Surface Code
Errors
Logical qubit:
1 logical qubit encoded in d² + (d−1)² physical qubits (surface code).
Code distance d:
Minimum weight logical operator. Corrects ⌊(d−1)/2⌋ errors.
Threshold theorem:
p < p_th → logical error suppressed as (p/p_th)^{⌊d/2⌋}
Surface code:
p_th ≈ 1% (best known). Logical X/Z = string across lattice.
1 logical qubit encoded in d² + (d−1)² physical qubits (surface code).
Code distance d:
Minimum weight logical operator. Corrects ⌊(d−1)/2⌋ errors.
Threshold theorem:
p < p_th → logical error suppressed as (p/p_th)^{⌊d/2⌋}
Surface code:
p_th ≈ 1% (best known). Logical X/Z = string across lattice.