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. 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 codes 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 p_L ≈ 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 enabled the first experiment past the Page time with the Hayden-Preskill black hole circuit. More about the experiment.

CIQA is an optional module within the CIQS pipeline, but can also integrate other pipelines as a standalone error correction code with a simple integration step.

A free online version of CIQA is available at arcadialab.fr. Supports Qiskit, OpenQASM 2.0, and JSON gate list input. Encode, syndrome, correct, and concatenate directly in the browser. No account, no ads, no questions.

[edit] v2 includes error correction confirmation on real quantum hardware:

• Hardware validation on IBM ibm_fez (Heron r2, 156 qubits).
• Three independent runs, 8192 shots each.
• Mean fidelity improvement +0.640 up to +0.832 on optimal hardware paths, above unprotected baseline across all runs.
• Full analysis of the runs in section 5.2
• The raw data from IBM have been added to the download list.