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Efficient Quantum Algorithm for All Quantum Wavelet Transforms by Bagherimehrab, Mohsen; Aspuru-Guzik, Alan is a scholarly article available to read on EtoBox.

What is Efficient Quantum Algorithm for All Quantum Wavelet Transforms about?

Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet transform is specified by a sequence of numbers associated with the type of wavelet used and an order parameter specifying the length of the sequence. While the quantum Fourier transform, a quantum analog of the classical Fourier transform, has been pivotal in quantum computing, prior works on quantum wavelet transforms~(QWTs) were limited to the second and fourth order of a particular wavelet, the Daubechies wavelet. Here we develop a simple yet efficient quantum algorithm for executing any wavelet transform on a quantum computer. Our approach is to decompose the kernel matrix of a wavelet transform as a linear combination of unitaries (LCU) that are compilable by easy-to-implement modular quantum arithmetic operations and use the LCU technique to construct a probabilistic procedure to implement a QWT with a \textit{known} success probability. We then use properties of wavelets to make this approach deterministic by a few executions of the amplitude amp

Author

Bagherimehrab, Mohsen; Aspuru-Guzik, Alan

Published

2023

Language

EN