Applications of the Quantum Algorithm for st-Connectivity
Kai DeLorenzo, Shelby Kimmel, R. Teal Witter · arXiv (Cornell University) · 2019
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.