|
| related topics |
| {group, space, representation} |
| {let, theorem, proof} |
| {algorithm, log, probability} |
| {qubit, qubits, gate} |
| {error, code, errors} |
|
Efficient Quantum Transforms
Peter Hoyer
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9702028
- categories:
- quant-ph
- comments:
- 30 pages, LaTeX2e, 7 figures included
- arxiv_id:
- quant-ph/9702028
- created:
- 1997-02-11
Full article ▸
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