The site search in the header is broken. To reproduce:
go to http://qt-project.org/
enter something into the search box on the top right of the page and click "search"
this redirects to http://qt-project.org/search?search=qapplication
The result displays
bq. GTE Cyber Trust Root.Us
within the text box to enter the search for Google. If you change that text to your actual search string, the results are ok.
The same happens if you do not enter anything in step 2.
The issue is reported, find it in Jira under QTWEBSITE-434.