Quantum Complexity of Integration

@article{Novak2001QuantumCO,
  title={Quantum Complexity of Integration},
  author={Erich Novak},
  journal={J. Complex.},
  year={2001},
  volume={17},
  pages={2-16}
}
  • E. Novak
  • Published 29 August 2000
  • Computer Science, Mathematics
  • J. Complex.
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical Holder classes Fk, ?d on 0, 1]d and define ? by ?=(k+?)/d. The known optimal orders for the complexity of deterministic and (general) randomized methods are comp(Fk, ?d, ?)???1/? and comprandom(Fk, ?d, ?)???2/(1+2?). For a quantum computer we prove… 

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