Emergent Non-Markovianity in Logical Qubit Dynamics

Understand

Logical qubits encoded in quantum error correcting codes can exhibit non-Markovian dynamical evolution, even when the underlying physical noise is Markovian.

• To understand this emergent non-Markovianity, we define a Markovianity condition appropriate to logical gate operations, and study it by relating logical operations to their physical implementation (operations on the data qubits into which the logical qubit is encoded).
• We apply our analysis to small quantum codes, and show that they exhibit non-Markovian dynamics even for very simple physical noise models.
• We show that non-Markovianity can emerge from Markovian physical operations if (and only if) the physical qubits are not necessarily returned to the code subspace after every round of QEC.