Hardware & Errors
Gate Fidelity
A measure of how accurately a quantum gate performs its intended operation, expressed as a percentage close to 100%.
Definition
Gate fidelity quantifies how closely a real, physically implemented quantum gate matches its theoretically perfect operation. A fidelity of 99.9% means the gate introduces an error roughly 0.1% of the time it's used — a critical metric since errors compound across the many gates in a real circuit.
In depth
Gate fidelity measures how close a physical operation is to the ideal one, on a scale from 0 to 1, usually quoted as a percentage. A fidelity of 99.9 percent means an error of one in a thousand per gate. The error rate, one minus the fidelity, is the more convenient number for planning, since errors add up over a circuit. If a circuit has N gates, each with error e, the chance that no error occurs is roughly e to the power of minus N times e, so a circuit with 1,000 gates at an error of 0.1 percent succeeds only about a third of the time.
There are several definitions of fidelity, and they are not interchangeable. Average gate fidelity averages over input states and is the usual output of randomized benchmarking. Process fidelity compares the full operation to the ideal one and is lower. Fidelities for two-qubit gates are measured on isolated pairs in some reports and on full-chip simultaneous operation in others, and the second is usually worse because of crosstalk. Leading numbers in 2025 include single-qubit gates with errors around 10 to the minus 4 or below on superconducting chips and as low as 10 to the minus 7 in a laboratory ion result, and two-qubit gates at about 99.9 percent on superconducting devices and 99.9 to 99.99 percent on trapped ions.
Fidelity targets are linked to error correction. Codes such as the surface code have thresholds around 1 percent, so two-qubit fidelity must be above 99 percent for correction to help, and well above that for it to be efficient. Each extra nine in fidelity reduces the number of physical qubits needed per logical qubit. This is why hardware announcements emphasize fidelity: it controls the overhead of the entire fault-tolerant roadmap.
Technical Definition
Fidelity is typically measured using randomized benchmarking, which applies long sequences of random gates and measures how the output distribution decays from the ideal expected result, isolating gate error from state preparation and measurement error.
Visual Explanation: An Analogy
Think of gate fidelity like the accuracy of a skilled craftsperson repeating the same precise cut thousands of times — even a tiny, consistent imprecision adds up to a noticeably flawed result after enough repetitions.
Key facts
| Item | Detail |
|---|---|
| Error rate | One minus the fidelity; 99.9 percent fidelity is 0.1 percent error |
| Success of N gates | Roughly e to the minus N times the error per gate |
| Typical measurement | Randomized benchmarking gives average gate fidelity |
| Leading two-qubit values | About 99.9 percent on superconducting chips and 99.9 to 99.99 percent on ions |
| Error-correction threshold | About 99 percent for the surface code |
Where the idea comes from
Fidelity as a figure of merit comes from quantum information theory, and gate fidelities above 99 percent were reached for two-qubit gates around 2014 to 2016 on ions and superconducting devices. Reaching 99.9 percent happened around 2020 to 2023.
Real-World Use Cases
- The primary metric used to compare hardware quality across different quantum processors
- Determines how many gates can be chained together before a circuit becomes unreliable
- Directly determines the physical-to-logical qubit overhead needed for error correction
How it differs from related ideas
- Gate fidelity describes a single operation, while circuit fidelity describes a whole computation.
- Average gate fidelity and process fidelity are different quantities with different values.
- Readout fidelity concerns measurement and is reported separately.
Frequently asked questions
What is gate fidelity?
A measure of how closely a real quantum gate matches the ideal one, with 100 percent being perfect.
What fidelity is needed for error correction?
Two-qubit gates above about 99 percent for the surface code, and much higher to keep overhead low.
How is it measured?
Most often by randomized benchmarking, which gives an average gate fidelity robust to state preparation and measurement errors.
Related Terms
Keep exploring
- Algorithm: Quantum Error Mitigation Techniques
- Hardware: IBM Heron (r1, r2, and r3)
- Hardware: Quantinuum H2
- Hardware: IonQ Forte (and Forte Enterprise)