On the Quantum Query Complexity of Detecting Triangles in Graphs

Mario Szegedy

On the Quantum Query Complexity of Detecting Triangles in Graphs

量子物理 2007-05-23 v2

作者: Mario Szegedy

摘要

We show that in the quantum query model the complexity of detecting a triangle in an undirected graph on $n$ nodes can be done using $O(n^{1+{3\over 7}}\log^{2}n)$ quantum queries. The same complexity bound applies for outputting the triangle if there is any. This improves upon the earlier bound of $O(n^{1+{1\over 2}})$ .

关键词

quantum search algorithms random graph theory positive maps in quantum information

引用

@article{arxiv.quant-ph/0310107,
  title  = {On the Quantum Query Complexity of Detecting Triangles in Graphs},
  author = {Mario Szegedy},
  journal= {arXiv preprint arXiv:quant-ph/0310107},
  year   = {2007}
}

备注

13 pages

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