Gate set phase tomography

As quantum processors continue to scale, low-overhead characterization experiments that measure calibration parameters will become essential to maintain long-term stability. One approach to characterization is tomographic reconstruction, exemplified by gate set tomography (GST) experiments, which fully characterizes both the coherent and incoherent parameters of a quantum gate set under a Markovian approximation. However, GST is resource-intensive and not scalable. An alternative technique, robust phase estimation (RPE), efficiently measures only the coherent parameters of a gate while remaining resilient to the effects of incoherent parameters. In this work, we integrate RPE with the principles of gate set tomography to derive gate set phase tomography (GSPT). GSPT fully characterizes the unitary representation of a gate set without the need to measure nuisance parameters describing incoherent errors. This approach significantly reduces the number of required circuits compared to standard GST; for instance, characterizing a two-qubit unitary requires only 42 base circuits, in contrast to the 731 needed for full gate set tomography. Additionally, the analytic structure of GSPT circuits facilitates the efficient implementation of approximately optimal estimators, further mitigating the classical overhead associated with GST experiments. Our protocols yield a streamlined experimental design that enables high-precision measurement of relevant unitary parameters without the extensive overhead of a full GST experiment.