Ultra low overhead syndrome extraction for the Steane code

Abstract We establish a new performance benchmark for the fault-tolerant (FT) syndrome extraction of the [ [ 7 , 1 , 3 ] ] Steane code with a dynamic protocol. Our method is built on two highly optimized circuits derived using fault-equivalent Z X -rewrites: a primary FT circuit with 14 CNOTs and an efficient non-FT recovery circuit with 11 CNOTs. The protocol uses an adaptive response to internal faults, discarding flagged measurements and falling back to the recovery circuit to correct potentially detrimental errors. Monte Carlo simulations confirm the efficiency of our protocol, reducing the logical error rate per cycle by an average of ∼ 14.3 % relative to the optimized Steane method Rodatz et al (2025 arXiv: 2506.17181 ) and ∼ 17.3 % compared to Reichardt’s three-qubit method Reichardt (2020 Quantum Sci. Technol. 6 015007), the leading prior techniques.