Quantum algorithms for problems in number theory, algebraic geometry, and group theory

R. Schoof, Elliptic curves over finite fields and the computation of square roots mod p \bmod\ p , Mathematics of Computation, Volume 44 (1985), 483–494

1985

Earlier work this paper cites.

J. Pila, Frobenius maps of abelian varieties and finding roots of unity in finite fields , Mathematics of Computation, Volume 55 (1990), 745–763

1990

Earlier work this paper cites.

L. M. Adleman, and M.-D. Huang, Counting points on curves and Abelian varieties over finite fields , Journal of Symbolic Computation, Volume 32 (2001), 171–189. preliminary version in ANTS-II 1996

1996

Earlier work this paper cites.

L. Grover, A fast quantum-mechanical algorithm for database search , Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC ’96), 1996, pp. 212–219

1996

Earlier work this paper cites.

R. Lidl and H. Niederreiter, Finite Fields , Encyclopedia of Mathematics and Its Applications, Vol. 20, Cambridge Univ. Press, Cambridge, 1997

1997

Earlier work this paper cites.

P. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer , SIAM Journal on Computing, Volume 26 (1997), 1484–1509

1997

Earlier work this paper cites.

M. Boyer, G. Brassard, P. Høyer and A. Tapp, Tight bounds on quantum searching , Fortschritte der Physik, Volume 46 (1998), 493–505

1998

Earlier work this paper cites.

R. Cleve, The query complexity of order-finding , Inf. Comput., Volume 192 (2004), 162–171, preliminary version in CCC 2000, eprint quant-ph/9911124

2000

Cited alongside, same era.

M. Ettinger and P. Høyer, On quantum algorithms for noncommutative hidden subgroups , Advances in Applied Mathematics, Volume 25 (2000), pp. 239–251

2000

Cited alongside, same era.

S. Hallgren, A. Russell, and A. Ta-Shma, The hidden subgroup problem and quantum computation using group representations , SIAM Journal on Computing, Volume 32 (2003), 916–934, preliminary version in STOC 2000

2000

Cited alongside, same era.

M. Grigni, L.J. Schulman, M. Vazirani and U. Vazirani, Quantum mechanical algorithms for the nonabelian hidden subgroup problem , Combinatorica, Volume 24 (2004), 137–154, preliminary version in STOC 2001

2001

Cited alongside, same era.

J. Proos and C. Zalka, Shor’s discrete logarithm quantum algorithm for elliptic curves , Quantum Information and Computation, Volume 3 (2003), 317–344

2003

Later among the works it cites.

R. Crandall and C. Pomerance, Prime Numbers: A computational perspective , Springer-Verlag, Berlin, 2005

2005

Later among the works it cites.

P. Kaye, Optimized quantum implementation of elliptic curve arithmetic over binary fields , Quantum Information and Computation, Volume 5 (2005), 474–491

2005

Later among the works it cites.

C. Moore, A. Russell and L. J. Schulman, The symmetric group defies strong Fourier sampling , Proceedings of the 46th IEEE Symposium on Foundations of Computer Science, 2005, pp. 479–490

2005

Later among the works it cites.

K. S. Kedlaya, Quantum computation of zeta functions of curves , Computational Complexity, Volume 15 (2006), 1–19

2006