Significance Until recently, simulating ice nucleation with quantum accuracy was deemed impossible due to the prohibitive computational cost of quantum-mechanical calculations. Recent progress enabled by machine learning has made these calculations tractable and thus greatly extended the field of application of molecular dynamics based on ab initio quantum-mechanical theory. We apply these advances to predict the rate of formation of ice nuclei in supercooled water and to study other quantities relevant to nucleation without relying on empirical force fields, albeit invoking the organizing framework of classical nucleation theory. This work is a step toward modeling nucleation processes in more realistic environments and at conditions in which chemical reactions play an important role.