Bit Flip Error Correction
Master the 3-qubit repetition code for protecting quantum information
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Decoherence & Noise
Introduction to Bit Flip Code
The 3-qubit bit flip code is the simplest quantum error correction code. It protects against single bit flip (X) errors by encoding one logical qubit into three physical qubits using redundancy.
Encoding:
|0⟩L → |000⟩
|1⟩L → |111⟩
Why Error Correction?
❌
No Cloning
Cannot simply copy quantum states
📏
Measurement Destroys
Direct measurement collapses superposition
🎯
Redundancy Works
Use entanglement for error detection
🔧
Indirect Detection
Measure syndromes without measuring qubits
Classical vs Quantum Error Correction
💻Classical (3-bit code)
- →Copy bit: 0 → 000, 1 → 111
- →Majority voting detects errors
- →Direct measurement allowed
⚛️Quantum (3-qubit code)
- →Entangle: |ψ⟩ → |ψψψ⟩ via CNOT gates
- →Measure syndrome (parity checks)
- →Never measure data qubits directly
Code Properties
3
Physical Qubits
1
Logical Qubit
1
Error Correctable
d=3
Code Distance