Quantum Fourier Transform for Image Processing

TL;DR

This paper introduces a quantum algorithm for image processing in the frequency domain, enabling various filtering techniques and matrix transposition schemes, verified through simulations on IBM Qiskit.

Contribution

It presents a versatile quantum filtering oracle, novel matrix transposition schemes, and demonstrates their implementation and validation on a quantum simulator.

Findings

Quantum filtering techniques implemented successfully on IBM Qiskit.

The proposed algorithms can perform various image filtering operations.

Matrix transposition schemes show potential for quantum image processing tasks.

Abstract

Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing information, such as one-dimensional time series and two-dimensional images, in the frequency domain. The information of interest is encoded into the magnitude of probability amplitude or the coefficient of each basis state. The oracle for filtering operates based on postselection results, and its explicit circuit design is presented. This oracle is versatile enough to perform all basic filtering, including high pass, low pass, band pass, band stop, and many other processing techniques. Finally, we present two novel schemes for transposing matrices in this paper. They use similar encoding rules but with deliberate choices in terms of selecting basis states. These schemes could potentially be useful for other quantum information processing tasks, such as edge detection. The proposed techniques are implemented on the IBM Qiskit quantum simulator. Some results are compared with traditional information processing results to verify their correctness and are presented in this paper.