Span Programs and Quantum Algorithms for st-Connectivity and Claw Detection

  • Aleksandrs Belovs
  • Ben W. Reichardt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)

Abstract

We use span programs to develop quantum algorithms for several graph problems. We give an algorithm that uses \(O(n \sqrt d)\) queries to the adjacency matrix of an n-vertex graph to decide if vertices s and t are connected, under the promise that they either are connected by a path of length at most d, or are disconnected. We also give O(n)-query algorithms that decide if a graph contains as a subgraph a path, a star with two subdivided legs, or a subdivided claw. These algorithms can be implemented time efficiently and in logarithmic space. One of the main techniques is to modify the natural st-connectivity span program to drop along the way “breadcrumbs,” which must be retrieved before the path from s is allowed to enter t.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Aleksandrs Belovs
    • 1
  • Ben W. Reichardt
    • 2
  1. 1.University of LatviaLatvia
  2. 2.University of Southern CaliforniaUSA

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