC 1993, Lect. Notes in Comput. Sci., Vol. 673, Springer, Berlin (1993), pp. 162–169.

    Google Scholar 

  8. D. Grigoriev and Y. Lakshman, “Algorithms for computing sparse shifts for multivariate polynomials,” In:Proc. Intern. Symp. on Symbol. Algebr. Comput. (ACM, Montreal, 1995), pp. 96–103.

  9. R. Karp, M. Luby, and N. Madras, “Monte-Carlo approximation algorithms for enumeration problems,”J. Algorithms,10, No. 3, 429–448 (1989).

    MathSciNet  Google Scholar 

  10. M. Karpinski and I. Shparlinski,Efficient approximation algorithms for sparse polynomials over finite fields, technical report 94-029, ICSI, Berkeley, 1994.

    Google Scholar 

  11. Y. Lakshman and D. Saunders, “On computing sparse shifts for univariate polynomials,” In:Proc. Intern. Symp. on Symbol. Algebr. Comput. (ACM, Oxford, 1994).

    Google Scholar 

  12. R. Loos, “Generalized polynomial remainder sequences,” In: B. Buchberger, J. Calmet, and R. Loos, eds.Computer Algebra, Springer, Berlin (1982).

    Google Scholar 

  13. T. Schwartz, “Fast probabilistic algorithms for verification of polynomial identities,”J. ACM,27, 701–717 (1980).

    Article  MATH  Google Scholar 

  14. P. W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” In:Proc. FOCS, (IEEE, 1994), pp. 124–134.

  15. D. R. Simon, “On the power of quantum computation,” In:Proc. FOCS, IEEE (1994), pp. 116–123.

  16. R. Smolensky, Private communication, 1995.

  17. A. Yao, “Quantum circuit complexity,” In:Proc. FOCS, IEEE (1993), pp. 352–360.

  18. A. Yu. Kitaev,Quantum measurements and the Abelian stabilizer problem, preprint of the Institute of Theoretical Physics, Moscow, October 1995.

  19. D. Boneh and R. Lipton, “Quantum cryptanalysis of hidden linear functions,” In:Lect. Notes Comput. Sci., Vol. 963 (1995), pp. 424–437.

Download references

Authors

Additional information

Translated from Itogi Naukii Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 34, Algebraic Geometry-5, 1996.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigoriev, D. Testing the shift-equivalence of polynomials using quantum machines. J Math Sci 82, 3184–3193 (1996). https://doi.org/10.1007/BF02362466

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02362466

Keywords

Navigation