  Fault-tolerant quantum computation (FTQC) schemes that use multi-qubit large
block codes can potentially reduce the resource overhead to a great extent. A
major obstacle is the requirement of a large number of clean ancilla states of
different types without correlated errors inside each block. These ancilla
states are usually logical stabilizer states of the data code blocks, which are
generally difficult to prepare if the code size is large. Previously we have
proposed an ancilla distillation protocol for Calderbank-Shor-Steane (CSS)
codes by classical error-correcting codes. It was assumed that the quantum
gates in the distillation circuit were perfect; however, in reality, noisy
quantum gates may introduce correlated errors that are not treatable by the
protocol. In this paper, we show that additional postselection by another
classical error-detecting code can be applied to remove almost all correlated
errors. Consequently, the revised protocol is fully fault-tolerant and capable
of preparing a large set of stabilizer states sufficient for FTQC using large
block codes. At the same time, the yield rate can be boosted from $O(t^{-2})$
to $O(1)$ in practice for an $[[n,k,d=2t+1]]$ CSS code. Ancilla preparation for
the $[[23,1,7]]$ quantum Golay code is numerically studied in detail through
Monte Carlo simulation. The results support the validity of the protocol when
the gate failure rate is reasonably low. To the best of our knowledge, this
approach is the first attempt to prepare general large block stabilizer states
free of correlated errors for FTQC in a fault-tolerant and efficient manner.
