Magic state cultivation: growing T states as cheap as CNOT gates

Craig Gidney, Noah Shutty, Cody Jones

We refine ideas from Knill 1996, Jones 2016, Chamberland 2020, Gidney 2023+2024, Bombin 2024, and Hirano 2024 to efficiently prepare good $|T⟩$ states. We call our constructi…