Approximate Bacon-Shor code and holography

We explicitly construct a class of holographic quantum error correction codes with non-trivial centers in the code subalgebra. Specifically, we use Bacon-Shor and perfect tensors to gauge (or stabilizer gauge-fixing), which call hybrid code. This admits local log-depth encoding/decoding circuit, can be represented as tensor network satisfies an analog Ryu-Takayanagi formula reproduces features sub-region duality. then approximate versions by "skewing" subspace, where size skewing is analogous gravitational constant holography. These are not necessarily codes, but they expressed superposition networks that codes. For such constructions, different logical states, representing bulk matter content, "back-react" on emergent geometry, resembling key feature gravity. The locality degrees freedom becomes subspace-dependent approximate. Such subspace-dependence manifest from point view "entanglement wedge" operator reconstruction boundary. Exact complementary breaks down for certain bipartition boundary freedom; however, limited, state-dependent form preserved particular subspaces. also example connected two-point correlation functions have power-law decay. Coupled known constraints holography, weakly back-reacting forces these skewed models "large $N$ limit" built concatenating large number copies.