References
E. Bernstein and U. Vazirani, “Quantum complexity theory”, In:Proc. STOC, ACM (1993), pp. 11–20.
T. Beth,Verfahren der schnellen Fourier-transformation, Teubner, Stuttgart (1984).
A. Chistov, private communication, 1995.
A. Chistov, D. Grigoriev,Solving algebraic systems in subexponential time. I, II, preprints LOMI E-9-83, E-10-83, Leningrad, 1983.
D. Coppersmith,An approximate Fourier transform useful in quantum factoring, research report 19642, IBM, 1994.
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.
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.
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.
R. Karp, M. Luby, and N. Madras, “Monte-Carlo approximation algorithms for enumeration problems,”J. Algorithms,10, No. 3, 429–448 (1989).
M. Karpinski and I. Shparlinski,Efficient approximation algorithms for sparse polynomials over finite fields, technical report 94-029, ICSI, Berkeley, 1994.
Y. Lakshman and D. Saunders, “On computing sparse shifts for univariate polynomials,” In:Proc. Intern. Symp. on Symbol. Algebr. Comput. (ACM, Oxford, 1994).
R. Loos, “Generalized polynomial remainder sequences,” In: B. Buchberger, J. Calmet, and R. Loos, eds.Computer Algebra, Springer, Berlin (1982).
T. Schwartz, “Fast probabilistic algorithms for verification of polynomial identities,”J. ACM,27, 701–717 (1980).
P. W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” In:Proc. FOCS, (IEEE, 1994), pp. 124–134.
D. R. Simon, “On the power of quantum computation,” In:Proc. FOCS, IEEE (1994), pp. 116–123.
R. Smolensky, Private communication, 1995.
A. Yao, “Quantum circuit complexity,” In:Proc. FOCS, IEEE (1993), pp. 352–360.
A. Yu. Kitaev,Quantum measurements and the Abelian stabilizer problem, preprint of the Institute of Theoretical Physics, Moscow, October 1995.
D. Boneh and R. Lipton, “Quantum cryptanalysis of hidden linear functions,” In:Lect. Notes Comput. Sci., Vol. 963 (1995), pp. 424–437.
Additional information
Translated from Itogi Naukii Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 34, Algebraic Geometry-5, 1996.
Rights 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
Issue Date:
DOI: https://doi.org/10.1007/BF02362466