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<p>In this paper, we present a detailed mathematical description of the error correction process for Kitaev’s model for finite Abelian groups. The number of errors Kitaev’s model can correct depends on the lattice and its topology. Although there is a theoretical maximum number of errors that can be corrected, we prove that correcting this number of errors, in general, is an NP-complete problem. Consequently, we introduce a polynomial-time correction algorithm that corrects a number of errors below the theoretical maximum.</p>

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Quantum error correction in Kitaev’s quantum double model for Abelian groups

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Shawn X. Cui,
  • César Galindo,
  • Diego Romero

摘要

In this paper, we present a detailed mathematical description of the error correction process for Kitaev’s model for finite Abelian groups. The number of errors Kitaev’s model can correct depends on the lattice and its topology. Although there is a theoretical maximum number of errors that can be corrected, we prove that correcting this number of errors, in general, is an NP-complete problem. Consequently, we introduce a polynomial-time correction algorithm that corrects a number of errors below the theoretical maximum.