An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Nil-2 Groups

  title={An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Nil-2 Groups},
  author={G. Ivanyos and L. Sanselme and M. Santha},
  • G. Ivanyos, L. Sanselme, M. Santha
  • Published 2010
  • Mathematics, Physics, Computer Science
  • Algorithmica
  • In this paper we show that the hidden subgroup problem in nil-2 groups, that is in groups of nilpotency class at most 2, can be solved efficiently by a quantum procedure. The algorithm is an extension of our earlier method for extraspecial groups in Ivanyos et al. (Proceedings of the 24th Symposium on Theoretical Aspects of Computer Science (STACS), vol. 4393, pp. 586–597, 2007), but it has several additional features. It contains a powerful classical reduction for the hidden subgroup problem… CONTINUE READING
    16 Citations
    The status of polycyclic group-based cryptography: A survey and open problems
    • Jonathan Gryak, Delaram Kahrobaei
    • Computer Science, Mathematics
    • Groups Complex. Cryptol.
    • 2016
    • 16
    • PDF
    Finding conjugate stabilizer subgroups in PSL and related groups
    • 10
    • Highly Influenced
    • PDF
    Abelian Hypergroups and Quantum Computation
    • 2
    • PDF
    On Solving Systems of Diagonal Polynomial Equations Over Finite Fields
    • 1
    • PDF
    How hard is deciding trivial versus nontrivial in the dihedral coset problem?


    From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
    • 117
    • PDF
    An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups
    • 26
    • PDF
    The Hidden Subgroup Problem and Quantum Computation Using Group Representations
    • 74
    • PDF
    Las Vegas algorithms for matrix groups
    • R. Beals, L. Babai
    • Mathematics, Computer Science
    • Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science
    • 1993
    • 43
    • PDF
    Efficient Quantum Algorithms For Some Instances Of The Non-Abelian Hidden Subgroup Problem
    • 69
    • PDF
    Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem
    • 50
    • PDF
    Normal subgroup reconstruction and quantum computation using group representations
    • 116
    • PDF
    Computing in solvable matrix groups
    • E. Luks
    • Mathematics, Computer Science
    • Proceedings., 33rd Annual Symposium on Foundations of Computer Science
    • 1992
    • 67
    • PDF
    On the impossibility of a quantum sieve algorithm for graph isomorphism
    • 26
    • PDF