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Concatenating Algebraic Codes over High-Rate Quantum LDPC Codes

Adam Wills, Michael E. Beverland, Lev S. Bishop, Jay M. Gambetta, Patrick Rall, Vikesh Siddhu, Andrew W. Cross

Featured June 6, 2026

Original Paper

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Simply

By grouping many small quantum error-correcting blocks into bigger "super-blocks" (called Galois qudits), the paper shows how to use a powerful outer code to protect them, making quantum computers much more efficient and robust against errors.

In depth
The paper introduces a novel quantum error correction scheme that significantly reduces memory overhead by treating blocks of high-rate inner quantum LDPC codes as single Galois qudits. This abstraction enables the use of powerful quantum Reed-Solomon outer codes with list decoders, which are robust against correlated errors within inner code blocks and allow operation in the teraquop regime.

Key Takeaways

  • 1
    The use of Galois qudits enables the concatenation of high-rate qLDPC inner codes with powerful algebraic outer codes, effectively managing correlated errors within inner code blocks.
  • 2
    A novel fault-tolerant Shor scheme for Galois qudits is developed, employing "time-like" Reed-Solomon protection and lightweight fault tolerance for robust syndrome extraction.
  • 3
    The proposed concatenated gross code system achieves operation in the teraquop regime with lower space overhead and significant engineering advantages compared to alternative bivariate bicycle codes.

Conceptual Flow

HIGH LEVEL
1
Methodology: Grouping Small Blocks into Super-Blocks

The paper combines many small error-protected quantum blocks into bigger 'super-blocks' that act like single, powerful data units.

Small Error Blocks
Group into Super-Blocks
Protected Super-Blocks
2
Results: Achieving Higher Performance with Less Overhead

This new protection method allows the quantum computer to perform many more operations with fewer errors, making it much more powerful and efficient.

Old Error Rate
High Space Use
New Protection Method
Much Lower Error Rate
Less Space Needed