STACS 2007: STACS 2007 pp 586-597 | Cite as
An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups
Conference paper
Abstract
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p 3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.
Keywords
Abelian Group Heisenberg Group Quantum Algorithm Quantum Procedure Left Coset
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