Applications of the quantum algorithm for st-connectivity

12 Apr 2019  ·  DeLorenzo Kai, Kimmel Shelby, Witter R. Teal ·

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. read more

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Quantum Physics Computational Complexity Data Structures and Algorithms