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