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A geometrically local quantum code is an error correcting code situatedwithin $\mathbb{R}^D$, where the checks only act on qubits within a fixedspatial distance. The main question is: What is the optimal dimension anddistance for a geometrically local code? This question was recently answered byPortnoy which constructed codes with optimal dimension and distance up topolylogs. This paper extends Portnoy's work by constructing a code whichadditionally has an optimal energy barrier up to polylogs. The key ingredientis a simpler code construction obtained by subdividing the balanced productcodes. We also discuss applications to classical codes.

Geometrically Local Quantum and Classical Codes from Subdivision