Multi-agent discovery of practical quantum LDPC codes

Research Objective

Quantum low-density parity-check (qLDPC) codes are promising for fault-tolerant quantum computing due to their potential for finite encoding rates and improved scaling. However, designing practical, finite-length qLDPC codes is difficult because it requires balancing multiple competing objectives—such as code rate, distance, and stabilizer weight—within a vast and complex search space. This paper introduces a multi-agent AI framework designed to automate the discovery of these codes by treating the search as a structured, iterative scientific process.

The Multi-Agent Framework

The framework employs three distinct agent roles that operate in a closed-loop system:

• Researcher Council: Formulates scientific hypotheses and proposes mathematical directions for the search.
• Curator: Synthesizes proposals, maintains a persistent memory of lessons and anti-lessons, and manages task allocation.
• Worker Agents: Evolve executable programs that generate families of qLDPC codes, which are then evaluated for performance.

By evolving executable programs rather than individual parity-check matrices, the framework can explore structural variations across different scales, from local terms to the underlying group families. The search focuses on coset-orbit balanced-product codes, a broad class that includes bicycle and lifted-product constructions, while incorporating non-normal subgroup actions to expand the design space.

The framework successfully identified several high-performing finite-length codes that match or exceed the performance of existing benchmarks across various weight constraints (w ≤ 10). Notable discoveries include the [[288, 16, 18]] code at weight 7 and the [[234, 28, 18]] code at weight 10, both of which demonstrate superior rate-distance trade-offs. The search also uncovered structurally unique constructions, such as those utilizing non-normal subgroup actions, which were previously underexplored. These results highlight the effectiveness of agentic search in navigating complex scientific design spaces.