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Quantum LDPC Codes Based on Cocyclic Block Matrices.

Yuan Li1, Ying Guo2

  • 1School of Electronic Information Engineering, Shanghai Dianji University, Shanghai 200240, China.

Entropy (Basel, Switzerland)
|September 28, 2023
PubMed
Summary
This summary is machine-generated.

We present a novel construction for long-length quantum error-correction codes (QECCs) using binary cocyclic block matrices. This method yields stabilizer quantum codes (SQCs) with fast construction and low-density properties, beneficial for quantum computing.

Keywords:
cocyclic block matriceslong-length quantum codeslow-density parity check codesstabilizer codes

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Area of Science:

  • Quantum Information Science
  • Coding Theory
  • Algebraic Methods in Quantum Computing

Background:

  • Stabilizer quantum codes (SQCs) are crucial for fault-tolerant quantum computation.
  • Efficient construction methods for long-length QECCs are needed to scale quantum technologies.
  • Existing methods may lack speed or desirable code properties.

Purpose of the Study:

  • To propose a new construction method for long-length quantum error-correction codes (QECCs).
  • To leverage binary cocyclic block matrices for generating SQCs.
  • To ensure the constructed codes possess desirable properties like fast generation and low-density parity-check (LDPC) characteristics.

Main Methods:

  • Utilized a family of binary cocyclic block matrices over GF(2).
  • Employed the recursive relation of block matrices for generator matrix construction.
  • Derived SQCs from the rows of circulant permutation matrices.

Main Results:

  • Successfully constructed a generator matrix for long-length quantum cocyclic codes.
  • The proposed method allows for fast algorithm-based code generation.
  • The resulting quantum codes exhibit a low-density advantage, with no 4-cycles in their Tanner graphs.

Conclusions:

  • The proposed construction method offers an efficient way to generate long-length QECCs.
  • The derived SQCs possess advantageous low-density properties, important for practical implementation.
  • This work contributes to the development of robust quantum error correction.