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<p>Asymmetric quantum error-correcting codes (AQECCs) are error correction schemes designed for asymmetric errors in quantum computing. Unlike traditional symmetric quantum error-correcting codes, AQECCs assume that the probabilities of qubits occurring in different types of errors (such as bit flipping and phase flipping) are different, thereby optimizing resource allocation and improving error correction efficiency. This paper explores the construction of optimal asymmetric quantum codes by utilizing generalized Reed-Solomon (GRS) codes. The construction approach focuses on selecting two appropriate subsets, either disjoint or intersecting, of finite fields, ensuring that the resulting MDS codes possess Euclidean hulls of arbitrary dimensions. From these MDS codes, we present a variety of new constructions for optimal asymmetric quantum codes, with flexible parameter configurations.</p>

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Construction of asymmetric quantum codes via two subsets

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Guohui Wang,
  • Yucheng Chen,
  • Chunming Tang

摘要

Asymmetric quantum error-correcting codes (AQECCs) are error correction schemes designed for asymmetric errors in quantum computing. Unlike traditional symmetric quantum error-correcting codes, AQECCs assume that the probabilities of qubits occurring in different types of errors (such as bit flipping and phase flipping) are different, thereby optimizing resource allocation and improving error correction efficiency. This paper explores the construction of optimal asymmetric quantum codes by utilizing generalized Reed-Solomon (GRS) codes. The construction approach focuses on selecting two appropriate subsets, either disjoint or intersecting, of finite fields, ensuring that the resulting MDS codes possess Euclidean hulls of arbitrary dimensions. From these MDS codes, we present a variety of new constructions for optimal asymmetric quantum codes, with flexible parameter configurations.