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<p>Subsystem codes <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Q=A\otimes B\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Q</mi> <mo>=</mo> <mi>A</mi> <mo>⊗</mo> <mi>B</mi> </mrow> </math></EquationSource> </InlineEquation> are a generalization of noiseless subsystems, decoherence-free subspaces, and quantum error-correcting codes. In this paper, we provide an effective method for constructing subsystem codes via matrix-product codes. In addition, the lengths, dimensions of subsystem <i>A</i> and the co-subsystem <i>B</i>, and minimum distances of our subsystem codes <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Q=A\otimes B\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Q</mi> <mo>=</mo> <mi>A</mi> <mo>⊗</mo> <mi>B</mi> </mrow> </math></EquationSource> </InlineEquation> are easily calculated.</p>

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New subsystem codes from matrix-product codes

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Jie Liu,
  • Peng Hu,
  • Xiusheng Liu

摘要

Subsystem codes \(Q=A\otimes B\) Q = A ⊗ B are a generalization of noiseless subsystems, decoherence-free subspaces, and quantum error-correcting codes. In this paper, we provide an effective method for constructing subsystem codes via matrix-product codes. In addition, the lengths, dimensions of subsystem A and the co-subsystem B, and minimum distances of our subsystem codes \(Q=A\otimes B\) Q = A ⊗ B are easily calculated.