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Almost optimal geometrically local quantum LDPC codes in any dimension.

Xingjian Li1, Ting-Chun Lin2,3, Adam Wills3,4

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|February 5, 2026
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Researchers developed a new method to create nearly optimal geometrically local quantum codes from quantum low-density parity-check (LDPC) codes. This technique uses a simple procedure to extract 2D structures, advancing quantum error correction.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Computational Geometry

Background:

  • Geometrically local quantum codes are crucial for quantum error correction, embedding qubits and checks in Euclidean space (ℝ^D).
  • A significant challenge lies in constructing codes that optimize code dimension and distance under geometric constraints.

Purpose of the Study:

  • To introduce a novel construction for creating almost optimal geometrically local quantum codes.
  • To provide a method for transforming existing quantum low-density parity-check (LDPC) codes into this desired geometric form.

Main Methods:

  • The study employs a novel procedure to extract a two-dimensional structure from a three-term chain complex.
  • This geometric extraction process connects chain complex operations directly to quantum code construction.

Main Results:

  • A construction is presented that converts any good quantum LDPC code into an almost optimal geometrically local quantum code.
  • The method is shown to be effective in addressing the challenge of maximizing code dimension and distance within geometric constraints.

Conclusions:

  • The introduced procedure offers a pathway to nearly optimal geometrically local quantum codes.
  • This technique is expected to have broader applications in areas like weight reduction and the geometric realization of chain complexes in quantum information.