发表机构
RIKEN, Center for Computational Science; The University of Tokyo; RIKEN, TRIP Headquarters（理化学研究所计算科学中心; 东京大学; 理化学研究所TRIP总部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于Lasp对角化的电子哈密顿量模拟方法，无需泡利展开，通过三元组优化将CX门数从O(n²)降至O(n)，且避免Trotter误差，显著提升电路效率。
AI 中文摘要
电子哈密顿量模拟通常通过将费米子算符映射为量子比特算符，随后将所得的阶梯算符乘积展开为泡利字符串来实现。尽管这种方法具有通用性，但它掩盖了更高层次的费米子结构，并可能隐藏电路优化的机会。基于最初为偏微分方程哈密顿量模拟而开发的阶梯字符串对（Lasp）对角化方法，我们构建了第二量子化电子哈密顿量的时间演化电路，而无需进行泡利展开。对于最一般的复值系数情形，我们提出了一个双体费米子Lasp算符的时间演化电路，该算符在泡利展开方法中对应16个泡利字符串，但在此阶段不遭受Trotter误差。将优化范围从单个算符扩展到共享相同四个自旋轨道指标的三个费米子Lasp算符的三元组，能够系统地抵消CX门，在所考虑的示例中将CX门数量从36减少到12，且在此阶段仍不引入Trotter误差。对于$n$个自旋轨道，进一步将优化范围扩展到$O(n)$个适当排序的三元组序列，能够在三元组边界实现CX门的级联减少，将CX门数量从$O(n^2)$降至$O(n)$。基于Lasp的方法还自然支持受控时间演化，并为实值哈密顿量带来进一步优化。这些结果表明，基于Lasp的方法通过保留高层电路结构并扩大优化范围，能够实现更高效的时间演化电路，为更高效的电子哈密顿量模拟提供了系统化路径。
英文摘要
Electronic Hamiltonian simulation is commonly formulated by mapping fermionic operators to qubit operators and subsequently expanding the resulting ladder-operator products into Pauli strings. While general, this procedure obscures the higher-level fermionic structure and can hide opportunities for circuit optimization. Building on ladder-string-pair (Lasp) diagonalization originally developed for Hamiltonian simulation of partial differential equations, we construct time-evolution circuits for the second-quantized electronic Hamiltonian without performing a Pauli expansion. For the most general case of complex-valued coefficients, we present a time-evolution circuit for a two-body fermionic Lasp operator that corresponds to 16 Pauli strings in the Pauli-expansion approach but does not suffer from Trotter error at this stage. Expanding the optimization scope from a single operator to a triad of three fermionic Lasp operators sharing the same four spin-orbital indices enables systematic cancellation of CX gates, reducing the CX-gate count from 36 to 12 in the example considered, still without introducing Trotter error at this stage. For $n$ spin orbitals, further expanding the optimization scope to a sequence of $O(n)$ suitably ordered triads enables a cascade of CX-gate reductions across triad boundaries, reducing the CX-gate count from $O(n^2)$ to $O(n)$. The Lasp-based approach also naturally accommodates controlled time evolution and yields further optimizations for real-valued Hamiltonians. These results demonstrate that the Lasp-based approach enables more efficient time-evolution circuits by preserving high-level circuit structures and thereby expanding the scope of optimization, providing a systematic route toward more efficient electronic Hamiltonian simulation.
