Gate set tomography for logical qubits

Recent advances in qubit technologies have supported the implementation of quantum error correcting codes with physical qubits, leading to the creation of nascent logical qubits. Like their constituent physical qubits, however, these logical qubits still experience non-trivial errors. How to best characterize these errors is an open question. One option is to ignore the logical qubit's internal structure and simply treat it as another two-level quantum system, allowing for standard qubit characterization protocols to be used. We investigate this approach and apply single-qubit gate set tomography (GST) to a simulated logical qubit, examining a variety of QEC codes. We explore how different underlying physical errors manifest at the logical level, and how Markovian physical errors can result in non-Markovian logical errors.