Code

Manual Error

5-qubit code:
Encodes 1 logical qubit into 5 physical. Distance 3: corrects any 1 error.

Stabilizers: XZZXI, IXZZX, XIXZZ, ZXIXZ

Syndrome:
Measure all stabilizers → 4-bit binary → points to error location and type.

Perfect code:
[[5,1,3]]: saturates Hamming bound. No smaller code corrects all 1-qubit errors.