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

2026-02-03

AI Summary

This work proposes a black-box optimization framework based on large language models (LLMs) to overcome the performance bottlenecks of conventional methods in generating highly entangled quantum circuits. The approach formulates quantum circuit synthesis as a closed-loop test-time optimization problem: the LLM generates editing suggestions for gate sequences, which are evaluated by an external simulator using the Meyer–Wallach entanglement measure. Iterative refinement is achieved through a lightweight test-time learning strategy that integrates explicit memory traces, score-difference feedback prompting, and optimal restart sampling. Experiments on 20–25 qubit circuits demonstrate significant improvements in both entanglement quality and synthesis success rates. The study further reveals that high-performing circuits often correspond to stabilizer or graph states and highlights the critical influence of entanglement metric properties and prompt design on overall effectiveness.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• quantum circuit synthesis
• large language models
• black-box optimization
• entanglement
• test-time learning

Innovation

• test-time learning
• large language models
• quantum circuit synthesis
• Meyer-Wallach entanglement
• closed-loop optimization