Characterizing parity checks with gate set tomography

Parity checks—non-demolition measurements of the parity of a collection of qubits—are critical components of quantum error correction (QEC). However, parity check error behavior and its connection with logical qubit performance remains poorly understood, despite parity checks having been extensively demonstrated in QEC experiments. By modeling the parity check as a multi-qubit mid-circuit measurement (which can in turn by described as a quantum instrument), we develop a new gate set tomography protocol to fully tomographically characterize the parity check as part of a complete gate set. We deploy this protocol on experimental hardware and reconstruct the parity check instrument from the data. We develop techniques to classify and understand parity check error modes. Finally, we explore logical qubit performance in simulation using both the reconstructed experimental quantum instrument and a variety of other physically-inspired theoretical noise models for the parity check.