3-Qubit Bit-Flip Code

Logical state
|0⟩
α (|0⟩)
1.000
β (|1⟩)
0.000
Errors detected
0
Corrections
0
0.10
θ=0°
The 3-qubit code encodes |ψ⟩ = α|0⟩+β|1⟩ into α|000⟩+β|111⟩. Syndrome measurement (Z₀Z₁, Z₁Z₂) identifies which qubit flipped without measuring α,β. Majority vote corrects any single-qubit error. Logical error prob ≈ 3p²(1−p) + p³ ≪ p for p<0.5.