Quantum stabilizer code constructed from two classical linear codes C1 and C2 where the dual of C2 is a subset of C1. Corrects quantum errors (bit-flip X and phase-flip Z errors). Steane [[7,1,3]] code corrects one qubit error. Foundation for fault-tolerant quantum computing. Used in quantum computers by IBM, Google.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Quantum Code |
| Security status | 🎓 Educational Only |
| Complexity | Expert |
| Inventor | Robert Calderbank, Peter Shor, Andrew Steane |
| Year | 1996 |
| Origin | 🇺🇸 United States |
| Source | algorithms/ecc/css-quantum-code.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Single Qubit Error Correction Only | Steane [[7,1,3]] code can only correct 1 arbitrary qubit error (bit-flip, phase-flip, or both). Multiple errors cause decoding failure. | — |
| Overhead Cost | Encodes 1 logical qubit into 7 physical qubits (7x overhead). Higher-distance CSS codes have even larger overhead. | — |
| Classical Simulation Limitations | This implementation treats quantum states as classical bit arrays for educational purposes. Real quantum error correction requires quantum hardware and preserves superposition states. | — |
| Measurement Errors | Does not account for measurement errors in syndrome extraction, which real quantum systems must address through fault-tolerant protocols. | — |
2 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Steane [[7,1,3]] encode logical qubit state 0
| Field | Value |
|---|---|
input |
00 |
expected |
00000000000000 |
Vector 2 — Steane [[7,1,3]] encode logical qubit state 1
| Field | Value |
|---|---|
input |
01 |
expected |
01010101010101 |