  The field of quantum deep learning presents significant opportunities for
advancing computational capabilities, yet it faces a major obstacle in the form
of the "information loss problem" due to the inherent limitations of the
necessary quantum tomography in scaling quantum deep neural networks. This
paper introduces an end-to-end Quantum Vision Transformer (QViT), which
incorporates an innovative quantum residual connection technique, to overcome
these challenges and therefore optimize quantum computing processes in deep
learning. Our thorough complexity analysis of the QViT reveals a theoretically
exponential and empirically polynomial speedup, showcasing the model's
efficiency and potential in quantum computing applications. We conducted
extensive numerical tests on modern, large-scale transformers and datasets,
establishing the QViT as a pioneering advancement in applying quantum deep
neural networks in practical scenarios. Our work provides a comprehensive
quantum deep learning paradigm, which not only demonstrates the versatility of
current quantum linear algebra algorithms but also promises to enhance future
research and development in quantum deep learning.
