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Quantum Coding via Quasi-Cyclic Block Matrix.

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

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Summary
This summary is machine-generated.

Researchers developed a new method for constructing long quantum error-correction codes (QECCs) using classical codes and number decomposition. This approach simplifies the process and yields codes with potential for large-scale quantum data applications.

Keywords:
jacket matrixlong-length quantum codesquasi-cyclic codesstabilizer codes

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Area of Science:

  • Quantum Information Theory
  • Quantum Error Correction
  • Coding Theory

Background:

  • The development of quantum computing necessitates effective methods for constructing long-length quantum codes.
  • Quantum error-correction codes (QECCs) are crucial for reliable quantum information processing and large-scale data applications.
  • Existing construction methods can be complex for long-length codes.

Purpose of the Study:

  • To propose a simplified and effective construction method for long-length quantum quasi-cyclic (QC) codes.
  • To leverage number decomposition and properties of block jacket matrices for code construction.
  • To analyze the properties and performance of the newly constructed QC codes.

Main Methods:

  • Utilized block jacket matrices and their circulant permutations.
  • Employed number decomposition for simplifying the construction process.
  • Constructed quantum quasi-cyclic (QC) codes using two classical codes.

Main Results:

  • Developed a method to construct long-length quantum error-correction codes (QECCs).
  • Achieved code lengths N scaling as O(n^2) with an appropriate prime number n.
  • Obtained codes exhibit four cycles in generator matrices and good performance for low-density parity-check (LDPC) codes.

Conclusions:

  • The proposed construction method simplifies the creation of long-length QECCs.
  • The method offers a viable approach for developing quantum codes applicable to large-scale quantum data.
  • The resulting codes possess favorable properties for efficient quantum information processing.