发表机构
International Institute of Physics, Federal University of Rio Grande do Norte; Instituto de Física de São Carlos, Universidade de São Paulo（北里奥格兰德联邦大学国际物理研究所; 圣保罗大学圣卡洛斯物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在2-设计假设下提出表征理论框架，将变分量子势能分解为不可约表征通道，得到适用于任意初态和可观测量的代价函数方差表达式，扩展了贫瘠高原的分析理论。
AI 中文摘要
变分量子算法的可扩展性受限于贫瘠高原效应，即代价函数方差随系统规模消失，导致优化难以实施。近期针对深度参数化的李代数方法实现了对该挑战的统一分析理解，但要求初态或测量可观测量属于电路生成的动力学李代数。本文在2-设计假设下引入表征理论框架，证明变分量子势能可自然分解为不可约表征通道，得到适用于任意初态和可观测量的代价函数方差精确表达式与分析界，此前的李代数结果为其特例。通过分析一维ANNNI模型在多种电路架构下的势能，揭示了现有方法无法触及的可训练区域，建立了分析变分量子势能的通用表征理论框架，大幅扩展了贫瘠高原的分析理论。
英文摘要
The scalability of variational quantum algorithms is fundamentally limited by the barren plateau effect, where the cost-function variance vanishes with system size, rendering optimization impractical. Recent Lie-algebraic approaches for deep parameterized have enabled a unified analytical understanding of this challenge but require either the initial state or the measurement observable to belong to the dynamical Lie algebra generated by the circuit. Here, we introduce a representation-theoretic framework under $2$-design hypothesis showing that variational quantum landscapes admit a natural decomposition into irreducible representation channels. This yields exact expressions and analytical bounds for the cost-function variance applicable to arbitrary initial states and observables, with previous Lie-algebraic results emerging as a special case. We illustrate the framework by analyzing the energy landscape of the one-dimensional ANNNI model for several circuit architectures, revealing trainability regimes inaccessible to existing methods. Our results establish a general representation-theoretic framework for analyzing variational quantum landscapes, substantially extending the analytical theory of barren plateaus.
Comments15 pages, 4 figures
