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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

Funding

Shelby Kimmel and Stacey Jeffery: sponsored by the U.S. Army Research Office and this work was accomplished under Grant Number W911NF-20-1-0327. 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.
  • Jeffery, Stacey: supported by NWO Klein project number OCENW.Klein.061, and the European Union (ERC, ASC-Q, 101040624). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. SJ is a CIFAR Fellow in the Quantum Information Science Program.

Acknowledgements

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

Cite As Get 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) https://doi.org/10.4230/LIPIcs.TQC.2023.5

Abstract

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
Keywords
  • Algorithm design and analysis
  • Query complexity
  • Graph algorithms
  • Span program algorithm
  • Path finding
  • Path detection

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