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Quantum learning algorithms can achieve cubic separations over classical randomized learners, shattering the longstanding belief that exact learning speedups are constrained by Grover search and Bernstein-Vazirani limits.
Worst-case complexity heavily masks practical quantum utility: applying smoothed analysis unlocks exponential quantum-classical separations on total functions and superpolynomial speedups for foundational string problems.
Quantum circuits can sample distributions that classical language models cannot, revealing a profound computational divide that challenges the supremacy of classical architectures.
