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

• URL: http://arxiv.org/abs/2408.01769v1
• Date: Sat, 3 Aug 2024 12:46:05 GMT
• Title: Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension
• Authors: Xingjian Li, Ting-Chun Lin, Min-Hsiu Hsieh,
• Abstract summary: A key challenge is identifying the optimal code construction that maximizes both dimension and distance. Recent advancements have produced several constructions, but these either depend on specific good quantum low-density parity-check (qLDPC) codes or are limited to three dimensions. We introduce a construction that can transform any good qLDPC code into an optimal geometrically local quantum code.
• Score: 11.695180823001566
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Geometrically local quantum codes, comprised of qubits and checks embedded in $\mathbb{R}^D$ with local check operators, have been a subject of significant interest. A key challenge is identifying the optimal code construction that maximizes both dimension and distance. Recent advancements have produced several constructions, but these either depend on specific good quantum low-density parity-check (qLDPC) codes or are limited 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 structure from an arbitrary three-term chain complex. We expect that this procedure will find broader applications in areas such as weight reduction and the geometric realization of chain complexes.

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