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Applications of the Quantum Algorithm for st-Connectivity

Authors Kai DeLorenzo, Shelby Kimmel, R. Teal Witter

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Subject Classification

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

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Abstract

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.TQC.2019.6

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

Funding

This research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-18-1-0286. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

Acknowledgements

We thank Chris Cade and Stacey Jeffery for helpful discussions.

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