Fidelity, Error and Calibration

A fidelity figure means nothing without its method, scope, how it was summed up, its date, and its uncertainty. Randomized benchmarking reports an average error per gate under a set test. It is not your circuit's success rate. Using the best pair of qubits instead of the worst can swing a ten-gate circuit's success from about 98% to about 78% on the same chip. Tuning drifts day by day, so numbers with no date cannot be used.

What does 99% fidelity actually mean?

Fidelity is a score from 0 to 1. It says how close the step the hardware really does is to the perfect step in the math. 1 means perfect. For rough work, error rate ≈ 1 − fidelity. So a gate with 99% (0.99) fidelity goes wrong about once every hundred uses.

Why care? Fidelity is quoted per step, and circuits multiply it. Think of a chain: each link can snap, and the whole chain fails if any one link does. Let's work an example: a circuit with 20 two-qubit gates at 0.99 each. We build the power by squaring:

0.99² = 0.9801
square it: 0.99⁴ = 0.9606
square it: 0.99⁸ = 0.9227
square it: 0.99¹⁶ = 0.8514
times 0.9606: 0.99²⁰ ≈ 0.818

So nearly one run in five is spoiled by gate error alone.

Now repeat at 99.9%. 0.999 multiplied by itself 20 times ≈ 0.980. That is one spoiled run in fifty. Moving one decimal place on the spec sheet changed how often the circuit fails by about nine times. That is why tiny fractions of a percent in fidelity are worth real money. It is also why the exact meaning of the quoted number matters so much.