Temporal Degeneracy Limits Message Passing Decoding of QLDPC Codes Under Repeated Noisy Syndrome Measurements

Practical quantum computations can require logical error rates of $10^{-12}$ or lower. Quantum low-density parity-check (QLDPC) codes are promising candidates for reaching such rates with low qubit overhead, provided that their syndromes can be decoded efficiently. Repeated noisy syndrome measuremen