An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

Details An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

2007-01-31

arxiv.org/abs/quant-ph/0701235v1

stacs 2007

Physics

Quantum Physics

10 pages

Scientific paper

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 p3 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.

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