Haah's 3D cubic code thermalizes rapidly

Abstract:Haah's 3D cubic code was introduced as a candidate for a self-correcting quantum memory in three dimensions, using the absence of string logical operators to obstruct thermal errors. It has been a long-standing open question whether it is a self-correcting quantum memory. Even though the memory time was explored numerically, no analytical upper bound was known. Here, we settle this question rigorously and show that the cubic code thermalizes rapidly at every positive temperature. Our proof relies on the framework of [Commun. Math. Phys. 407, 195 (2026)] to turn a decay-of-correlations condition into a modified logarithmic Sobolev inequality for the Davies generator. To the best of our knowledge, this is the first analytic proof of rapid mixing for all positive temperatures for any fracton code.

arXiv:2609.39959 [quant-ph]

(or arXiv:2609.39959v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.39959 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.