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Quantum Discrete Cosine Transform for Image Compression

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arxiv quant-ph/0601043 v2 pith:6NQCMDBC submitted 2006-01-08 quant-ph

Chao Yang Pang , Zheng Wei Zhou , Guang Can Guo This is my paper · ORCID
classification quant-ph
keywords compressionimagequantumalgorithmcomplexitycosinediscreteiteration
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Discrete Cosine Transform (DCT) is very important in image compression. Classical 1-D DCT and 2-D DCT has time complexity O(NlogN) and O(N²logN) respectively. This paper presents a quantum DCT iteration, and constructs a quantum 1-D and 2-D DCT algorithm for image compression by using the iteration. The presented 1-D and 2-D DCT has time complexity O(sqrt(N)) and O(N) respectively. In addition, the method presented in this paper generalizes the famous Grover's algorithm to solve complex unstructured search problem.

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  1. QRTlib: A Library for Fast Quantum Real Transforms

    quant-ph 2025-10 conditional novelty 6.0 of 10

    A new Qiskit library implements quantum Hartley, cosine, and sine transforms, with an LCU-based Hartley circuit whose leading gate-complexity term is four times smaller than the previous best.

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