In this paper, we present SCALAR (Symbolic Conjecture and LLM-Assisted Reasoning), a neurosymbolic framework for automated conjecture generation in quantum circuit analysis built on top of the CUDA-Q open source framework. The system integrates quantum simulation, symbolic conjecture generation, and LLM-based interpretation. We evaluate SCALAR on 82 MaxCut instances from the MQLib benchmark dataset and extend the analysis to 2,000 randomly generated graphs across four topologies: regular, Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz. The framework generates conjectured bounds relating optimal QAOA parameters to graph invariants, including known relationships such as periodicity constraints on the phase separation parameter $γ$. SCALAR also recovers previously reported parameter transfer phenomena across structurally similar instances. Additionally, the system identifies correlations between graph structural features and optimization landscape properties, which we characterize through invariant-based descriptors. Using CUDA-Q tensor network simulator, we scale experiments to instances of up to 77 qubits. We discuss the accuracy, generality, and limitations of the generated conjectures, including sensitivity to graph class and quantum circuit depth.

翻译：本文提出SCALAR（符号推测与大语言模型辅助推理）——一种基于CUDA-Q开源框架构建的神经符号框架，用于量子电路分析中的自动推测生成。该系统集成了量子模拟、符号推测生成与大语言模型解释功能。我们在MQLib基准数据集的82个MaxCut实例上评估SCALAR，并将分析扩展至覆盖四种拓扑结构（正则图、Erdos-Renyi图、Barabasi-Albert图与Watts-Strogatz图）的2000个随机生成图。该框架可生成将最优QAOA参数与图不变量关联的推测性界值，包括相位分离参数$γ$的周期性约束等已知关系。SCALAR还复现了先前报告的结构相似实例间的参数迁移现象。此外，系统识别出图结构特征与优化景观属性之间的相关性，我们通过基于不变量的描述符对其进行刻画。利用CUDA-Q张量网络模拟器，我们将实验规模扩展至77量子比特实例。本文讨论了所生成推测的准确性、普适性及局限性，包括对图类别和量子电路深度的敏感性。