Quantum integration in Sobolev classes

DOI10.1016/S0885-064X(02)00008-0zbMath1026.68057arXivquant-ph/0112153WikidataQ57636024 ScholiaQ57636024MaRDI QIDQ1394935

Stefan Heinrich

Publication date: 25 June 2003

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0112153

zbMATH Keywords

quantum algorithms

Mathematics Subject Classification ID

Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) (68Q10) Quantum computation (81P68)

Related Items (19)

From Monte Carlo to quantum computation ⋮ Quantum approximation. I: Embeddings of finite-dimensional \(L_{p}\) spaces ⋮ Quantum approximation. II: Sobolev embeddings ⋮ Quantum complexity of parametric integration ⋮ The quantum setting with randomized queries for continuous problems ⋮ The Sturm-Liouville eigenvalue problem and NP-complete problems in the quantum setting with queries ⋮ The quantum query complexity of elliptic PDE ⋮ On a problem in quantum summation. ⋮ Complexity of Monte Carlo integration for Besov classes on the unit sphere ⋮ Some Results on the Complexity of Numerical Integration ⋮ Randomized complexity of parametric integration and the role of adaption. II: Sobolev spaces ⋮ On the complexity of the multivariate Sturm-Liouville eigenvalue problem ⋮ Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms ⋮ Lower bound for quantum integration error on anisotropic Sobolev classes ⋮ The randomized information complexity of elliptic PDE ⋮ On the complexity of searching for a maximum of a function on a quantum computer ⋮ Optimal query error of quantum approximation on some Sobolev classes ⋮ Lower bound for quantum phase estimation ⋮ Classical and quantum complexity of the Sturm-Liouville eigenvalue problem

Cites Work

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• On a problem in quantum summation.
• Quantum summation with an application to integration.
• The quantum query complexity of approximating the median and related statistics
• Geometric quantum computation
• Equivalent Norms for Sobolev Spaces
• Quantum complexity of integration

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