# Quantum Summation with an Application to Integration

@article{Heinrich2002QuantumSW, title={Quantum Summation with an Application to Integration}, author={Stefan Heinrich}, journal={J. Complex.}, year={2002}, volume={18}, pages={1-50} }

We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences that satisfy a p-summability condition and for integration of functions from Lebesgue spaces Lp(0, 1]d), and analyze their convergence rates. We also prove lower bounds showing that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of G. Brassard et al. (2000, “Quantum…

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