If you set the option saveState to true, then jqtree remembers the tree state after a page reload.
<div id="tree1" data-url="/example_data/"></div>
$('#tree1').tree({
saveState: true
});
Giving the saveState a string value sets the storage key. The default key is 'tree'.
$('#tree1').tree({
saveState: 'my-tree'
});