发表机构
University of Science and Technology of China; State Key Laboratory of Precision and Intelligent Chemistry; Hefei National Laboratory（中国科学技术大学; 精密与智能化学国家重点实验室; 合肥国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究确定在保持粒子数和自旋对称性下，生成分子量子电路所有态旋转的最小额外操作，并证明边界上三轨道生成器可消除能量误差平台。
AI 中文摘要
保持粒子数和自旋有助于量子电路针对分子电子态，但并不保证能访问具有所需量子数的每个态。我们确定了哪些额外的操作，与连接所有空间轨道的自旋无关的轨道旋转相结合，能在每个固定粒子数 $N$、总自旋 $S$ 和自旋投影 $M_S$ 的完整子空间内生成所有实态空间旋转。我们考虑实轨道中的无自旋分子计算，不附加空间对称性限制，并考虑连续可调的操作，这些操作保持粒子数、完整自旋对称性和实振幅。在由电子和空穴数设定的最大自旋极限以下，任意两个固定空间轨道之间的重复单重态对转移是充分的。在非平凡的最大自旋边界上，对转移消失，并且由单电子和双电子项构建的额外生成器恰好在其目标子空间中的作用不是轨道旋转生成器的线性组合时是充分的。一个额外生成器所需的最小空间轨道数在内部为两个，在非平凡边界上为三个，即使允许涉及两个以上电子的项也是如此。两个最小值都仅使用单电子和双电子项实现。三轨道最优方案根据第三个轨道的占据数旋转两个轨道，其酉因子精确分解为八个对易的泡利旋转。分子基准测试表明，该操作消除了观察到的边界能量误差平台，而稀疏的内部构造在选定的固定轨道比较中，以更少的编译CNOT门达到规定的能量精度。
英文摘要
Preserving particle number and spin helps quantum circuits target molecular electronic states, but does not guarantee access to every state with the required quantum numbers. We determine which additional operations, combined with spin-independent orbital rotations connecting all spatial orbitals, generate every real state-space rotation within each complete subspace of fixed particle number $N$, total spin $S$, and spin projection $M_S$. We consider spin-free molecular calculations in real orbitals, without an additional spatial-symmetry restriction, and continuously tunable operations that preserve particle number, full spin symmetry, and real amplitudes. Below the maximal-spin limits set by the electron and hole numbers, repeated singlet-pair transfer between any two fixed spatial orbitals is sufficient. On nontrivial maximal-spin boundaries, pair transfer vanishes, and an additional generator built from one- and two-electron terms is sufficient exactly when its action in the target subspace is not a linear combination of orbital-rotation generators. The minimum number of spatial orbitals needed by one additional generator is two in the interior and three on nontrivial boundaries, even when terms involving more than two electrons are allowed. Both minima are attained using only one- and two-electron terms. The three-orbital optimum rotates two orbitals according to the occupation of a third, and its unitary factors exactly into eight commuting Pauli rotations. Molecular benchmarks show that this operation removes the observed boundary energy-error plateaus, while sparse interior constructions attain the prescribed energy accuracy with fewer compiled CNOT gates in selected fixed-orbital comparisons.
Comments72 pages, 7 figures; includes 25 pages of Supplementary Information. Data and code: https://doi.org/10.5281/zenodo.22230014
