Efficient quantum interpolation of natural data

TL;DR

This paper introduces efficient quantum algorithms for data interpolation that leverage quantum Fourier transforms and superposition, enabling potential quantum advantage in processing natural data and images.

Contribution

The paper develops new quantum interpolation methods, including a Quantum Cosine Transform, and demonstrates their application to probability distributions and images.

Findings

Quantum Fourier Transform-based interpolation methods are effective for natural data.

Quantum superposition enhances data processing capabilities.

Demonstrations show promising results on quantum-encoded images.

Abstract

We present efficient methods to interpolate data with a quantum computer that complement uploading techniques and quantum post-processing. The quantum algorithms are supported by the efficient Quantum Fourier Transform (QFT) and classical signal and imaging processing techniques, and open the door of quantum advantage to relevant families of data. We showcase a QFT interpolation method, a Quantum Cosine Transform (QCT) interpolation geared towards natural data, and we improve upon them by utilizing a quantum circuit's capabilities of processing data in superposition. A novel circuit for the QCT is presented. We demonstrate the methods on probability distributions and quantum encoded images, and discuss the precision of the resulting interpolations.