Turbo-Annihilation of Hook Errors in Stabilizer Measurement Circuits

Abstract: We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner graph that includes every possible source of noise. However, this results in a highly irregular graph with many short cycles, leading to poor performance of message-passing algorithms. To compensate, ordered statistics decoding is typically employed, but its cubic complexity renders it impractical for large codes or repeated stabilizer measurements. Our approach instead focuses on estimating the effective data errors caused by hook faults, modeling them as memory channels. We integrate trellis-based soft-input soft-output equalizers into the Tanner graph of the code, and show that the resulting decoding graph preserves the structural properties of the original Tanner graph such as node degree and girth, enabling efficient message passing. Applied to bivariate bicycle quantum LDPC codes, our decoder outperforms standard belief propagation on the circuit-level graph and closely approaches OSD0 performance, all while maintaining linear complexity and scalability.