AI 中文总结
本研究提出qutrit原生空间轨道编码，构建对应模拟框架，在H₂、LiH、H₂O测试中降低量子资源需求，提升能量计算精度，为qudit原生量子算法设计提供起点。
AI 中文摘要
qudit中的额外能级不仅可作为额外的计算容量，当算法设计反映问题的底层物理时，还可表示与物理相关的关联。我们针对量子化学模拟展示该原理，采用qutrit原生空间轨道编码，其中|0⟩、|1⟩、|2⟩表示轨道占据态。我们建立了一个qutrit模拟框架，该框架结合了守恒数的对转移和破对生成器，以及由qutrit布居和相干性构建的投影哈密顿量能量估计器。对H₂、LiH和H₂O的基准测试表明，该编码可复现相关势能曲线，同时保持紧凑的量子资源结构。与仅用对的限制直接对比证实，第三能级使LiH的误差减少了数十mHa，使H₂O的误差减少了100 mHa以上。尽管紧凑的H₂O编码中存在部分自旋耦合截断，所得势能曲线在测试范围内与FCI的偏差仅为几mHa。与传统基于qubit的UCCSD方法相比，qutrit方案所需的量子单元数量减半，并将参数化ansatz生成器的数量缩放从O(M⁴)降至O(M²)，其中M为空间轨道数。本研究阐明了基于物理动机的qutrit编码如何在保持受控电子结构精度的同时降低量子资源需求，从而为更广泛的qudit原生量子算法设计提供了具体起点。
英文摘要
Additional levels in a qudit can serve as more than extra computational capacity and can represent physically relevant correlations when the algorithmic design reflects the underlying physics of the problem. We demonstrate this principle for quantum chemistry simulation using a qutrit-native spatial-orbital encoding, where $|0\rangle$, $|1\rangle$, and $|2\rangle$ denote orbital occupation states. We establish a qutrit simulation framework that combines number-conserving pair-transfer and broken-pair generators with a projected-Hamiltonian energy estimator constructed from qutrit populations and coherences. Benchmarks for H$_2$, LiH, and H$_2$O show that the encoding reproduces the relevant potential-energy curves, while retaining a compact quantum resource structure. Direct comparison with the pair-only restriction confirms that the third level reduces errors by tens of mHa in LiH and by more than 100 mHa in H$_2$O. Despite a partial spin-coupling truncation in the compact H$_2$O encoding, the resulting energy curve deviates from FCI by only a few mHa over the tested range. Compared with a conventional qubit-based UCCSD approach, the qutrit scheme requires half as many quantum units and reduces the scaling of the parameterized ansatz generator count from $O(M^4)$ to $O(M^2)$, where $M$ is the number of spatial orbitals. This work elucidates how a physically motivated qutrit encoding can reduce quantum-resource requirements while retaining controlled electronic-structure accuracy, thereby providing a concrete starting point for broader qudit-native quantum algorithm design.
