Fidelity

Fidelity measures the similarity between two quantum states or operations. State fidelity F(ρ, σ) = (Tr√(√ρ σ √ρ))² measures how close a noisy quantum state ρ is to the target pure state σ. A fidelity of 1.0 means perfect; 0 means orthogonal. Gate fidelity measures how accurately a gate is implemented. Average gate fidelity is measured by running many random circuits (randomized benchmarking). For example, a single-qubit gate fidelity of 99.9% means 0.1% error per gate. Two-qubit gates typically have lower fidelity (99%–99.9% for top systems). Process fidelity extends this to full circuits. When comparing quantum hardware, 1-qubit gate fidelity, 2-qubit gate fidelity, and readout fidelity are key specs. IonQ trapped-ion systems currently hold some of the highest gate fidelities commercially available.