# Gate Fidelity **Gate fidelity** measures how close a real quantum operation comes to the perfect operation it was meant to perform. A fidelity of $0.999$ means that, on average, the operation is right $99.9\%$ of the time and introduces an error $0.1\%$ of the time. ## First principles A quantum **gate** is a controlled transformation of one or more [[Qubit|qubits]] — the quantum analogue of a logic operation. In practice every gate is imperfect: control pulses are slightly off, the qubit drifts, neighbours interfere. Fidelity $F$ quantifies the overlap between the state you actually produced and the ideal target state, so the **error per gate** is roughly $1 - F$. > [!intuition] Errors compound > If each gate has error $\varepsilon$ and an algorithm uses $N$ gates, the chance of getting through cleanly scales like $(1-\varepsilon)^N$. With $\varepsilon = 0.1\%$ you are in trouble after a few thousand gates. Real algorithms need *millions*, which is why raw fidelity alone is never enough. ## Why it matters - **The threshold connection.** [[Quantum Error Correction]] only helps if gate fidelity is already above a critical value — the [[Code Distance and Threshold Theorem|fault-tolerance threshold]]. Below it, adding error correction makes things *worse*; above it, errors can be suppressed arbitrarily. - **Two-qubit gates are the bottleneck.** Single-qubit gates are usually high-fidelity; the entangling two-qubit gates (e.g. via [[Rydberg Interactions]]) are harder and dominate the error budget. - Fidelity must be weighed against **speed** and [[Coherence Time]]: a fast, slightly worse gate may beat a slow, perfect one if coherence is limited. ## Related - [[Qubit]] - [[Rydberg Interactions]] - [[Coherence Time]] - [[Code Distance and Threshold Theorem]] - [[Quantum Error Correction]]