Quantum approximation I. Embeddings of finite-dimensional Lp spaces

@article{Heinrich2003QuantumAI,
  title={Quantum approximation I. Embeddings of finite-dimensional Lp spaces},
  author={Stefan Heinrich},
  journal={J. Complex.},
  year={2003},
  volume={20},
  pages={5-26}
}
  • S. Heinrich
  • Published 6 May 2003
  • Mathematics, Computer Science
  • J. Complex.

Quantum approximation II. Sobolev embeddings

  • S. Heinrich
  • Computer Science, Mathematics
    J. Complex.
  • 2004

Optimal query error of quantum approximation on some Sobolev classes

The results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.

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  • Ye PeixinYu Xiuhua
  • Computer Science
    2011 Fourth International Conference on Intelligent Computation Technology and Automation
  • 2011
Using a new and elegant reduction approach we derive a lower bound of quantum complexity for the approximation of imbeddings from anisotropic Sobolev classes B(Wrp([0,1]d)) to anisotropic Sobolev

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Convergence rate of quantum algorithm for multivariate approximation

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On the Power of Quantum Algorithms for Vector Valued Mean Computation

  • S. Heinrich
  • Mathematics, Computer Science
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It turns out that in contrast to the known superiority of quantum algorithms in the scalar case, in high dimensional L M P spaces classical randomized algorithms are essentially as powerful as quantum algorithms.

The quantum query complexity of elliptic PDE

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Quantum approximation II. Sobolev embeddings

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Quantum integration in Sobolev classes

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We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Holder or Sobolev spaces. First we discuss optimal deterministic and

Path Integration on a Quantum Computer

A lower bound is obtained for the minimal number of quantum queries which shows that this bound cannot be significantly improved, and it is proved that path integration on a quantum computer is tractable.

Quantum Summation with an Application to Integration

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The worst case, randomized, and quantum settings are considered and it is proved that strong tractability and tractability in the class $\lall$ are equivalent and this holds under the same assumption as for the class £lall in the worst case setting.

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These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which

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