Is a hybrid LDD+QEC protocol always superior to either method alone?

Determine whether a hybrid protocol that combines logical dynamical decoupling (implemented with elements of the code normalizer) together with quantum error correction is always better than either quantum error correction alone or dynamical decoupling alone when protecting quantum information, or establish counterexamples that show regimes where the hybrid approach does not strictly outperform the isolated methods.

Background

Quantum error correction and dynamical decoupling are two principal strategies for protecting quantum information, but their operating assumptions differ and their interplay can be subtle. Logical dynamical decoupling (LDD) seeks to preserve the codespace by using operations from the code’s normalizer while averaging away certain errors.

The paper develops a unified framework to analyze a hybrid protocol that interleaves LDD with a round of syndrome measurement and recovery, deriving closed-form entanglement-fidelity expressions and comparison criteria. Against this backdrop, the authors note an explicit open question: whether, in general, such a hybrid LDD+QEC protocol is always better than either approach in isolation.