What is fidelity? Simply put, we have expectations, and fidelity is a measure of how closely reality meets those expectations. In quantum computing, for example, we expect our quantum operations to achieve certain outcomes. We express the fidelity of these operations as a value from 0 to 1, with 0 indicating that the actual outcome (obtained state or operation) is the complete opposite of the expected outcome (ideal state or operation) and 1 indicating a perfect match. Fidelity, therefore, is an expression of similarity. It applies to quantum gates, state preparation, and readout processes.
Quantum Gates: High gate fidelity indicates that the quantum operations we implemented closely match the ideal operations we wanted to do.
State Preparation: When we try to prepare quantum state ∣ψ⟩, errors cause us to end up with state ∣ϕ⟩. Those are wavefunctions, so fidelity is a measure of overlap. Imagine two sine waves, one blue and one red, that look like one purple wave when placed one on top of the other. That’s perfect fidelity 1, no error. Now imagine the overlap looks like an infinity symbol instead. That’s fidelity 0, maximum error, also called complete orthogonality. If you’re a mathophile, the fidelity is the square of the absolute value of the inner product: 0<=|⟨ψ|φ⟩|²<=1.
Readout Process: When measuring quantum states, fidelity is the probability of an assignment error (incorrectly identifying the quantum state). The expression is F=1−P(error), which Google Translate might tell you means that the fidelity is 1 minus the probability of an error. A high readout fidelity implies a low probability of error.