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

We present a circuit construction for making resource states, known as magic states, for fault-tolerant quantum computing on a 2d nearest neighbor grid of physical qubits. 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 construction "magic state cultivation" because it gradually grows the size and reliability of one state. Cultivation fits inside a surface code patch and uses roughly the same number of physical gates as a lattice surgery CNOT gate of equivalent reliability. We estimate the infidelity of cultivation (from injection to idling at distance 15) using a mix of state vector simulation, stabilizer simulation, error enumeration, and Monte Carlo sampling. Compared to prior work, cultivation uses an order of magnitude fewer qubit-rounds to reach logical error rates as low as 2⋅10⁻⁹ when subjected to 10⁻³ uniform depolarizing circuit noise. Halving the circuit noise to 5⋅10⁻⁴ improves the achievable logical error rate to 4⋅10⁻¹¹. Cultivation's efficiency and strong response to improvements in physical noise suggest that further magic state distillation may never be needed in practice.