发表机构
Modelos Inteligencia Artificial S.L.; Faculty of Science, Masaryk University; Czech Metrology Institute（Modelos Inteligencia Artificial S.L.; 马萨里克大学理学院; 捷克计量研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对开壳层ADAPT-VQE，提出表示等价性审计框架，揭示投影空间与全空间振幅传递的失效机制，并通过全空间重优化及自旋保持构造缓解，提供电路级验证。
AI 中文摘要
在对称性投影空间中优化的变分态未必是通过对相应的未投影父生成元取指数而制备的态。对于正交目标空间投影算子$P$，$Q=I-P$，以及反厄米生成元$A$，对所有振幅的精确等价性要求目标空间不变性，即$QAP=0$。我们将此条件表述为开壳层ADAPT-VQE的表示等价性审计。对于典型的CAS(15e,9o)型I Cu(II)哈密顿量，323个裸Hartree-Fock起源的单、双和三激发中有274个违反此条件。投影双重态ADAPT以121个算子达到1.5719 m$E_h$的误差，而相同振幅在相应的全空间序列中给出464.730 m$E_h$的误差，与投影态的重叠度为0.07343，且四重态权重为54.45%。在硬约束$p_D\ge0.999$下，以相同顺序重新优化相同的121个父生成元，将最佳收敛误差降至8.482 m$E_h$，这表明灾难性的同角度失效主要是表示/参数传递失效，但固定序列的全空间重新优化并未完全修复该问题。一个独立的12量子比特NO基准表现出相同机制但程度较轻。一种自旋保持的广义全空间构造消除了表示歧义，并在18和24量子比特下分别达到1.493和1.181 m$E_h$的误差。对于18量子比特阳性对照，仅选择性细化四个Suzuki-2因子并使用固定编译器种子重新转译，通过了预先声明的电路等价性门限，受控-X（CX）门数为19,660，深度为23,016。因此，电路合成和最终能量测量构成独立的验证层。本工作的贡献在于提出了一个验证框架，而非新的自旋适配ADAPT算法。
英文摘要
A variational state optimized in a symmetry-projected space need not be the state prepared by exponentiating the corresponding unprojected parent generators. For an orthogonal target-space projector $P$, $Q=I-P$, and an anti-Hermitian generator $A$, exact equivalence for all amplitudes requires target-space invariance, $QAP=0$. We formulate this condition as a representation-equivalence audit for open-shell ADAPT-VQE. For a canonical CAS(15e,9o) type-1 Cu(II) Hamiltonian, 274 of 323 bare Hartree--Fock-origin single, double, and triple excitations violate this condition. Projected-doublet ADAPT reaches 1.5719 m$E_h$ with 121 operators, whereas the same amplitudes in the corresponding full-space sequence give 464.730 m$E_h$ error, 0.07343 fidelity with the projected state, and 54.45\% quartet weight. Reoptimizing the same 121 parent generators in the same order under the hard constraint $p_D\ge0.999$ reduces the best converged error to 8.482 m$E_h$, showing that the catastrophic same-angle failure is primarily a representation/parameter-transfer failure but is not completely repaired by full-space reoptimization of the fixed sequence. An independent 12-qubit NO benchmark exhibits the same mechanism more mildly. A spin-preserving generalized full-space construction removes the representation ambiguity and reaches 1.493 and 1.181 m$E_h$ at 18 and 24 qubits. For the 18-qubit positive control, selectively refining only four Suzuki-2 factors and re-transpiling with a fixed compiler seed passes the predeclared circuit-equivalence gate at 19,660 controlled-X (CX) gates and depth 23,016. Circuit synthesis and final-energy measurement therefore constitute separate validation layers. The contribution is a validation framework, not a new spin-adapted ADAPT algorithm.
Comments6 pages, 2 figures, 2 tables; 36-page supplementary material supplied as an ancillary PDF. Submitted to The Journal of Chemical Physics
