Improved performance of the Bacon Shor code with Steane syndrome extraction

The Steane syndrome extraction method (SSEM) is a simple single-shot alternative for error correction on Calderbank-Shor-Steane codes. On the other hand, the Bacon-Shor code allows for a very efficient fault-tolerant preparation of the logical |0〉and |+〉states, which is crucial for the SSEM. By performing stabilizer simulations using a depolarizing error model, we show that the SSEM outperforms the more traditional Shor syndrome extraction method on the Bacon-Shor code, as long as there is long-range qubit connectivity. Moreover, the performance improvement of the SSEM over the Shor's method increases with the code's distance. These results place the SSEM on the Bacon-Shor code as a promising route to implement a high-distance logical qubit.