Efficient Large Block Codes Ancilla States Preparation for Fault-tolerant Quantum Computation

Fault-tolerant quantum computation (FTQC) schemes using multi-qubit large block codes can potentially reduce the resource overhead to a great extent. The main obstacle is the requirement of huge amount of clean ancilla states of different types with weak error correlation inside each block. These ancilla states are usually logical stabilizer states of the data code blocks, which are generally difficult to prepare if code size is large. Meanwhile, the yield rate of preparation process are typically extremely low when the distance of block code is large. Here, we propose a protocol to distill various ancilla states necessarily for FTQC fault-tolerantly using classical error-correcting codes and error-detection codes. It is shown that correlated errors can be largely removed if good classical codes are chosen. At the same time, the yield rate can be high for general large block CSS code with arbitrary size, using proper classical codes. Preparation ancilla state for [[23,1,7]] quantum Golay code is numerically studied in detail through Monte Carlo simulation. The results support the validity of the protocol when gate failure rate is reasonably low.