Quantum Algorithm for Path-Edge Sampling
Quantum Physics
2023-07-21 v1 Data Structures and Algorithms
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.
Cite
@article{arxiv.2303.03319,
title = {Quantum Algorithm for Path-Edge Sampling},
author = {Stacey Jeffery and Shelby Kimmel and Alvaro Piedrafita},
journal= {arXiv preprint arXiv:2303.03319},
year = {2023}
}
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33 pages