Quantum Error Correction — 3-Qubit Bit-Flip Code

Error probability p: 0.05 Rounds: 1 Error type:

Bit-flip (X) Phase-flip (Z)

Logical state |ψ⟩:

|0⟩ → |000⟩ |1⟩ → |111⟩

Syndrome S1 (ZZI)—

Syndrome S2 (IZZ)—

Error location—

Logical error rate—

Threshold p_th≈ 0.50

3-qubit bit-flip code
|0⟩ → |000⟩, |1⟩ → |111⟩
S1=Z⊗Z⊗I, S2=I⊗Z⊗Z
000→ok, 001→flip q3
010→flip q2, 100→flip q1
Corrects 1 of 3 qubit errors