AI 中文总结
研究针对VQE及自适应变体中经典模拟的瓶颈问题，提出贪婪算子可交换性划分（GOCP）框架，通过五阶泰勒级数展开简化计算，在多种分子系统中评估性能，能高效模拟大量算子元素，为探索复杂量子多体系统提供可扩展途径。
AI 中文摘要
变分量子本征求解器（VQE）及其自适应变体（如ADAPT-VQE）是强关联量子系统研究的核心。然而，波函数增长过程的经典模拟仍受算子空间指数缩放和酉演化相关计算成本的限制。我们引入贪婪算子可交换性划分（GOCP）框架，通过将复杂酉旋转重新表述为五阶O(5)泰勒级数展开的链式序列，绕过显式矩阵求幂的需求，将计算任务简化为稀疏矩阵-向量运算序列。我们利用约旦-维格纳映射和布拉维-基塔耶夫映射，在包括BeH2和强关联H2O几何结构的各种分子系统中评估该框架的性能。结果表明，GOCP框架在态保真度方面保持了超过1 - 10^-6的出色数值保真度，同时在基态能量计算中达到了亚化学精度。通过高效模拟超过2.68 x 10^8个元素的算子流形，该方法为探索复杂量子多体系统中的深度变分电路提供了一条可扩展且严格的途径。
英文摘要
The Variational Quantum Eigensolver (VQE) and its adaptive variants, such as ADAPT-VQE, are central to the study of strongly correlated quantum systems. However, the classical simulation of the ansatz growth process remains constrained by the exponential scaling of operator space and the associated computational cost of unitary evolution. We introduce the Greedy Operator Commutativity Partitioning (GOCP) framework, an analytical methodology designed to optimize both operator selection and state evolution. By reformulating complex unitary rotations as a chained sequence of fifth-order O(5) Taylor series expansions, GOCP bypasses the need for explicit matrix exponentiation, reducing the computational task to a sequence of sparse matrix-vector operations. We evaluate the performance of this framework across diverse molecular systems, including BeH2 and strongly correlated H2O geometries, utilizing both Jordan-Wigner and Bravyi-Kitaev mappings. Our results demonstrate that the GOCP framework maintains exceptional numerical fidelity-exceeding 1 - 10^-6 in state fidelity-while achieving sub-chemical accuracy in ground-state energy calculations. By enabling the simulation of operator manifolds exceeding 2.68 x 10^8 elements with high efficiency, this approach provides a scalable and rigorous pathway for exploring deep variational circuits in complex quantum many-body systems.
Comments6 pages, 1 figure
