Quantum Integration Error for Some Sobolev Classes
Based on the quantum algorithms for approximating the mean of p-summable sequences, we develop quantum algorithms for approximating the integration from anisotropic and generalized Sobolev classes. Then we analyze query error of these algorithms and prove their optimality. It is proved that for these classes of functions the optimal convergence rates of quantum algorithms are essential smaller than those of classical deterministic and randomized algorithms. Our results extend recent works of Heinrich on classical Sobolev classes.
KeywordsQuantum Computation Quantum Algorithm Sobolev Class Quantum Search Algorithm Multivariate Integration
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