Ten lectures on wavelets
Quantum computation and quantum information
Quantum computation and quantum information
Reducing Quantum Computations to Elementary Unitary Operations
Computing in Science and Engineering
Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
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Many classical algorithms are known to efficiently compute the wavelet transforms. However,those classical algorithms cannot be directly translated to quantum algorithms. Recently,efficient and complete quantum algorithms for two representative wavelet transforms(quantum Haar and quantum Daubechies of fourth order) have been proposed. Inthis paper, we generalize these algorithms in order to they can be applied to Daubechieswavelet kernels of any order. Specifically, we develop a method that efficiently factorizethose kernels. The factorization is compatible with the existing pyramidal and packetquantum wavelet algorithms. All steps of the algorithm are unitary and easily implementableon a quantum computer.