Fidelity, Error and Calibration

A fidelity figure is meaningless without its method, scope, aggregation, date, and uncertainty: randomized benchmarking reports an average error per gate under a protocol, not your circuit's success rate, and best-pair versus worst-pair scope can swing a ten-gate circuit's success from about 98% to about 78% on the same chip. Calibration drifts day by day, so undated numbers are unusable.

What does 99% fidelity actually mean?

Fidelity is a score between 0 and 1 for how close the operation the hardware actually performs is to the ideal mathematical operation; 1 means perfect. For rough engineering purposes, error rate ≈ 1 − fidelity: a 99% (0.99) fidelity gate goes wrong about once per hundred uses.

Fidelity is quoted per operation, and circuits multiply it. Worked example: a circuit with 20 two-qubit gates at 0.99 each. Build the power by squaring: 0.99² = 0.9801; squared gives 0.99⁴ = 0.9606; squared gives 0.99⁸ = 0.9227; squared gives 0.99¹⁶ = 0.8514; times 0.9606 gives 0.99²⁰ ≈ 0.818. Nearly one run in five is spoiled by gate error alone.

Repeat at 99.9%: 0.999 multiplied by itself 20 times ≈ 0.980 — one spoiled run in fifty. Moving one decimal place in the spec sheet changed the circuit-level failure rate by a factor of about nine. That is why fractions of a percent in fidelity are worth real money, and why the exact meaning of the quoted number matters so much.