@inproceedings{pueschel1998quantum,
author = {Pueschel, Markus and Roetteler, Martin and Beth, Thomas},
title = {Quantum Fourier Transforms for a Class of Non-abelian Groups},
booktitle = {Proceedings 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC'99), Honolulu, Hawaii, Springer LNCS},
year = {1998},
month = {July},
abstract = {An algorithm is presented allowing the construction of fast Fourier transforms for any solvable group on a classical computer. The special structure of the recursion formula being the core of this algorithm makes it a good starting point to obtain systematically fast Fourier transforms for solvable groups on a quantum computer. The inherent structure of the Hilbert space imposed by the qubit architecture suggests to consider groups of order 2^n first (where n is the number of qubits). As an example, fast quantum Fourier transforms for all 4 classes of non-abelian 2-groups with cyclic normal subgroup of index 2 are explicitly constructed in terms of quantum circuits. The (quantum) complexity of the Fourier transform for these groups of size 2^n is O(n^2) in all cases.

 },
url = {http://approjects.co.za/?big=en-us/research/publication/quantum-fourier-transforms-class-non-abelian-groups/},
pages = {148-159},
volume = {1719},
edition = {Proceedings 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC'99), Honolulu, Hawaii, Springer LNCS},
}