Redundancy is a central concept in gauge theory, where gauge-invariant degrees of freedom are redundantly encoded into gauge-variant quantities (in order to preserve locality). Likewise, redundancy is a hallmark of any quantum error correcting code, which redundantly encodes logical quantum information into a larger quantum system (in order to protect it against certain interactions with the environment). I will explain how this simple observation can be turned into a precise correspondence relating the formalism of quantum error correction to that of quantum gauge theory. I will focus more concretely on the well-studied family of stabilizer codes, which can be interpreted as Abelian gauge theories with gauge group a product of $\mathbb{Z}_2$. It includes repetition codes such as the elementary three-qubit code, and topological codes such as Kitaev's toric code, which I will use as illustrative examples. The notion of quantum reference frame (QRF) will provide a crucial ingredient relating structures on both sides of the correspondence. In particular, I will explain how a choice of maximal set of correctable errors on the QECC side, is equivalent to a choice of QRF on the gauge theory side. The correspondence also reveals a new duality structure among maximal correctable error sets, which can be understood as a manifestation of Pontryagin duality of Abelian groups. Based on joint work with A. Chatwin-Davies, P. Höhn, and F. M. Mele [ [ https://arxiv.org/abs/2412.15317 | https://arxiv.org/abs/2412.15317 ] ].