Quantum wave packet transforms with compact frequency support

TL;DR

This paper presents a quantum circuit method for implementing a broad class of wave packet transforms with compact frequency support, enabling efficient multi-scale signal analysis on quantum computers.

Contribution

It introduces a novel quantum circuit approach for wave packet transforms with compact frequency support, extending existing quantum algorithms to a wider class of wave packets.

Findings

Enables quantum implementation of wave packet transforms with compact frequency support

Operates in frequency space through signal reallocation and reshuffling

Can be extended to other wave packets with similar properties

Abstract

Different kinds of wave packet transforms are widely used for extracting multi-scale structures in signal processing tasks. This paper introduces the quantum circuit implementation of a broad class of wave packets, including Gabor atoms and wavelets, with compact frequency support. Our approach operates in the frequency space, involving reallocation and reshuffling of signals tailored for manipulation on quantum computers. The resulting implementation is different from the existing quantum algorithms for spatially compactly supported wavelets and can be readily extended to quantum transforms of other wave packets with compact frequency support.