Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory

Understand

We examine two proposals for marginally self-correcting quantum memory, the cubic code by Haah and the welded code by Michnicki.

• In particular, we prove explicitly that they are absent of topological order above zero temperature, as their Gibbs ensembles can be prepared via a short-depth quantum circuit from classical ensembles.
• Our proof technique naturally gives rise to the notion of free energy associated with excitations.
• Further, we develop a framework for an ergodic decomposition of Davies generators in CSS codes which enables formal reduction to simpler classical memory problems.