We estimate the convergence rate of quantum algorithm for approximation from some smooth functions in the Lq([0, 1]d) norm for 1 ≤ q ≤ ∞. It turns out that for the Sobolev class B(Wpr ([0, 1]d)) (r ∈ ℕd), when p < q, the quantum algorithms can bring speedup over classical deterministic and randomized algorithms.
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机译：我们根据L q （[0，1] d ）范数中1≤q≤∞的一些光滑函数来估计近似量子算法的收敛速度。事实证明，对于Sobolev类B（W p r （[0，1] d ））（r∈ℕ d ），当p 展开▼
