Quantum Algorithm for Path-Edge Sampling

Authors Stacey Jeffery, Shelby Kimmel , Alvaro Piedrafita

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Author Details

Stacey Jeffery
  • QuSoft and CWI, Amsterdam, The Netherlands
Shelby Kimmel
  • Middlebury College, VT, USA
Alvaro Piedrafita
  • QuSoft and CWI, Amsterdam, The Netherlands


We thank Jana Sotáková and Mehrdad Tahmasbi for insightful discussions about path finding via edge sampling.

Cite AsGet BibTex

Stacey Jeffery, Shelby Kimmel, and Alvaro Piedrafita. Quantum Algorithm for Path-Edge Sampling. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 5:1-5:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We present a quantum algorithm for sampling an edge on a path between two nodes s and t in an undirected graph given as an adjacency matrix, and show that this can be done in query complexity that is asymptotically the same, up to log factors, as the query complexity of detecting a path between s and t. We use this path sampling algorithm as a subroutine for st-path finding and st-cut-set finding algorithms in some specific cases. Our main technical contribution is an algorithm for generating a quantum state that is proportional to the positive witness vector of a span program.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Quantum query complexity
  • Theory of computation → Algorithm design techniques
  • Algorithm design and analysis
  • Query complexity
  • Graph algorithms
  • Span program algorithm
  • Path finding
  • Path detection


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