dorsal/arxiv
View SchemaQuantum Approximation II. Sobolev Embeddings
| Authors | Stefan Heinrich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305031 |
| URL | https://arxiv.org/abs/quant-ph/0305031 |
Abstract
A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query complexity of this problem (up to logarithmic factors). It turns out that in certain regions of the domain of parameters p,q,r,d quantum computation can reach a speedup of roughly squaring the rate of convergence of classical deterministic or randomized approximation methods. There are other regions were the best possible rates coincide for all three settings.
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"abstract": "A basic problem of approximation theory, the approximation of functions from\nthe Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered\nfrom the point of view of quantum computation. We determine the quantum query\ncomplexity of this problem (up to logarithmic factors). It turns out that in\ncertain regions of the domain of parameters p,q,r,d quantum computation can\nreach a speedup of roughly squaring the rate of convergence of classical\ndeterministic or randomized approximation methods. There are other regions were\nthe best possible rates coincide for all three settings.",
"arxiv_id": "quant-ph/0305031",
"authors": [
"Stefan Heinrich"
],
"categories": [
"quant-ph"
],
"title": "Quantum Approximation II. Sobolev Embeddings",
"url": "https://arxiv.org/abs/quant-ph/0305031"
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