Automated discovery of quantum subsystem codes with an AI scientist

Quantum error correction (QEC) is essential for scalable fault-tolerant quantum computing, yet practical code design remains constrained by the connectivity and imperfections of the underlying hardware. This challenge is particularly acute for superconducting processors, where fixed and sparse couplings can restrict both the realizable code space and the level of logical protection that can be achieved. Here we introduce a verification-feedback-driven LLM framework for hardware-constrained subsystem-code discovery. The framework uses an LLM to generate hardware-aware code constructions, deterministic tools to verify them, and verified feedback to improve subsequent generations. Its central feature is that code generation is conditioned on the specific hardware instance, and independently verified code properties and failure evidence are fed back to guide subsequent refinement. We evaluate the framework on four calibration-informed defect layouts of the 105-qubit Willow graph and three connectivity-design tasks: two Willow augmentations and one free-connectivity search within the same qubit budget. On the four defect layouts, the selected subsystem implementations use weight-two gauge measurements and attain larger code and circuit fault distances than native surface-code templates, while reducing CZ count by \(12.5%\)–\(41.2%\) and CZ depth by \(70.0%\)–\(86.1%\) relative to code-distance-matched routed implementations. Under Willow augmentation, the search finds a distance-7 subsystem code protecting two logical qubits at maximum degree 5 and a distance-5 stabilizer code ($r=0$) protecting 10 logical qubits at maximum degree 6. A separate free-connectivity search finds a distance-9 subsystem construction at maximum degree 4. These results demonstrate the potential of self-evolving LLM search for QEC design under realistic hardware constraints, paving a path toward robust and resource-efficient fault-tolerant quantum computing.