Quantum frequency resampling

TL;DR

This paper introduces quantum algorithms for resampling data encoded in quantum states, leveraging the quantum Fourier transform to efficiently modify data resolution, with potential advantages over classical methods.

Contribution

It presents a novel quantum resampling framework that uses quantum Fourier transform to adjust data encoding, offering potential efficiency improvements.

Findings

Quantum algorithms for resampling data using quantum Fourier transform.

Discussion of advantages over classical resampling methods.

Potential for reduced resource costs in quantum data processing.

Abstract

In signal processing, resampling algorithms can modify the number of resources encoding a collection of data points. Downsampling reduces the cost of storage and communication, while upsampling interpolates new data from limited one, e.g. when resizing a digital image. We present a toolset of quantum algorithms to resample data encoded in the probabilities of a quantum register, using the quantum Fourier transform to adjust the number of high-frequency encoding qubits. We discuss advantage over classical resampling algorithms.