Introduction to Quantum Gate Set Tomography

TLDR

Quantum gate set tomography (GST) offers a full, self‑consistent characterization of quantum logic gates, correcting for SPAM errors and yielding more accurate estimates than quantum process tomography as gate fidelities approach the fault‑tolerant regime. The authors review GST and provide a self‑contained guide, aiming to demonstrate its utility as an accurate characterization technique and a simple diagnostic tool. The review presents GST step‑by‑step, includes necessary mathematical background, and illustrates its performance by comparing simulated GST and QPT outputs for a single qubit. Consistent with prior work, the study shows that QPT poorly estimates coherent errors near error‑correction thresholds, whereas GST remains accurate.

Abstract

Quantum gate set tomography (GST) has emerged as a promising method for the full characterization of quantum logic gates. In contrast to quantum process tomography (QPT), GST self-consistently and correctly accounts for state preparation and measurement (SPAM) errors. It therefore provides significantly more accurate estimates than QPT as gate fidelities increase into the fault-tolerant regime. We give a detailed review of GST and provide a self-contained guide to its implementation. The method is presented in a step-by-step fashion and relevant mathematical background material is included. Our goal is to demonstrate the utility of GST as both an accurate characterization technique and a simple and effective diagnostic tool. As an illustration, we compare the output of GST and QPT using simulated example data for a single qubit. In agreement with the original literature, we find that coherent errors are poorly estimated by QPT near quantum error correction thresholds, while GST is accurate in this regime.