Quantum Approximation I. Embeddings of Finite Dimensional L_p Spaces

Details Quantum Approximation I. Embeddings of Finite Dimensional L_p Spaces Quantum Approximation I. Embeddings of Finite Dimensional L_p Spaces

2003-05-06

arxiv.org/abs/quant-ph/0305030v1

Physics

Quantum Physics

27 pages, paper submitted to the Journal of Complexity

Scientific paper

We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The results show that for certain regions of the parameter domain quantum computation can essentially improve the rate of convergence of classical deterministic or randomized approximation, while there are other regions where the best possible rates coincide for all three settings. These results serve as a crucial building block for analyzing approximation in function spaces in a subsequent paper.

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