Efficient quantum interpolation of natural data
Sergi Ramos-Calderer
Abstract
We present efficient methods to interpolate data with a quantum computer to complement uploading techniques and quantum postprocessing. The quantum algorithms make use of the efficient quantum Fourier transform (QFT) as well as classical signal and imaging processing techniques, and may facilitate quantum advantages for some 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 circuit for the QCT is presented. We illustrate the methods on probability distributions and quantum encoded images, and discuss the precision of the resulting interpolations.