Gate-Set Tomography

Gate-set tomography reconstructs a full, self-consistent description of a set of gates, state preparation, and measurement without assuming any of them is perfect.

Beyond an Average Number

Randomized benchmarking gives one average error rate; it does not tell you what the gate actually does wrong. Standard process tomography would, but it assumes perfect state preparation and measurement to characterize a gate, which is circular because those operations are themselves imperfect. Gate-set tomography, or GST, removes this circularity by treating the gates, the initial state, and the measurement as one interdependent set to be estimated together.

Self-Consistency

GST runs a carefully chosen family of circuits built from the gates under test, arranged so that no perfect reference is assumed anywhere. From the measured outcome statistics it finds the set of process matrices, an initial-state vector, and a measurement description that jointly best explain the data. Because everything is estimated at once, the result is self-consistent: it does not blame the gate for readout error or vice versa. A gauge freedom, reflecting that only relative descriptions are observable, is fixed by a convention.

• Estimates full process matrices, not just a scalar fidelity.
• Makes no perfect-reference assumption about preparation or measurement.
• Reveals coherent errors, such as over-rotations and axis tilts, that benchmarking averages away.

Long-Sequence Amplification

To reach high precision, GST uses germ sequences repeated many times so that small systematic errors accumulate to a detectable level, much like error amplification in calibration. This gives estimates whose accuracy improves rapidly with the depth of the longest sequences used, letting GST detect very small coherent errors.

Cost and Use

The price of this detail is a large number of circuits and heavy classical post-processing, which grows quickly with the number of qubits, so GST is typically applied to one or two qubits at a time. It is the tool of choice when a lab needs to understand and fix the specific character of a gate error, complementing the fast, coarse picture from randomized benchmarking and the whole-device view from cross-entropy benchmarking.