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 dynamics present challenges to holistic logical qubit characterization and can also non-trivially degrade the performance of operational tasks performed on error-corrected quantum computers. To understand this emergent non-Markovianty, we construct a method for mapping arbitrary Markovian physical qubit dynamics to logical qubit dynamics. Examining a particular form of Markovianity relevant to gates, we provide illustrative examples in small quantum codes to explain these non-Markovian phenomena. Finally, we use measures of non-Markovianity to determine sufficient conditions for the use of gate-based characterization techniques (such as gate set tomography) in early fault-tolerant quantum devices.