Phase Flip Correction
Protect quantum information from phase errors using the dual code
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Bit Flip Error Correction
Introduction to Phase Flip Code
The 3-qubit phase flip code protects against phase errors (Z errors) by working in the Hadamard basis. It's the dual of the bit flip code.
Encoding in |±⟩ basis:
|+⟩L → |+++⟩
|-⟩L → |---⟩
Phase vs Bit Flip Errors
XBit Flip (X Error)
- →Flips |0⟩ ↔ |1⟩
- →Changes computational basis state
- →Corrected by bit flip code
ZPhase Flip (Z Error)
- →Flips |+⟩ ↔ |-⟩
- →Changes relative phase by π
- →Corrected by phase flip code
Hadamard Basis States
|+⟩ State
|+⟩ = (|0⟩ + |1⟩)/√2
Equal superposition with 0° phase
|-⟩ State
|-⟩ = (|0⟩ - |1⟩)/√2
Equal superposition with 180° phase
Why Phase Errors Matter
🌊
Interference
Phase errors destroy quantum interference patterns
⚛️
Superposition
Critical for algorithms using superposition states
📡
Invisible
Cannot detect by measuring in computational basis
🔄
Duality
Dual to bit flip—same structure, different basis