CIQA: Analytical 1:5 Quantum Error Correction | 200× Below Surface-Code Overhead

CIQA (Causal Iteration Quantum Awareness) is an analytic quantum error correction encoder for matter qubit architectures (photon qubits do not need QEC). Its encoding structure, syndrome thresholds, and correction operators are produced by a closed-form derivation. It achieves full single-qudit Pauli error correction at 1: 5 overhead, the minimum the encoder's structure permits. At d≥3, a second independent error channel activates, reducing the joint error floor by a factor of approximately 78 at no additional overhead. The current industry-standard surface code architectures require approximately 1, 000 physical qubits per logical qubit to reach the logical error rates needed for deep circuits. CIQA achieves the same class of error correction at 5 physical qubits per logical qubit, representing a 200-fold reduction in physical qubit overhead. Concatenated to three levels, CIQA reaches pL ≈ 10⁻¹⁷ at overhead 1: 125, sufficient to run Shor's algorithm, and still far below the surface code's practical overhead at any equivalent logical error rate. **CIQA is an optional module within the CIQS pipeline (CIQS paper) but can also integrate other pipelines as a standalone module with a very simple integration step. Free licenses are available for academic research use. edit v2 includes: hardware validation on IBM ibmfez (Heron r2, 156 qubits). Three independent runs, 8192 shots each. CIQA error correction confirmed on real quantum hardware: mean fidelity +0. 640 above unprotected baseline across all runs. Job IDs: d77tqj3c6das739h7j60 d77tr33c6das739h7jp0 d77trpak86tc739ukbgg (verifiable on IBM Quantum Platform)