Misc,
Efficient Quantum Transforms
(February 1997)
Abstract
Quantum mechanics requires the operation of quantum computers to be unitary,
and thus makes it important to have general techniques for developing fast
quantum algorithms for computing unitary transforms. A quantum routine for
computing a generalized Kronecker product is given. Applications include
re-development of the networks for computing the Walsh-Hadamard and the quantum
Fourier transform. New networks for two wavelet transforms are given. Quantum
computation of Fourier transforms for non-Abelian groups is defined. A slightly
relaxed definition is shown to simplify the analysis and the networks that
computes the transforms. Efficient networks for computing such transforms for a
class of metacyclic groups are introduced. A novel network for computing a
Fourier transform for a group used in quantum error-correction is also given.
