QUANTUM ERROR CORRECTION
3-qubit bit-flip code — detect & correct without measuring logical qubit
ENCODE & ERROR
Logical qubit angle θ:
θ = 45° → α|0⟩+β|1⟩
1. Encode logical qubit
Introduce bit-flip error:
Flip q₀
Flip q₁
Flip q₂
SYNDROME & CORRECTION
2. Measure syndrome
3. Correct error
Reset
Stage:
Idle
Syndrome (s₁,s₂):
—
Error on qubit:
none
Fidelity:
1.000
PHYSICAL QUBITS
q₀:
—
q₁:
—
q₂:
—
Logical |ψ_L⟩:
—
Encoding: |0_L⟩→|000⟩
|1_L⟩→|111⟩
Syndrome: s₁=q₀⊕q₁, s₂=q₁⊕q₂