/usr/lib/x86_64-linux-gnu/libQtSql.so is in libqt4-dev 4:4.8.7+dfsg-5ubuntu2.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libQtSql.so.4.8.7
/usr/lib/x86_64-linux-gnu/libQtSql.so.4.8.7