The Free Energy Barrier: An Eyring-Polanyi bound for stabilizer Hamiltonians, with applications to quantum error correction

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.