Characterizing mid-circuit measurements with a new form of gate set tomography part 1: Theory

While quantum circuits end with measurements, they can also include measurements in the middle. Such mid-circuit measurements are required for real-time feedforward control applications, such as quantum error correction. Understanding error processes in these mid-circuit measurements will be critical for building next-generation quantum processors. To that end, we extend gate set tomography (GST), a highly accurate and self-consistent protocol for diagnosing quantum gate errors, to be able to also characterize mid-circuit measurements. We will describe this extension and demonstrate its success in simulations.