  We design quantum algorithms for maximum matching. Working in the query
model, in both adjacency matrix and adjacency list settings, we improve on the
best known algorithms for general graphs, matching previously obtained results
for bipartite graphs. In particular, for a graph with $n$ nodes and $m$ edges,
our algorithm makes $O(n^{7/4})$ queries in the matrix model and
$O(n^{3/4}(m+n)^{1/2})$ queries in the list model. Our approach combines
Gabow's classical maximum matching algorithm [Gabow, Fundamenta Informaticae,
'17] with the guessing tree method of Beigi and Taghavi [Beigi and Taghavi,
Quantum, '20].
