Bonaparte Quantum Foundations

Error & Fidelity

Quantum error comes from noise and imperfections, while fidelity measures how accurately a quantum state matches its ideal form.

What Is Error? Quantum error arises when the actual state or operation differs from the ideal one. Noise, decoherence, and imperfect control can lead to common errors.

Relationship: Error Rate = 1 − F

Common Error Types:
  • Bit-flip error: ∣0⟩ ↔ ∣1⟩
  • Phase-flip error: ∣0⟩+∣1⟩ → ∣0⟩−∣1⟩
  • Decoherence: Loss of quantum information due to environmental interactions
What Is Fidelity?
Fidelity measures how accurately a quantum state or gate reproduces its ideal form:
  • F = 1: Perfect match
  • F < 1: Deviation or noise present