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Let $H$ be a fixed $k$-vertex graph with $m$ edges and minimum degree $d >0$.We use the learning graph framework of Belovs to show that the bounded-errorquantum query complexity of determining if an $n$-vertex graph contains $H$ asa subgraph is $O(n^{2-2/k-t})$, where $ t = \max{\frac{k^2-2(m+1)}{k(k+1)(m+1)}, \frac{2k - d - 3}{k(d+1)(m-d+2)}}$. The previous bestalgorithm of Magniez et al. had complexity $\widetilde O(n^{2-2/k})$.

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