Quantum LDPC Code
Quantum extension of low-density parity-check codes using sparse parity-check matrices for both X and Z stabilizers. Enables scalable quantum error correction with lower overhead than surface codes. Under active research for fault-tolerant quantum computing by IBM, Google, and Microsoft.
Properties
| Property |
Value |
| Category |
Error Correction |
| Sub-category |
Quantum Code |
| Security status |
🧪 Experimental |
| Complexity |
Expert |
| Inventor |
Daniel Gottesman, David MacKay |
| Year |
2003 |
| Origin |
🇺🇸 United States |
| Source |
algorithms/ecc/quantum-ldpc.js |
Security
Status: 🧪 Experimental
Known vulnerabilities
| Issue |
Description |
Mitigation |
| Decoding Complexity |
Iterative belief propagation decoding has high computational complexity and may not converge for all error patterns. |
— |
| Error Floor Phenomenon |
Like classical LDPC codes, QLDPC codes exhibit error floors at very low error rates due to near-codewords and trapping sets. |
— |
| Classical Simulation Limitations |
This implementation treats quantum states as classical bit arrays for educational purposes. Real quantum error correction operates on superposition states requiring quantum hardware. |
— |
| Limited Distance |
The [[7,1,3]] example code corrects only 1 arbitrary qubit error. Practical quantum computing requires larger codes with higher distance. |
— |
Documentation
References
Test vectors
2 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
| Vector 1 — [QLDPC [[7,1,3]] encode logical |
0⟩](https://errorcorrectionzoo.org/c/steane) |
| Field |
Value |
input |
00 |
expected |
00000000000000 |
| Vector 2 — [QLDPC [[7,1,3]] encode logical |
1⟩](https://errorcorrectionzoo.org/c/steane) |
| Field |
Value |
input |
01 |
expected |
01010101010101 |
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