General Construction of Quantum Error-Correcting Codes
Published:Dec 26, 2025 18:57
•1 min read
•ArXiv
Analysis
This paper introduces a generalized method for constructing quantum error-correcting codes (QECCs) from multiple classical codes. It extends the hypergraph product (HGP) construction, allowing for the creation of QECCs from an arbitrary number of classical codes (D). This is significant because it provides a more flexible and potentially more powerful approach to designing QECCs, which are crucial for building fault-tolerant quantum computers. The paper also demonstrates how this construction can recover existing QECCs and generate new ones, including connections to 3D lattice models and potential trade-offs between code distance and dimension.
Key Takeaways
- •Proposes a generalized construction method for QECCs from multiple classical codes.
- •Extends the hypergraph product (HGP) construction.
- •Allows for the creation of QECCs from an arbitrary number of classical codes (D).
- •Recovers existing QECCs and generates new ones.
- •Connects to 3D lattice models and explores trade-offs between code distance and dimension.
Reference
“The paper's core contribution is a "general and explicit construction recipe for QECCs from a total of D classical codes for arbitrary D." This allows for a broader exploration of QECC design space.”