Quantum machine learning (QML) is an emerging research field, which is devoted to devising and implementing quantum algorithms that could enable machine learning faster than that of classical computers. In this paper, a hierarchic quantum mechanics-based framework is investigated to implement both the feature extraction and classification in the electroencephalogram (EEG) signal. Firstly, the classical EEG signal dataset is prepared as a quantum state while the sign of the data point is preserved. The prepared quantum state is then evolved with the quantum wavelet packet transformation (QWPT) and the wavelet packet energy entropy (WPEE) feature is extracted as the input of the subsequent quantum classifier. We finally propose the improved quantum support vector machine with the arbitrary nonlinear kernel, which is employed to predict the label of the EEG signal. The complexity analysis indicates that the proposed framework provides exponential speedup over the same structured classical counterpart. Besides, the quantitative experimental results verify the feasibility and validity.

In this paper, a novel frequency domain quantum watermarking scheme is proposed based on the Flexible Representation of Quantum Images, which can embed a 2n-1×2n-1 binary watermark image into a 2n×2n grayscale carrier image. The quantum Haar wavelet transform is developed and used to decompose quantum images. The diagonal detail coefficients of the carrier image are obtained from the image decomposition. Then, according to the watermark image information, the diagonal detail coefficients are either unchanged or slightly modified. Since all of the used quantum operations are invertible, extraction of the watermark image is performed in a straightforward manner by reversing the watermarking embedding process. Finally, the proposed quantum image watermarking scheme is simulated on a classical computer and evaluated using different carrier and watermark images. The simulation results and performance analyses indicate the high performance of the presented watermarking scheme in terms of the similarity between the watermarked and carrier images.