Fig. 1: Illustration of magic state distillation and its role in universal fault-tolerant quantum computation.

a A Clifford circuit for the implementation of a T gate with an ancilla state. Note that the input qubit is destructively measured and the ancillary qubit serves as the output. b Illustration of magic state distillation. One qubit of an entangled pair is encoded into the [[15, 1, 3]] quantum Reed–Muller code and a logical T gate is applied via transversal T^† gates. Each T^† gate is implemented using a noisy ancilla. After measurement on the 15-qubit code and a conditioned Z on the other qubit of the EPR pair, the latter qubit is transformed to a more accurate ancilla. c Universal fault-tolerant quantum computation (FTQC) with magic state distillation. The ancilla factory supplies noisy ancillae that are encoded to QEC codes of various sizes and undergo many-round distillation until the desired fidelity is achieved. The produced ancillae are then maintained by standard error correction procedure for quantum memory. When a logical T is required in the main thread of the computation, a good ancilla is moved out from the factory to the computation region.