Difference between revisions of "Hidden Subgroup Zoo"
From Quantum Computing Theory Group
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===Solvable Groups of Bounded Exponent and of Bounded Derived Series=== | ===Solvable Groups of Bounded Exponent and of Bounded Derived Series=== | ||
| − | ===Groups with Small Commutator Subgroup== | + | ===Groups with Small Commutator Subgroup=== |
===Groups with an Elementary Abelian Normal 2-Subgroup of Small Index or with Cyclic Factor Group=== | ===Groups with an Elementary Abelian Normal 2-Subgroup of Small Index or with Cyclic Factor Group=== | ||
Revision as of 18:45, 17 June 2008
Contents
- 1 The Problem
- 2 Groups Which Admit an Efficient Algorithm
- 2.1 Finite Abelian Groups
- 2.2 Normal Subgroups
- 2.3 Near Abelian Groups
- 2.4 Near Hamiltonian Groups
- 2.5 Semidirect Products of Abelian Groups
- 2.6 Extraspecial Groups and Nil-2 Groups
- 2.7 Solvable Groups of Bounded Exponent and of Bounded Derived Series
- 2.8 Groups with Small Commutator Subgroup
- 2.9 Groups with an Elementary Abelian Normal 2-Subgroup of Small Index or with Cyclic Factor Group
- 3 Groups Which Admit an Subexponential Time Algorithm
- 4 Existential Results
The Problem
Hidden Subgroup Problem (HSP)
Given: A function <math>f</math> from a group <math>G</math> to a set <math>S</math>, <math>f:G \rightarrow S</math> which is promised to be constant and distinct on different left cosets of an unknown subgroup <math>H</math>:
Problem: Find the hidden subgroup <math>H</math> by returning a set of generators for <math>H</math>
An algorithm for the hidden subgroup problem is efficient if the algorithm runs in a time polynomial in the logarithm of the size of the group (for infinite groups the definition is more subtle.
