Almost optimal geometrically local quantum LDPC codes in any dimension.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 41644532.
- Also identified by DOI 10.1038/s41467-026-69031-w and PMC identifier 12982749.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
Abstract
Geometrically local quantum codes, comprised of qubits and checks embedded in <math xmlns="http://www.w3.org/1998/Math/MathML"> <msup><mrow><mi>R</mi></mrow> <mrow><mi>D</mi></mrow> </msup> </math> with local check operators, have been a subject of significant interest. A key challenge is identifying the optimal code construction that maximizes both code dimension and distance under the geometric constraints. In this work, we introduce a construction that can transform any good quantum LDPC code into an almost optimal geometrically local quantum code. Our approach hinges on a novel yet simple procedure that extracts a two-dimensional structure from an arbitrary three-term chain complex, building a connection between geometric operations and code constructions. We expect that this procedure will find broader applications in areas such as weight reduction and the geometric realization of chain complexes.