Error Propagation Paths in Quantum Error Correction: A Five-Stage Model for Quantifying Noise Suppression from Physical Source to Logical Qubit

We introduce a five-stage error propagation path model that traces quantum errors from noise origin through physical qubit, syndrome extraction, QEC decoding, to logical qubit. Each stage carries a quantified error rate. The suppression factor S = log10(p_physical / p_logical) captures QEC effectiveness in a single scalar. We catalog propagation paths across 12 noise types and 6 QEC codes, revealing suppression factors from S > 9 (excellent) to S < 1 (weak/reachable). The model enables bottleneck identification: for a typical superconducting processor, measurement error is the bottleneck (S = 4.0) while all other noise types achieve S > 9. Improving measurement readout by 2x yields 30x improvement in bottleneck logical error rate — more cost-effective than increasing code distance.