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.
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.