Fault-tolerant magic state preparation with flag qubits. (arXiv:1811.00566v2 [quant-ph] UPDATED)

Magic state distillation is one of the leading candidates for implementing
universal fault-tolerant logical gates. However, the distillation circuits
themselves are not fault-tolerant, so there is additional cost to first
implement encoded Clifford gates with negligible error. In this paper we
present a scheme to fault-tolerantly and directly prepare magic states using
flag qubits. One of these schemes uses a single extra ancilla, even with noisy
Clifford gates. We compare the physical qubit and gate cost of this scheme to
the magic state distillation protocol of Meier, Eastin, and Knill, which is
efficient and uses a small stabilizer circuit. In some regimes, we show that
the overhead can be improved by several orders of magnitude.

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