用神经符号框架自动发现量子线路优化规律，可推广到77比特系统。
SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis
- 结合量子模拟与大模型推理，自动生成参数与图结构的猜想关系
- 在82个最大割实例及2000个随机图上验证，发现周期性约束与参数迁移现象
- 适用于量子近似优化算法研究者，尤其关注参数规律挖掘的团队
本文提出SCALAR（符号猜想与大模型辅助推理），一个基于CUDA-Q开源框架的神经符号框架，用于自动化生成量子电路分析中的猜想。系统融合量子仿真、符号猜想生成与大模型解释能力。我们在MQLib基准数据集的82个MaxCut实例上评估该框架，并扩展至4种拓扑结构（规则图、Erdos-Renyi、Barabasi-Albert、Watts-Strogatz）的2,000个随机生成图。框架生成了最优QAOA参数与图不变量之间的猜想边界，包括相位分离参数γ的周期性约束等已知关系。同时，系统复现了先前报道的参数迁移现象，并识别出图结构特征与优化景观性质间的相关性，通过不变量描述符进行刻画。借助CUDA-Q张量网络模拟器，实验规模扩展至最多77量子比特。我们讨论了生成猜想的准确性、泛化性及其局限性，包括对图类和量子线路深度的敏感性。
原文摘要 · Abstract (English)
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.
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