An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups
arXiv:quant-ph/0701235
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 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.
10 pages
References in corpus (4)
- Quantum Error Correction and Orthogonal Geometry
- From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
- Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups
- On the Power of Random Bases in Fourier Sampling: Hidden Subgroup Problem in the Heisenberg Group