# The quantum complexity of approximating the frequency moments

@article{Montanaro2016TheQC, title={The quantum complexity of approximating the frequency moments}, author={Ashley Montanaro}, journal={Quantum Inf. Comput.}, year={2016}, volume={16}, pages={1169-1190} }

The $k$'th frequency moment of a sequence of integers is defined as $F_k = \sum_j n_j^k$, where $n_j$ is the number of times that $j$ occurs in the sequence. Here we study the quantum complexity of approximately computing the frequency moments in two settings. In the query complexity setting, we wish to minimise the number of queries to the input used to approximate $F_k$ up to relative error $\epsilon$. We give quantum algorithms which outperform the best possible classical algorithms up to…

## 13 Citations

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By providing a quantum generalization of the argument of Jain and Nayak, this work leverages this to obtain a lower bound on the space complexity of multi-pass, unidirectional quantum streaming algorithms for the Dyck(2) language.

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