Characterizing a trapped ion logical qubit with gate set tomography

Recent quantum error correction demonstrations on a variety of experimental platforms have shown the successful creation of logical qubits. While these results are impressive and exciting, they also pose an intriguing challenge—how ought we best characterize the performance of logical qubits? Can we simply "promote" physical qubit characterization techniques to the logical level, or will that fail to properly capture logical qubit dynamics? We explore this question by performing, both in simulation and experiment, single-qubit gate set tomography on a logical qubit made of ten physical qubits running the Steane [7,1,3] code. We use our results to highlight how extensions of physical qubit characterization methods to logical qubit characterization methods can be more or less appropriate, depending strongly on device operating regimes and underlying physical noise processes. SNL is managed and operated by NTESS under DOE NNSA contract DE- NA0003525.