Emergent Non-Markovianity in Logical Qubit Dynamics

TL;DR

This paper investigates how logical qubits in quantum error correction can show non-Markovian behavior even when physical noise is Markovian, highlighting the role of syndrome qubits as memory in quantum dynamics.

Contribution

It introduces a Markovianity condition for logical gate operations and demonstrates how non-Markovianity emerges from physical operations that do not reset qubits to the code space.

Findings

Logical qubits can exhibit non-Markovian dynamics despite Markovian physical noise.

Non-Markovianity arises when syndrome qubits act as memory due to incomplete qubit resets.

Conditions are proposed for reliable gate characterization in early fault-tolerant quantum devices.

Abstract

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. In this situation, the syndrome qubits can act as a memory, mediating time correlations and enabling violation of the Markov condition. We quantify the emergent non-Markovianity in simple examples, and propose sufficient conditions for reliable use of gate-based characterization techniques like gate set tomography in early fault-tolerant quantum devices.