A Polynomial Quantum Query Lower Bound for the Set Equality Problem

  • Gatis Midrijānis
Conference paper

DOI: 10.1007/978-3-540-27836-8_83

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)
Cite this paper as:
Midrijānis G. (2004) A Polynomial Quantum Query Lower Bound for the Set Equality Problem. In: Díaz J., Karhumäki J., Lepistö A., Sannella D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg

Abstract

The set equality problem is to tell whether two sets A and B are equal or disjoint under the promise that one of these is the case. This problem is related to the Graph Isomorphism problem. It was an open problem to find any ω(1) query lower bound when sets A and B are given by quantum oracles. We will show that any error-bounded quantum query algorithm that solves the set equality problem must evaluate oracles \(\Omega(\sqrt[5]{\frac{n}{\ln n}})\) times, where n=|A|=|B|.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Gatis Midrijānis
    • 1
  1. 1.University of LatviaRigaLatvia

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