A learning graph based quantum query algorithm for finding constant-size subgraphs

Details A learning graph based quantum query algorithm for finding constant-size subgraphs A learning graph based quantum query algorithm for finding constant-size subgraphs

2011-09-23

arxiv.org/abs/1109.5135v2

Physics

Quantum Physics

The previous algorithm given does not have the claimed complexity. The algorithm has been modified in order to obtain the same

Scientific paper

We use the learning graph framework of Belovs to show that the quantum query
complexity of determining if an $n$-vertex graph contains a fixed $k$-vertex
subgraph $H$ is $O(n^{2-2/k-t})$ where $t=(2k-d-3)/(k(d+1)(m+2))$ and $d$ and
$m$ are such that $H$ has a vertex of degree $d$ and $m+d$ edges. The previous
best algorithm of Magniez et al. had complexity $\widetilde O(n^{2-2/k})$.

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