Discovering state-of-the-art quantum circuits with large language models

Useful quantum advantage requires efficient quantum algorithms as well as large-scale processors. In many practical problems the dominant resource costs come from a small set of computational primitives, and optimising them in the quantum setting is hard, partly because of a reversibility constraint absent from classical computation. Andi Gu presents an evolutionary framework in which large language models propose circuit designs and an independent evaluator verifies and scores them. On tasks spanning numerical computation, chemistry, optimisation, quantum simulation and number theory, the discovered circuits significantly reduce both Toffoli and qubit counts relative to the state of the art in seven of eight cases. In the eighth, the search finds a new reversible architecture for prime-field modular inversion that makes divsteps viable and substantially improves the Toffoli-qubit trade-off. The results open the way to evaluator-guided co-design of new algorithmic structures for quantum computation with LLMs.