SURFACE CODE (d×d)
Code distance d
5
Error rate p
0.050
Inject Random Errors
Run Minimum-Weight Decoder
Clear All Errors
Kitaev surface code: d×d grid
of physical qubits (data).
Stabilizers: X-type (vertices)
& Z-type (plaquettes).
Error threshold ~1% per gate.
Logical error rate ≈ (p/p_th)^(d+1)/2
Anyons (syndrome excitations)
move in pairs — braiding
implements logical operations.
● data qubit
✕ X error (bit flip)
Z Z error (phase flip)
⬟ Z stabilizer syndrome
■ X stabilizer syndrome
— correction chain