If only White could give check on the back rank with the black King at b1, it would all be over. White finds an ingenious zugzwang to bring it about:
1.Qc3 Kb1 2.Qd3+ Ka1 3.Qd4 Kb1 4.Qe4+ Ka1 5.Qe5 Kb1 6.Qf5+ Ka1 7.Qf6 Kb1 8.Qg6+ Ka1 9.Qg7 Kb1 10.Qh7+ Ka1 11.Qh8 Kb1 12.Qh1#