Abstract:Deploying large language models (LLMs) as optimizers for black-box scientific design problems requires efficient test-time refinement under expensive evaluations and without training data. We propose a \emph{memory-augmented test-time optimization} framework that combines episodic memory of high-scoring candidates, score-difference feedback, and restart-from-best sampling to improve iterative search. We evaluate the approach on quantum circuit synthesis, where the objective is to maximize the Meyer--Wallach (MW) global entanglement measure under an exponentially expensive black-box oracle. On 20-qubit circuits, the framework achieves $Q(\psi)=0.99$ without feedback. On the more challenging 25-qubit task, feedback and restart mechanisms enable multiple runs to reach $Q(\psi)=1.0$ within 45 oracle calls, while a budget-matched random hill-climbing baseline stalls below $Q(\psi)\approx0.29$. These results demonstrate that memory and evaluator feedback substantially improve the sample efficiency of LLM-based black-box optimization and establish quantum circuit synthesis as a challenging benchmark for test-time optimization.
From: Adriano Macarone-Palmieri [view email]
[v1]
Tue, 3 Feb 2026 12:41:25 UTC (714 KB)
[v2]
Thu, 5 Feb 2026 16:53:11 UTC (714 KB)
[v3]
Fri, 6 Feb 2026 22:10:56 UTC (715 KB)
[v4]
Thu, 12 Feb 2026 11:53:26 UTC (715 KB)
[v5]
Tue, 7 Jul 2026 22:50:14 UTC (722 KB)
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