Almost optimal geometrically local quantum LDPC codes in any dimension

Xingjian Li

Ting-Chun Lin

Adam Wills

Min-Hsiu Hsieh

出版日期

February 19, 2026

研究中心

量子計算研究所

發表資訊

Nature Communications volume 17, Article number: 2389 (2026)

主題

Quantum Computing

內容目錄

Geometrically local quantum codes, comprised of qubits and checks embedded in 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.