Average-Case Quantum Query Complexity

  • Andris Ambainis
  • Ronald de Wolf
Conference paper

DOI: 10.1007/3-540-46541-3_11

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)
Cite this paper as:
Ambainis A., de Wolf R. (2000) Average-Case Quantum Query Complexity. In: Reichel H., Tison S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg


We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial [3]. We show that for average-case complexity under the uniform distribution, quantum algorithms can be exponentially faster than classical algorithms. Under non-uniform distributions the gap can even be super-exponential. We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Ronald de Wolf
    • 2
    • 3
  1. 1.Computer Science DepartmentUniversity of CaliforniaBerkeley
  2. 2.CWIAmsterdamThe Netherlands
  3. 3.ILLCUniversity of AmsterdamAmsterdam

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