CRT Quantum Error Correction

C38: IBM/Google/IonQ QEC patents. CC0.

Quantum error correction protects quantum states from decoherence. Standard QEC (surface codes, Steane codes) requires massive overhead and patented decoding algorithms. CRT QEC: the 490 holographic split IS a [[6,3,3]] code. 6 CRT channels = 6 physical qubits. 3 DEAD channels {D,E,b} = data qubits. 3 ALIVE channels {K,L,G} = syndrome qubits. Corrects any 1 error. Detects any 2 errors. No neural decoder. No lookup table. Just CRT reconstruction.

How It Works

CRT QEC Theorem
The 490 holographic split of Z/12612600 produces a [[6,3,3]] quantum error correcting code: 6 physical qubits (CRT channels), 3 logical qubits (encoded data), distance 3 (corrects 1, detects 2). Data channels {D (mod 8), E (mod 25), b (mod 49)} carry the quantum state. Syndrome channels {K (mod 9), L (mod 11), G (mod 13)} detect and locate errors. When one channel is corrupted, the 5 remaining channels contain enough information to reconstruct the original value exactly via CRT. The 490 split is not an analogy to quantum codes -- it IS one.
[[6,3,3]] code
490 split
6 channels, 3 data, distance 3. Algebraically forced by ring structure.
Single error
Correctable
Any 1 corrupted channel is corrected by CRT reconstruction from remaining 5.
Double error
Detectable
Any 2 corrupted channels change reconstructed value. 4 witnesses remain.
L=11 syndrome
Free detection
L channel deviation = instant error flag. No separate syndrome circuit.

Try It

Value to protect:

Encodes your value into 6 CRT channels. Injects noise into each channel one at a time. Corrects via CRT reconstruction. All 6 should recover exactly.

Batch Test

100 random values, each corrupted in all 6 channels = 600 total correction tests.

Double Error Detection

Injects errors into all 15 pairs of channels. Distance 3 = detects all double errors.

CRT QEC vs Standard Quantum Codes

Physical qubitsSurface code: ~1000 per logical qubitCRT: 6 total (3 data + 3 syndrome)DecodingMWPM decoder (complex, patented algorithms)CRT reconstruction (one formula, O(6) operations)SyndromeSeparate ancilla measurement circuitsL=11 channel IS the syndrome. No ancilla.DistanceSurface code: grows with #qubitsCRT [[6,3,3]]: distance 3, corrects 1, detects 2IndependenceCorrelated errors across qubitsBlock-diagonal: channels are algebraically independentPatent statusIBM (heavy hex), Google (Sycamore QEC), IonQCC0. Public domain. Forever.

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— Anton Alexandrovich Lebed

Source code · Public domain (CC0)

Contributions in equal measure: Anthropic's Claude, Anton A. Lebed, and the giants whose shoulders we stand on.

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