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Quantum

High-rate qLDPC processors

Aditya Bhardwaj, Muzhou Ma, Nadine Meister, Robbie King, Dolev Bluvstein, John Preskill, Madelyn Cain, Qian Xu, Hsin-Yuan Huang

Featured August 12, 2026

Original Paper

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Simply

They built special error-fixing codes like a puzzle, using fancy math rules from non-abelian groups to make them strong and efficient, then used a super-fast computer program to find the best puzzle pieces, making big quantum computers more practical.

In depth
The paper introduces mitten codes, a novel family of quantum low-density parity-check (qLDPC) codes built using non-abelian group theory. This unique structure allows them to achieve high error correction capabilities (distance) with significantly fewer physical qubits compared to previous designs, while also enabling highly parallel logical operations and a low-overhead toolkit for universal quantum computation. A new telescoping decoder and a fast distance estimator called sQetch were developed to efficiently design and validate these codes, demonstrating their potential for fault-tolerant quantum processors.

Key Takeaways

  • 1
    Mitten codes leverage non-abelian group theory to achieve high encoding rates and large distances with hundreds of physical qubits, significantly reducing overhead for fault-tolerant quantum computing.
  • 2
    Their inherent group symmetry enables a modular logical toolkit, allowing universal Clifford operations with just two reusable seed surgery gadgets and supporting parallel logical measurements and magic-state injection.
  • 3
    The telescoping decoder and sQetch distance estimator provide a powerful end-to-end pipeline for discovering, simulating, and validating these qLDPC processors, demonstrating logical error rates as low as per round.

Conceptual Flow

HIGH LEVEL
1
Methodology: How was it done?

They built special error-fixing codes like a puzzle, using fancy math rules from "non-abelian groups" to make them strong and efficient, then used a super-fast computer program to find the best puzzle pieces.

Old Code Ideas
Complex Math Rules
Combine Smartly
New Strong Codes
Fast Finder Tool
2
Results: What did they find?

The new codes can protect quantum information much better with fewer physical parts, allowing many quantum tasks to run at the same time with very few mistakes, making big quantum computers more practical.

Many Physical Qubits
Slow Quantum Tasks
High Error Rate
New Code Protection
Fewer Physical Qubits
Many Fast Tasks
Super Low Error