Stabilizer Quantum Code
Most general framework for quantum error correction using stabilizer formalism. Stabilizer group S consists of commuting Pauli operators that define the code space as the simultaneous +1 eigenspace of all stabilizers. Includes CSS codes, Shor code, and surface codes as special cases. This implementation demonstrates the [[5,1,3]] five-qubit perfect code - the smallest quantum code that can correct an arbitrary single-qubit error. Foundation of fault-tolerant quantum computing.
Properties
| Property |
Value |
| Category |
Error Correction |
| Sub-category |
Quantum Code |
| Security status |
🎓 Educational Only |
| Complexity |
Expert |
| Inventor |
Daniel Gottesman |
| Year |
1996 |
| Origin |
🇺🇸 United States |
| Source |
algorithms/ecc/stabilizer-quantum-code.js |
Parameters
| Parameter |
Supported values |
| Block sizes |
1 byte (8 bits) |
Capabilities
| Flag |
Value |
supportsErrorDetection |
Yes |
supportsErrorCorrection |
Yes |
Security
Status: 🎓 Educational Only
No vulnerabilities are recorded for this implementation.
Documentation
References
Test vectors
3 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
| Vector 1 — [Five-qubit code encode logical |
0⟩](https://errorcorrectionzoo.org/c/stab_5_1_3) |
| Field |
Value |
input |
00 |
expected |
0000000000 |
| Vector 2 — [Five-qubit code encode logical |
1⟩](https://errorcorrectionzoo.org/c/stab_5_1_3) |
| Field |
Value |
input |
01 |
expected |
0101010101 |
Vector 3 — Encode two logical qubits
| Field |
Value |
input |
0001 |
expected |
00000000000101010101 |
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