Emergent Non-Markovian Dynamics in Logical Qubit Systems*

Simulations of error-corrected logical qubits have demonstrated that logical qubit dynamics can exhibit non-Markovian behavior, even when the underlying physical noise is Markovian. Such non-Markovian errors present challenges to holistic logical qubit characterization and can also non-trivially degrade the performance of error-corrected hardware in unexpected ways. By examining the gate composability requirement for Markovian dynamics, we provide illustrative examples to explain the emergence of logical non-Markovianity. We use these results to comment on the utility of characterization protocols for logical qubits.