Short answer: Gate set tomography (GST) is a protocol for characterizing the logic gates of a quantum processor, and papers describe it as calibration-free: it does not rely on pre-calibrated state preparations and measurements. A 2015 review says it accounts for state preparation and measurement (SPAM) errors self-consistently, unlike quantum process tomography (QPT). A 2017 experiment in Nature Communications used it on a single trapped-ion qubit.
What GST is
A 2021 paper in Quantum, "Gate Set Tomography", says GST is a protocol for detailed, predictive characterization of logic operations on quantum computing processors. It says early versions emerged around 2012-13 and have since been refined, demonstrated and used in a large number of experiments. Its most important feature, compared to older state and process tomography protocols, is that it is calibration-free. Instead of pre-calibrated state preparations and measurements, it characterizes all the operations in a gate set simultaneously and self-consistently, relative to each other.
How it differs from process tomography
A 2015 arXiv review, "Introduction to Quantum Gate Set Tomography", says that in contrast to QPT, GST self-consistently and correctly accounts for SPAM errors. It says this provides significantly more accurate estimates than QPT as gate fidelities increase into the fault-tolerant regime. As an illustration the authors compare the two on simulated single-qubit data. They report that coherent errors are poorly estimated by QPT near quantum error correction thresholds, while GST is accurate in that regime. This is a simulation result from that paper.
Precision and analysis
The 2021 paper says long-sequence GST can estimate gates with very high precision and efficiency, achieving Heisenberg scaling in regimes of practical interest. It covers the intellectual history, the techniques and experiments, data analysis, gauge freedom and fixing, error bars, and the interpretation of gauge-fixed estimates of gate sets. It says its focus is the fundamental mathematical aspects of GST rather than implementation details.
An experiment
A 2017 paper in Nature Communications, "Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography", notes that quantum error correction can protect against general noise only if the error in each physical qubit operation is smaller than a certain threshold, quantified by the diamond norm. It says qubits have mostly been assessed by randomized benchmarking, which reports a different error rate that is not sensitive to all errors and cannot be compared directly to diamond norm thresholds. The authors used GST to completely characterize operations on a trapped-ytterbium-ion qubit and report, with greater than 95 percent confidence, that they satisfy a rigorous threshold for fault-tolerant error correction (diamond norm of 6.7 x 10^-4 or less). They describe the result as the first single-qubit gates whose errors are demonstrably below such a threshold. That is the authors' claim about one single-qubit device.
What this does not tell you
This article summarises abstracts and introductions of three papers. It does not say how widely GST is used on current machines, it does not cover multi-qubit systems, and the QPT comparison above comes from simulated data. It is not a guide to running GST.
FAQ
What does calibration-free mean for GST?
It does not rely on pre-calibrated state preparations and measurements, and characterizes all gates in the set relative to each other, per the 2021 paper.
How is GST different from process tomography?
The 2015 review says GST accounts for SPAM errors self-consistently, while QPT does not.
Why not just use randomized benchmarking?
The 2017 paper says randomized benchmarking is not sensitive to all errors and cannot be compared directly to diamond norm thresholds.
What did the 2017 experiment show?
The authors report that single-qubit operations on a trapped-ion qubit met a diamond norm threshold of 6.7 x 10^-4 with greater than 95 percent confidence.
What is Heisenberg scaling here?
The 2021 paper says long-sequence GST can reach it in regimes of practical interest. It does not define the scaling in the abstract.
All field notes