OmniQEC: discovering practical quantum error-correcting codes by an AI scientist

As quantum processors move toward fault-tolerant operation, the design of quantum error-correcting (QEC) codes must account for practical hardware constraints like syndrome extraction and decoding. Traditional code-centric approaches often rely on algebraic metrics (e.g., code distance or rate) that fail to capture real-world performance. This paper asks: can an autonomous AI agent, guided by large language models (LLMs), discover QEC codes that are optimized for actual circuit-level logical error rates?

OmniQEC implements an iterative, dual-loop discovery process. In the 'fast loop,' an LLM-based orchestrator generates candidate code constructions, which are screened using inexpensive code-level metrics. Promising candidates are promoted to the 'slow loop,' where they are compiled into concrete syndrome-extraction circuits and evaluated through noisy sampling and decoding. The results from this rigorous circuit-level evaluation are fed back into the orchestrator, allowing the AI to refine its search strategy and 'evolve' better code designs over time.

OmniQEC demonstrates that circuit-level logical error rates (LER) are a more reliable indicator of performance than common code-level figures of merit. Across multiple qLDPC code families and LLM backends, the framework consistently discovered codes that show improved error suppression as the physical-qubit budget increases. Notably, the discovered codes outperformed established bivariate-bicycle (BB) benchmarks at fixed resource budgets, proving that physically grounded co-design—where the code, circuit, and decoder are optimized together—is superior to purely algebraic optimization.