受挫量子自旋模型VQE的优化地形几何

中文摘要 AI 辅助

我们在受控层级的受挫自旋模型上，针对精确态矢量VQE计算，对8种经典优化器进行基准测试，模型范围从对角伊辛玻璃到横场伊辛模型和各向异性海森堡模型。该基准测试包含局部、随机梯度、进化、协方差自适应以及基于群的优化方法，且函数评估预算匹配。为理解优化器在最终能量之外的性能，我们从局部极小值、梯度、曲率和基态可达性角度刻画 underlying哈密顿量- ansatz地形。我们使用简单变分电路，对角模型采用$R_y$乘积态ansatz，非对易模型采用浅$R_y$-CNOT硬件高效电路，并研究电路深度增加如何改变其表达能力、可达性和优化几何。我们发现，优化器性能在模型层级间差异显著，且与地形结构密切相关，而变分间隙是独立的误差来源。这些结果表明，经典优化、变分表达能力和地形几何共同决定了受挫自旋模型的VQE性能。

英文摘要

We benchmark eight classical optimizers for exact-statevector VQE calculations on a controlled hierarchy of frustrated spin models, ranging from a diagonal Ising glass to transverse-field Ising and anisotropic Heisenberg models. The benchmark includes local, stochastic-gradient, evolutionary, covariance-adaptation, and swarm-based optimization methods under matched function-evaluation budgets. To understand their performance beyond final energies, we characterize the underlying Hamiltonian--ansatz landscapes in terms of local minima, gradients, curvature, and ground-state reachability. We use simple variational circuits, from an $R_y$ product-state ansatz for the diagonal model to shallow $R_y$--CNOT hardware-efficient circuits for the noncommuting models, and study how increasing circuit depth changes their expressivity, reachability, and optimization geometry. We find that optimizer performance changes substantially across the model hierarchy and is closely connected to landscape structure, while the variational gap represents a separate source of error. These results show how classical optimization, variational expressivity, and landscape geometry jointly determine VQE performance for frustrated spin models.

发表机构

• VSB–Technical University of Ostrava（俄斯特拉发理工大学）
• IT4Innovations National Supercomputing Center, VSB–Technical University of Ostrava（俄斯特拉发理工大学 IT4创新国家超级计算中心）
• Marine Research Institute, Klaipeda University（克莱佩达大学海洋研究所）
• Indian Statistical Institute（印度统计研究所）
• Università dell’Aquila（阿奎拉大学）

机构由 AI 辅助整理，请以论文原文为准。