Two-Flag Fault-Tolerant Quantum Error Correction

This research focuses on advancing fault-tolerant quantum error correction by developing multi-flag protocols that extend beyond traditional single-flag limitations. The work investigates concatenated Steane codes across distances 3-9, with a particular emphasis on resource optimization for practical quantum computing implementations. Key aspects of this research include: - Development of novel two-flag syndrome extraction circuits - Analysis of error propagation in multi-flag configurations - Resource overhead comparisons with existing protocols - Simulation studies using the Stim framework for large-scale analysis