Nouédyn Baspin (Sep 23 2025).

Abstract: The lack of an energy barrier in stabilizer Hamiltonians is well known to be an indication of short thermalisation times; and serves as a simple criteria to rule out self-correction. Its applicability has recently been challenged by the discovery of stabilizer codes with maximal energy barriers whose self-correcting status remains unclear. We address this question by introducing the more general notion of a free energy barrier, whose absence is also demonstrated to guarantee fast thermalisation. Applying these new results to the Layer codes, we prove that they lack self-correction.

Arxiv: https://arxiv.org/abs/2509.17356