Three-dimensional quantum wavelet transforms

Wavelet transform is being widely used in the field of information processing. One-dimension and two-dimension quantum wavelet transforms have been investigated. However, three-dimensional quantum wavelet transforms have not been reported.

A team led by Hai-Sheng Li has proposed a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos. The team constructed the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms, respectively. Next, quantum circuits of the two wavelet transforms using iterative methods were designed. Finally, the proposed quantum wavelet transforms were selected to realize quantum video compression as a primary application.

The research is published in the journal Frontiers of Computer Science.

In the research, the team analyzes the complexities of the proposed 3D quantum wavelet transforms. Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts. Furthermore, simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimensional quantum wavelet transforms.

For future work, the team will extend the results to implement quantum versions of other wavelet transforms such as Daubechies D8 wavelet transform and cross wavelet transform.

More information:
Haisheng Li et al, Three-dimensional quantum wavelet transforms, Frontiers of Computer Science (2022). DOI: 10.1007/s11704-022-1639-y

Provided by Frontiers Journals