Gate Set Tomography

TL;DR

Gate set tomography (GST) is a calibration-free quantum gate characterization method that self-consistently estimates all operations in a set with high precision, enabling detailed and predictive understanding of quantum logic gates.

Contribution

This paper provides a comprehensive mathematical foundation for GST, detailing its principles, techniques, and analysis methods, highlighting its calibration-free and high-precision capabilities.

Findings

GST achieves Heisenberg scaling in gate estimation.

GST characterizes all operations simultaneously and self-consistently.

The paper discusses gauge fixing, error bars, and interpretation of results.

Abstract

Gate set tomography (GST) is a protocol for detailed, predictive characterization of logic operations (gates) on quantum computing processors. Early versions of GST emerged around 2012-13, and since then it has been refined, demonstrated, and used in a large number of experiments. This paper presents the foundations of GST in comprehensive detail. The most important feature of GST, compared to older state and process tomography protocols, is that it is calibration-free. GST does not rely on pre-calibrated state preparations and measurements. Instead, it characterizes all the operations in a gate set simultaneously and self-consistently, relative to each other. Long sequence GST can estimate gates with very high precision and efficiency, achieving Heisenberg scaling in regimes of practical interest. In this paper, we cover GST's intellectual history, the techniques and experiments used to achieve its intended purpose, data analysis, gauge freedom and fixing, error bars, and the interpretation of gauge-fixed estimates of gate sets. Our focus is fundamental mathematical aspects of GST, rather than implementation details, but we touch on some of the foundational algorithmic tricks used in the pyGSTi implementation.