Parity Measurement Gate Set Tomography*

Parity measurements, used for detecting errors during the execution of a logical quantum circuit, are essential components of quantum error correction. We seek to fully characterize a parity measurement in order to understand its error mechanisms and how to mitigate them. However, parity measurements admit complex error modes, including those found neither in quantum gates nor terminating measurements. We experimentally characterize a two-qubit mid-circuit parity measurement using quantum instrument gate set tomography (arXiv:2103.03008) on IBM Quantum hardware, modeling the parity check as a two-qubit quantum instrument; this allows us to both fully reconstruct the parity measurement's corresponding process matrices as well as detect the presence of non-Markovian errors introduced by the measurement.