Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension

Geometrically local quantum codes, comprised of qubits and checks embedded in RD with local check operators, have been a subject of significant interest. A central challenge has been to identify the optimal code construction that maximizes both dimension and distance. Recent advancements have yielded several constructions, yet these have either depended on specific good quantum low-density parity-check (qLDPC) codes or have been restricted to three dimensions. In this work, we introduce a construction that can transform any good qLDPC code into an optimal geometrically local quantum code. Our approach hinges on a novel procedure that extracts a two-dimensional c