Ready to encode logical qubit
Logical Qubit State
|ψ⟩ = α|0⟩ + β|1⟩
where β = √(1 - α²)
where β = √(1 - α²)
Encoded as: |ψL⟩ = α|000⟩ + β|111⟩
Bit-Flip Error Location
Protocol Steps
Preset States
Syndrome Measurement
s₁ (Z₁Z₂): --
s₂ (Z₂Z₃): --
s₂ (Z₂Z₃): --
Error location: --
(0,0) → no error
(1,1) → qubit 0
(1,0) → qubit 1
(0,1) → qubit 2
(1,1) → qubit 0
(1,0) → qubit 1
(0,1) → qubit 2
State Fidelity
F = 1.000
Fidelity with initial state
Perfect recovery: F = 1
Perfect recovery: F = 1
About the 3-Qubit Code
The 3-qubit bit-flip code protects against single bit-flip (X) errors by encoding one logical qubit into three physical qubits. The syndrome measurements tell us which qubit flipped without measuring the logical state itself, preserving quantum information.