Applications of the Quantum Algorithm for st-Connectivity

Authors Kai DeLorenzo, Shelby Kimmel, R. Teal Witter

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Author Details

Kai DeLorenzo
  • Middlebury College, Computer Science Department, Middlebury, VT, USA
Shelby Kimmel
  • Middlebury College, Computer Science Department, Middlebury, VT, USA
R. Teal Witter
  • Middlebury College, Computer Science Department, Middlebury, VT, USA


We thank Chris Cade and Stacey Jeffery for helpful discussions.

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Kai DeLorenzo, Shelby Kimmel, and R. Teal Witter. Applications of the Quantum Algorithm for st-Connectivity. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity. Furthermore, we show that our algorithm for cycle detection has improved performance under the promise of large circuit rank or a small number of edges. We also provide algorithms for detecting even-length cycles and for estimating the circuit rank of a graph. All of our algorithms have logarithmic space complexity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum query complexity
  • Theory of computation → Graph algorithms analysis
  • graphs
  • algorithms
  • query complexity
  • quantum algorithms
  • span programs


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