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Propose innovative quantum computing algorithms and applications beyond factoring and classical simulation, showcasing their potential to revolutionize fields such as artificial intelligence, cryptography, and optimization

Propose innovative quantum computing algorithms and applications beyond factoring and classical simulation, showcasing their potential to revolutionize fields such as artificial intelligence, cryptography, and optimization problems. Provide detailed explanations of how these new approaches leverage unique quantum features, such as superposition and entanglement, to surpass traditional methods' limitations.

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