This is a blessed loss. Mate can be forced, but a draw can be achieved under the fifty-move rule.
To probe all KQQPvKQB positions, these tables and their transitive dependencies are also required:
KQQQvKQB · KQBvKQP · KQQPvKB · KQQRvKQB · KQQBvKQB · KQQPvKQ · KQQNvKQB · KQQvKQB