Fast Quantum Fourier Transforms for a Class of Nonabelian Groups
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 nonabelian 2groups 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.
 Publication:

arXiv eprints
 Pub Date:
 July 1998
 arXiv:
 arXiv:quantph/9807064
 Bibcode:
 1998quant.ph..7064P
 Keywords:

 Quantum Physics
 EPrint:
 16 pages, LaTeX2e