Applications of the quantum algorithm for st-connectivity
Quantum Physics
2019-10-03 v1 Computational Complexity
Data Structures and Algorithms
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
@article{arxiv.1904.05995,
title = {Applications of the quantum algorithm for st-connectivity},
author = {Kai DeLorenzo and Shelby Kimmel and R. Teal Witter},
journal= {arXiv preprint arXiv:1904.05995},
year = {2019}
}