SURFACE CODE (d×d)

Code distance d5
Error rate p0.050
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