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Image compression and entanglement
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The pixel values of an image can be casted into a real ket of a Hilbert space using an appropriate block structured addressing. The resulting state can then be rewritten in terms of its matrix product state representation in such a way that quantum entanglement corresponds to classical correlations between different coarse-grained textures. A truncation of the MPS representation is tantamount to a compression of the original image. The resulting algorithm can be improved adding a discrete Fourier transform preprocessing and a further entropic lossless compression.
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Quantum-inspired tensor networks in machine learning models
Tensor networks developed for quantum states are reviewed as tools for machine learning models, with assessment of their potential computational, explanatory, and privacy advantages alongside remaining challenges.
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