Discovering state-of-the-art quantum circuits with large language models
Andi Gu, Alek Kemeny, Susanne Yelin and Mikhail Lukin (Harvard) use an evolutionary loop in which LLMs propose quantum circuits and an independent evaluator verifies and scores them, and report circuits that beat the state of the art on seven of eight tasks.
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Problem. Quantum resource costs are dominated by a few primitives, and optimizing them is hard because circuits must be reversible.
Method. LLMs propose circuit designs, an independent evaluator checks correctness and scores Toffoli and qubit counts, and the best designs seed the next round.
Coverage. Tasks span numerical computation, chemistry, optimization, quantum simulation and number theory.
Result. On seven of eight tasks the discovered circuits significantly reduce both Toffoli count and qubit count relative to the best known circuits.
New architecture. On the eighth, the search found a reversible architecture for prime-field modular inversion that makes divsteps practical for reversible arithmetic and improves the Toffoli-qubit trade-off.
Abstract
Significant efforts are currently being directed toward the implementation of large-scale quantum information processors, but realizing useful quantum advantage also requires the development of efficient quantum algorithms. While for many practical problems the dominant resource costs are associated with a small set of computational primitives, optimizing them in the quantum setting presents unique challenges, including a reversibility constraint absent from ordinary classical computation. Here we introduce an evolutionary framework in which large language models (LLMs) propose circuit designs and an independent evaluator verifies and scores them. We apply this framework to tasks spanning numerical computation, chemistry, optimization, quantum simulation, and number theory. In seven of the eight tasks, the discovered circuits significantly reduce both Toffoli and qubit counts relative to the state of the art. In the eighth, the search discovers a new reversible architecture for prime-field modular inversion. By handling reversibility differently, the architecture makes divsteps -- a classical algorithm previously impractical for reversible integer arithmetic -- viable and substantially improves the Toffoli-qubit trade-off for modular inversion. These results open the door for evaluator-guided LLM co-design of new algorithmic structures for quantum computation.