AI 中文总结
该研究提出用于电子结构计算的量子 - 经典算法ON - VQE，通过避免RDM测量并限制变分假设，将VQE测量成本从O(M^4)降至O(M/2)，经量子硬件模拟验证，能以低测量成本在NOF框架内准确评估电子能量，为强关联电子系统量子模拟提供可扩展途径。
AI 中文摘要
我们提出了一种用于电子结构计算的量子 - 经典算法，该算法显著降低了变分量子本征求解器（VQE）方法的量子测量成本。传统VQE方法的测量成本随系统大小M按O(M^4) 缩放，而所提出的占据数VQE（ON - VQE）通过避免约化密度矩阵（RDM）测量并仅依赖占据数将此成本降低到O(M/2)。该方法仅利用自然轨道表示中单粒子RDM的对角元素，通过将变分假设限制在与电子对相关的轨道子空间内的双激发，所需测量可分组为少量量子比特可对易可观测量，产生高效且可扩展的测量策略。通过在量子硬件上对立方H$_8$簇进行模拟和执行验证了该方法，证明了从量子测量中提取准确占据数并在自然轨道泛函（NOF）框架内评估电子能量的可行性。在代表性分子系统中，提取的占据数能够在保持显著降低测量成本的同时，使用最先进的NOF进行准确的能量评估。这些结果为强关联电子系统的量子模拟建立了一条可扩展的途径，表明仅从占据数的量子测量中就能获得准确的电子能量。
英文摘要
We present a quantum-classical algorithm for electronic structure calculations that dramatically reduces the quantum measurement cost of variational quantum eigensolver (VQE) approaches. While conventional VQE methods require measurements scaling as O(M^4) with system size M, the proposed occupation-number VQE (ON-VQE) reduces this cost to O(M/2) by avoiding reduced density matrix (RDM) measurements and relying exclusively on ONs. The method exploits only the diagonal elements of the one-particle RDM in the natural orbital representation, where occupations are obtained directly from computational-basis measurement outcomes. By restricting the variational ansatz to double excitations within orbital subspaces associated with electron pairs, the required measurements can be grouped into a small number of qubit-wise commuting observables, yielding an efficient and scalable measurement strategy. The approach is validated through simulations and executions on quantum hardware for the cubic H$_8$ cluster, demonstrating the feasibility of extracting accurate ONs from quantum measurements and evaluating electronic energies within the natural orbital functional (NOF) framework. Across representative molecular systems, the extracted ONs enable accurate energy evaluation with state-of-the-art NOFs while maintaining a dramatically reduced measurement cost. These results establish a scalable route toward quantum simulation of strongly correlated electronic systems, demonstrating that accurate electronic energies can be obtained from quantum measurements of ONs alone.
Comments8 pages, 4 figues, 2 tables
