Sha Shi | Searcharxiv

arXiv2026

LEAD: A Local Ensemble-Assisted Parallel Decoding Framework for Quantum Tanner Codes

Quantum Tanner codes are a recently developed family of quantum error-correcting codes characterized by favorable asymptotic performance characteristics. Despite their theoretical potential, practical decoding algorithms that effectively leverage their structural properties remain limited. This work introduces LEAD (Local Ensemble-Assisted Decoder), a structure-aware decoding framework tailored for quantum Tanner codes. The proposed scheme leverages the decomposable structure of Cayley complexes to project the global code onto overlapping local subcodes defined by vertex neighborhoods, where error probabilities are estimated in parallel. To ensure global consistency, LEAD utilizes the inherent topological symmetry of the complex and introduces a soft-information regularization mechanism to mitigate local overconfidence during information aggregation. This framework enables highly parallelized, low-complexity decoding that is intrinsically compatible with various local search heuristics. Simulation results demonstrate that LEAD achieves significantly lower logical error rates than standard decoding framework while substantially reducing the average decoding latency and iteration count.

quant-ph↗

arXiv2026

Towards Minimal Fault-tolerant Error-Correction Sequence with Quantum Hamming Codes

The high overhead of fault-tolerant measurement sequences (FTMSs) poses a major challenge for implementing quantum stabilizer codes. Here, we address this problem by constructing efficient FTMSs for the class of quantum Hamming codes $[\![2^r-1, 2^r-1-2r, 3]\!]$ with $r=3k+1$ ($k \in \mathbb{Z}^+$). Our key result demonstrates that the sequence length can be reduced to exactly $2r+1$-only one additional measurement beyond the original non-fault-tolerant sequence, establishing a tight lower bound. The proposed method leverages cyclic matrix transformations to systematically combine rows of the initial stabilizer matrix and preserving a self-dual CSS-like symmetry analogous to that of the original quantum Hamming codes. This induced symmetry enables hardware-efficient circuit reuse: the measurement circuits for the first $r$ stabilizers are transformed into circuits for the remaining $r$ stabilizers simply by toggling boundary Hadamard gates, eliminating redundant hardware. For distance-3 fault-tolerant error correction, our approach simultaneously reduces the time overhead via shorting the FTMS length and the hardware overhead through symmetry-enabled circuit multiplexing. These results provide an important advance towards the important open problem regarding the design of minimal FTMSs for quantum Hamming codes and may shed light on similar challenges in other quantum stabilizer codes.

quant-ph↗