Difference between revisions of "Hidden Subgroup Zoo"
From Quantum Computing Theory Group
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''Given:'' <math>f</math>, a function 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>: | ''Given:'' <math>f</math>, a function 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>: | ||
| − | <center><math>~f(g)=f(h) | + | <center><math>~f(g)=f(h)~{\rm iff}~gH = hH</math></center> |
''Problem:'' Find the hidden subgroup problem <math>H</math> by returning a set of generators for <math>H</math> | ''Problem:'' Find the hidden subgroup problem <math>H</math> by returning a set of generators for <math>H</math> | ||
Revision as of 00:48, 13 June 2008
Hidden Subgroup Problem (HSP)
Given: <math>f</math>, a function 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 problem <math>H</math> by returning a set of generators for <math>H</math>
