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This summary is machine-generated.

We introduce new quantum error-correcting codes that generalize existing hypergraph-product and toric codes. These codes offer explicit parameters, including minimum distances, derived from associated binary codes.

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Area of Science:

  • Quantum information science
  • Coding theory
  • Quantum computing

Background:

  • Quantum error-correcting codes are essential for building fault-tolerant quantum computers.
  • Existing codes like hypergraph-product and toric codes have limitations in their applicability and generalization.
  • There is a need for more versatile and systematically constructible quantum error-correcting codes.

Purpose of the Study:

  • To introduce a novel family of quantum error-correcting codes.
  • To demonstrate that these codes generalize existing constructions, including hypergraph-product and toric codes.
  • To provide explicit methods for determining the parameters of these new codes.

Main Methods:

  • Construction of quantum codes based on a generalization of hypergraph-product and toric code frameworks.
  • Utilizing matrices associated with binary codes to define the structure of the quantum codes.
  • Derivation of code parameters, specifically the minimum distance, from the properties of the underlying binary codes.

Main Results:

  • A new family of quantum error-correcting codes is presented.
  • The constructed codes encompass and generalize previously known families of quantum codes.
  • Explicit formulas for the minimum distance of the new codes are derived based on the parameters of associated binary codes.

Conclusions:

  • The introduced quantum codes offer a unified framework for several existing code families.
  • The explicit parameter calculation simplifies the analysis and application of these codes.
  • This work advances the development of robust quantum error correction for future quantum technologies.