  In fault-tolerant quantum computing schemes, the overhead is often dominated
by the cost of preparing codewords reliably. This cost generally increases
quadratically with the block size of the underlying quantum error-correcting
code. In consequence, large codes that are otherwise very efficient have found
limited fault-tolerance applications. Fault-tolerant preparation circuits
therefore are an important target for optimization.
  We study the Golay code, a 23-qubit quantum error-correcting code that
protects the logical qubit to a distance of seven. In simulations, even using a
naive ancilla preparation procedure, the Golay code is competitive with other
codes both in terms of overhead and the tolerable noise threshold. We provide
two simplified circuits for fault-tolerant preparation of Golay code-encoded
ancillas. The new circuits minimize error propagation, reducing the overhead by
roughly a factor of four compared to standard encoding circuits. By adapting
the malignant set counting technique to depolarizing noise, we further prove a
threshold above 1.32 x 10^{-3} noise per gate.
