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.

翻译：量子信息处理及其子领域量子图像处理，随着量子力学实用性的提升而迅速发展。本文提出一种在频域中处理一维时间序列和二维图像等信息的量子算法。目标信息被编码为概率幅值或各基态系数，基于后选择结果运行的滤波预言机及其显式电路设计被给出。该预言机具有通用性，可执行所有基础滤波操作，包括高通、低通、带通、带阻及其他多种处理技术。此外，本文提出两种新型矩阵转置方案。这些方案采用相似的编码规则，但在基态选择上具有特定考量，可能对边缘检测等其他量子信息处理任务具有潜在应用价值。所提技术已在IBM Qiskit量子模拟器上实现，部分结果与传统信息处理结果进行对比以验证其正确性，并在本文中展示。