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Gate Fidelity

Gate fidelity is the probability that the physical operation performed by the hardware matches the ideal logical gate it is supposed to implement.

What it means

At the circuit layer, a gate is a perfect mathematical object — the CZ gate is exactly the matrix diag(1, 1, 1, −1), with no noise and no time.On real hardware, that same gate is an analog microwave or flux waveform lasting roughly 40 nanoseconds, and its amplitude, timing, and envelope shape determine how close the realized operation comes to the ideal matrix.Gate fidelity quantifies that closeness: it is the probability that the physical operation performed by the hardware matches the ideal logical operation.A fidelity of 99.92% means about 8 errors per 10,000 operations.As of 2026, leading superconducting processors target 99.9%+ fidelities, with two-qubit gates as the bottleneck — they are much harder than single-qubit gates, and their values differ from connection to connection and drift over time.Average fidelity is measured with Randomized Benchmarking, while Interleaved RB isolates a specific gate.Fidelity also embodies a trade-off: gates that are too fast leak into higher states, while gates that are too slow lose coherence.

Everyday analogy

The CZ written in the score (the circuit diagram) is a perfect note; the CZ the hardware plays is a real 40 ns wave. Fidelity is "how close the performance came to the score" — the same note played by different fingers has different quality, and a fidelity of 99.92% means 8 wrong notes per 10,000 played.
The word fidelity comes from Latin fidelis, "faithful" — the same Fi as in Hi-Fi audio, "high-fidelity sound" that faithfully reproduces the original recording. A high-fidelity gate faithfully reproduces the ideal operation.

Common misconceptions

  • Fidelity is NOT the same as calibration data — calibration data are the pulse numbers themselves (frequencies, amplitudes, durations), while fidelity is a quality metric grading how good the resulting operations are. People routinely confuse the two.
  • A single fidelity number hides structure: single-qubit and two-qubit gate fidelities differ substantially (two-qubit gates are much harder), and per-connection values vary from qubit pair to qubit pair and drift over time.

Key takeaways

  • Gate fidelity is the probability that the physical operation performed by the hardware matches the ideal logical operation.
  • As of 2026, leading processors target 99.9%+ gate fidelities; two-qubit gates are the bottleneck.
  • Average fidelity is measured via Randomized Benchmarking; the fidelity of a specific gate is measured via Interleaved RB.
  • A fidelity of 99.92% means about 8 errors per 10,000 operations — tiny per gate, but compounding across thousands of gates.

Check your understanding

A gate has fidelity 99.92%. On average, how many of 10,000 applications of this gate will deviate from the ideal operation?

  1. A.0.8
  2. B.8
  3. C.80
  4. D.800
Show the answer

Answer: B. 8

Why: The error rate is 1 − 0.9992 = 0.0008, and 0.0008 × 10,000 = 8 errors per 10,000 operations.

Which technique measures the fidelity of one specific gate (such as CNOT) rather than an average over a whole gate set?

  1. A.Standard Randomized Benchmarking
  2. B.Interleaved Randomized Benchmarking
  3. C.Ramsey interferometry
  4. D.Spectroscopy
Show the answer

Answer: B. Interleaved Randomized Benchmarking

Why: Standard RB yields an average over random gate sequences; Interleaved RB inserts the target gate between random gates and compares decay rates to isolate that gate's fidelity.

Builds on

Quantum MeasurementDecoherence

Primary source: Magesan, Gambetta & Emerson, Phys. Rev. Lett. 106, 180504 (2011), doi:10.1103/PhysRevLett.106.180504

Average gate fidelity via RB per Magesan 2011; definition per Nielsen, Phys. Lett. A 303, 249 (2002).

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