A bilinear interpolation scheme for polar coordinate quantum images

Abstract

The amplitude-phase coding for the polar coordinate quantum image processing (APQI) model efficiently encodes images with $2^{2m}$ pixels and requires only $m+1$ qubits for grayscale images. Based on APQI, a quantum bilinear interpolation scheme is proposed that includes two sub-algorithms: a scaling-up algorithm and a scaling-down algorithm, each of which consists of four loops. In the scaling-up algorithm, each loop has four steps, while each loop has two steps in the scaling-down algorithm. Within each loop, individual steps are implemented using quantum circuits, which significantly reduces the required number of auxiliary qubits. In addition, unlike existing quantum algorithms, the proposed scheme eliminates garbage output. Simulations on the open-source quantum computing platform Qpanda demonstrate that this algorithm is both accurate and faster than its classical counterpart, which is due to the parallel processing capabilities of quantum computing. Performance analysis further demonstrates that this method reconstructs images that are free from artefacts or jagged edges and achieves a higher quality than certain state-of-the-art quantum algorithms.