发表机构
McMaster University; Brockhouse Institute for Materials Research（麦克马斯特大学; 布罗克豪斯材料研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对量子能量估计中的测量分组问题，提出基于团选择和混合整数线性规划的二元优化方法，显著降低采样成本，并引入O-clique直接优化重叠分组，在分子和晶格哈密顿量上均优于现有策略。
AI 中文摘要
重复测量可能主导量子能量估计所需的资源，这使得选择哪些泡利可观测量一起测量成为变分量子算法的一个核心优化问题。我们将完全对易测量分组表述为基于团选择的经典二元优化问题，并使用混合整数线性规划（MILP）构造非重叠分组。对于分子哈密顿量的基准测试，使用近似协方差优化的分组平均将非重叠测量需求$\varepsilon^2M$相对于排序插入（SI）降低了$51.8\\%$。使用MILP分组初始化迭代系数分裂（ICS），记为MILP-ICS，相对于从SI初始化的ICS（SI-ICS）平均降低了$24.3\\%$。优化的分组还可以在邻近的分子几何结构之间转移，同时保持显著的测量节省。我们进一步引入O-clique，它通过候选团选择和系数分布直接优化重叠对易支撑。尽管O-clique相对于MILP-ICS仅提供了适度的额外改进，但它仅使用五次最终系数细化迭代，相对于SI-ICS在100次迭代下平均降低了$27.3\\%$的测量需求，表明支撑质量有所提高。最后，我们将比较扩展到Fermi-Hubbard、Kitaev-Heisenberg-$\Gamma$和XYZ晶格哈密顿量，其中基于MILP的分组显著优于相应的基于SI的策略。总之，这些结果表明，基于方差信息的测量组结构优化可以大幅降低分子和晶格哈密顿量的采样成本，优化的非重叠分组提供了强大且可转移的初始化，而直接重叠优化则提供了进一步的收益。
英文摘要
Repeated measurements can dominate the resources required for quantum energy estimation, making the choice of which Pauli observables to measure together a central optimization problem for variational quantum algorithms. We formulate fully commuting measurement grouping as a classical binary optimization problem based on clique selection and construct non-overlapping groups using mixed-integer linear programming (MILP). For a benchmark of molecular Hamiltonians, groupings optimized with approximate covariances reduce the non-overlapping measurement requirement $\varepsilon^2M$ by $51.8\%$ on average relative to sorted insertion (SI). Using the MILP groups to initialize iterative coefficient splitting (ICS), denoted MILP-ICS, yields an average $24.3\%$ reduction relative to ICS initialized from SI (SI-ICS). The optimized groups also transfer across nearby molecular geometries while preserving substantial measurement savings. We further introduce O-clique, which directly optimizes overlapping commuting supports through candidate-clique selection and coefficient profiles. Although O-clique provides only modest additional reductions beyond MILP-ICS, it reduces the measurement requirement by $27.3\%$ on average relative to SI-ICS with 100 iterations, despite using only five final coefficient refinement iterations, indicating improved support quality. Finally, we extend the comparison to Fermi--Hubbard, Kitaev--Heisenberg--$Γ$, and XYZ lattice Hamiltonians, where MILP-based groupings substantially outperform the corresponding SI-based strategies. Together, these results show that variance-informed optimization of measurement-group structure can substantially reduce sampling costs across molecular and lattice Hamiltonians, with optimized non-overlapping groups providing strong, transferable initializations and direct overlapping optimization offering further gains.
Comments18 pages, 4 figures, 6 tables
