CRT Quantum Error Correction

IBM/Google/IonQ QEC patents. CC0 alternative.

Quantum error correction protects quantum states from decoherence. Standard QEC (surface codes, Steane codes) requires massive overhead and patented decoding algorithms. CRT QEC: 7 CRT channels over Z/214,414,200 = 7 physical qubits. 3 data channels {mod 8, mod 25, mod 49} carry the quantum state. 4 parity channels {mod 9, mod 11, mod 13, mod 17} detect and locate errors. Corrects any single-channel error. Detects double errors. No neural decoder. No lookup table. Just CRT reconstruction.

How It Works

CRT QEC Theorem
A value in Z/214,414,200 decomposes into 7 channel registers: mod 8, mod 9, mod 25, mod 49, mod 11, mod 13, mod 17. Three data channels {mod 8, mod 25, mod 49} carry the quantum state. Four parity channels {mod 9, mod 11, mod 13, mod 17} detect and locate errors. When one channel is corrupted, the 6 remaining channels contain enough information to reconstruct the original value exactly via CRT. The 3+4 split is algebraically forced by the ring's prime factorization.
7 channels
3 data + 4 parity
Algebraically forced by the ring 8 x 9 x 25 x 49 x 11 x 13 x 17.
Single error
Correctable
Any 1 corrupted channel is corrected by CRT reconstruction from remaining 6.
Double error
Detectable
Any 2 corrupted channels change reconstructed value. 5 witnesses remain.
Triple parity
Free detection
mod-11, mod-13, mod-17 channels flag deviations. No separate syndrome circuit.

Try It

Value to protect:

Encodes your value into 7 CRT channels. Injects noise into each channel one at a time. Corrects via CRT reconstruction. All 7 should recover exactly.

Batch Test

100 random values, each corrupted in all 7 channels = 700 total correction tests.

Double Error Detection

Injects errors into all 21 pairs of channels. Double errors are always detected.

CRT QEC vs Standard Quantum Codes

Physical qubitsSurface code: ~1000 per logical qubitCRT: 7 total (3 data + 4 parity)DecodingMWPM decoder (complex, patented algorithms)CRT reconstruction (one formula, O(7) operations)SyndromeSeparate ancilla measurement circuits4 parity channels ARE the syndrome. No ancilla.Error capacitySurface code: grows with #qubitsCRT: corrects 1, detects 2. 4 parity channels.IndependenceCorrelated errors across qubitsBlock-diagonal: channels are algebraically independentPatent statusIBM (heavy hex), Google (Sycamore QEC), IonQCC0. Public domain. Forever.

Source code · Public domain (CC0)

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