From the documentation:
For the QODBC driver, the name can either be a DSN, a DSN filename (in which case the file must have a .dsn extension), or a connection string.

For example, Microsoft Access users can use the following connection string to open an .mdb file directly, instead of having to create a DSN entry in the ODBC manager:

...
db = QSqlDatabase::addDatabase("QODBC");
db.setDatabaseName("DRIVER={Microsoft Access Driver (*.mdb)};FIL={MS Access};DBQ=myaccessfile.mdb");
if (db.open()) {
// success!
}
...