Probing logical error models with gate set tomography

Qubit technologies are becoming sufficiently advanced to support the implementation of error- corrected logical qubits. These logical qubits still experience errors, just like their constituent physical qubits, but they may not experience all the same kinds of errors observed in physical qubits — e.g. coherent errors. It has been widely conjectured that logical qubit error processes will be well approximated by Pauli-stochastic channels, regardless of what errors afflict their component physical qubits. Testing this conjecture requires precise, reliable probes of logical error processes. We demonstrate that logical gate set tomography (GST) can probe the dynamics of a numerically simulated logical qubit precisely enough to test the nature of its error process. We use GST to fit nested error models for logical qubit behavior, and apply rigorous statistical tests to determine whether any Pauli-stochastic logical error process captures the logical qubit’s dynamics. We demonstrate regimes where this conjecture holds, and we examine regimes where this conjecture may be less well-founded.