Numerical analysis on a quantum computer

  • Authors:

  • Stefan Heinrich

  • Affiliations:

  • Fachbereich Informatik, Universität Kaiserslautern, Kaiserslautern, Germany

  • Venue:
  • LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
  • Year:
  • 2005

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Abstract

We give a short introduction to quantum computing and its relation to numerical analysis. We survey recent research on quantum algorithms and quantum complexity theory for two basic numerical problems — high dimensional integration and approximation. Having matching upper and lower complexity bounds for the quantum setting, we are in a position to compare them with those for the classical deterministic and randomized setting, previously obtained in information-based complexity theory. This enables us to assess the possible speedups quantum computation could provide over classical deterministic or randomized algorithms for these numerical problems.