Quantum Circuit Generation via test-time learning with large language models

TL;DR

This paper introduces a test-time learning approach using large language models to iteratively optimize quantum circuit synthesis, demonstrating improvements in circuit quality and success rate for 20-25 qubits.

Contribution

It presents a novel test-time learning method with memory and feedback mechanisms for quantum circuit generation using LLMs, enhancing optimization performance.

Findings

Loop without feedback improves random circuits.

Full learning strategy mitigates performance plateaus.

High MW solutions relate to stabilizer or graph states.

Abstract

Large language models (LLMs) can generate structured artifacts, but using them as dependable optimizers for scientific design requires a mechanism for iterative improvement under black-box evaluation. Here, we cast quantum circuit synthesis as a closed-loop, test-time optimization problem: an LLM proposes edits to a fixed-length gate list, and an external simulator evaluates the resulting state with the Meyer-Wallach (MW) global entanglement measure. We introduce a lightweight test-time learning recipe that can reuse prior high-performing candidates as an explicit memory trace, augments prompts with a score-difference feedback, and applies restart-from-the-best sampling to escape potential plateaus. Across fixed 20-qubit settings, the loop without feedback and restart-from-the-best improves random initial circuits over a range of gate budgets. To lift up this performance and success rate, we use the full learning strategy. For the 25-qubit, it mitigates a pronounced performance plateau when naive querying is used. Beyond raw scores, we analyze the structure of synthesized states and find that high MW solutions can correspond to stabilizer or graph-state-like constructions, but full connectivity is not guaranteed due to the metric property and prompt design. These results illustrate both the promise and the pitfalls of memory evaluator-guided LLM optimization for circuit synthesis, highlighting the critical role of prior human-made theoretical theorems to optimally design a custom tool in support of research.