Optimization of Magic State Distillation on Surface Codes

At large code distances, magic state distillation is known to have an O(d³) spacetime cost on a distance-d surface code, but there are not yet any detailed estimates of its asymptotic cost prefactor for specific implementations. In this talk, I present a recursive implementation of multilevel magic state distillation on the surface code using lattice surgery and calculate its asymptotic cost prefactor.